Enabled reconstruction of the total flux for rotated HDG.

This reverts commit e6ae361737.

.gitignore

@@ -54,6 +54,15 @@ doc/warnings.log
 # Example and miniapp binaries and outputs
 
 examples/ex[0-9]
+examples/ex5-max
+examples/ex5-hdg
+examples/ex5p-hdg
+examples/ex5-heat
+examples/ex5-nguyen
+examples/ex5p-nguyen
+examples/ex5-plasma
+examples/ex5-aniso
+examples/ex5-scatter
 examples/ex[0-9]p
 examples/ex1[04-9]
 examples/ex1[0-9]p
@@ -67,7 +76,7 @@ examples/ex4[0-9]p
 examples/refined.mesh
 examples/displaced.mesh
 examples/mesh.*
-examples/ex5.mesh
+examples/ex5*.mesh
 examples/Example5*
 examples/ParaView
 examples/Example9*
@@ -77,6 +86,8 @@ examples/sphere_refined.*
 examples/sol.*
 examples/sol_u.*
 examples/sol_p.*
+examples/sol_q.*
+examples/sol_t.*
 examples/sol_r.*
 examples/sol_i.*
 examples/ex6p-checkpoint.*
@@ -90,7 +101,7 @@ examples/velocity.*
 examples/elastic_energy.*
 examples/mode_*
 examples/mode_deriv_*
-examples/ex5-p-*.bp
+examples/ex5*-p-*.bp
 examples/ex9-p-*.bp
 examples/ex12-p-*.bp
 examples/ex16-p-*.bp

doc/CodeDocumentation.conf.in

@@ -959,6 +959,7 @@ INPUT                  = @MFEM_SOURCE_DIR@/doc/CodeDocumentation.dox \
                          @MFEM_SOURCE_DIR@/fem/moonolith \
                          @MFEM_SOURCE_DIR@/fem/qinterp \
                          @MFEM_SOURCE_DIR@/fem/tmop \
+                         @MFEM_SOURCE_DIR@/fem/darcy \
                          @MFEM_SOURCE_DIR@/examples \
                          @MFEM_SOURCE_DIR@/examples/amgx \
                          @MFEM_SOURCE_DIR@/examples/caliper \

examples/coupledop.cpp

@@ -0,0 +1,794 @@
+// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#include "coupledop.hpp"
+
+namespace mfem
+{
+CoupledOperator::CoupledOperator(const Array<int> &bdr_u_is_ess,
+                                 const Array<int> &bdr_E_is_ess, Coefficient *sigma_,
+                                 const Array<LinearForm*> &lfs_, const Array<Coefficient*> &coeffs_,
+                                 FiniteElementSpace *u_space_, FiniteElementSpace *n_space_,
+                                 FiniteElementSpace *E_space_, FiniteElementSpace *B_space_,
+                                 FiniteElementSpace *tr_space_, real_t td)
+   : TimeDependentOperator(0, IMPLICIT), sigma(sigma_), lfs(lfs_),
+     coeffs(coeffs_), u_space(u_space_), n_space(n_space_),
+     E_space(E_space_), B_space(B_space_), tr_space(tr_space_)
+{
+   offsets = ConstructOffsets(u_space, n_space, E_space, B_space, tr_space);
+
+   width = height = offsets.Last();
+
+   //plasma
+
+   const int dim = u_space->GetMesh()->Dimension();
+   const bool fec_disc = (u_space->FEColl()->GetContType() ==
+                          FiniteElementCollection::DISCONTINUOUS);
+   const bool fec_vec = (u_space->FEColl()->GetRangeType(dim) ==
+                         FiniteElement::VECTOR);
+   const bool dg = (fec_disc && !fec_vec);
+   const bool brt = (fec_disc && fec_vec);
+
+   if (!dg)
+   {
+      u_space->GetEssentialTrueDofs(bdr_u_is_ess, ess_u_tdofs_list);
+   }
+
+   darcy = new DarcyForm(u_space, n_space);
+
+   Mu = darcy->GetFluxMassForm();
+   Mn = darcy->GetPotentialMassForm();
+   Du = darcy->GetFluxDivForm();
+
+   idtcoeff = new FunctionCoefficient([&](const Vector &) { return idt; });
+   dtcoeff = new FunctionCoefficient([&](const Vector &) { return 1./idt; });
+
+   if (dg)
+   {
+      Mu->AddDomainIntegrator(new VectorMassIntegrator(*idtcoeff));
+   }
+   else
+   {
+      Mu->AddDomainIntegrator(new VectorFEMassIntegrator(idtcoeff));
+   }
+
+   if (dg)
+   {
+      Du->AddDomainIntegrator(new VectorDivergenceIntegrator());
+      Du->AddInteriorFaceIntegrator(new TransposeIntegrator(
+                                       new DGNormalTraceIntegrator(-1.)));
+      Du->AddBdrFaceIntegrator(new TransposeIntegrator(new DGNormalTraceIntegrator(
+                                                          -1.)), const_cast<Array<int>&>(bdr_u_is_ess));
+   }
+   else
+   {
+      Du->AddDomainIntegrator(new VectorFEDivergenceIntegrator());
+      if (brt)
+      {
+         Du->AddInteriorFaceIntegrator(new TransposeIntegrator(
+                                          new DGNormalTraceIntegrator(-1.)));
+         Du->AddBdrFaceIntegrator(new TransposeIntegrator(new DGNormalTraceIntegrator(
+                                                             -1.)), const_cast<Array<int>&>(bdr_u_is_ess));
+      }
+   }
+
+   if (dg && td > 0.)
+   {
+      Mn->AddInteriorFaceIntegrator(new HDGDiffusionIntegrator(*dtcoeff, td));
+      Mn->AddBdrFaceIntegrator(new HDGDiffusionIntegrator(*dtcoeff, td),
+                               const_cast<Array<int>&>(bdr_u_is_ess));
+   }
+
+   Mn->AddDomainIntegrator(new MassIntegrator(*idtcoeff));
+
+   if (tr_space)
+   {
+      darcy->EnableHybridization(tr_space,
+                                 new NormalTraceJumpIntegrator(),
+                                 ess_u_tdofs_list);
+   }
+
+   //Maxwell
+
+   E_space->GetEssentialTrueDofs(bdr_E_is_ess, ess_E_tdofs_list);
+
+   ME = new BilinearForm(E_space);
+   ME->AddDomainIntegrator(new VectorFEMassIntegrator());
+   CE = new MixedBilinearForm(E_space, B_space);
+   CE->AddDomainIntegrator(new MixedCurlIntegrator());
+   CdE = new DiscreteLinearOperator(E_space, B_space);
+   CdE->AddDomainInterpolator(new CurlInterpolator());
+
+   ME->Assemble();
+   ME->Finalize();
+
+   CE->Assemble();
+   CE->Finalize();
+
+   CdE->Assemble();
+   CdE->Finalize();
+}
+
+CoupledOperator::~CoupledOperator()
+{
+   delete ME;
+   delete CE;
+   delete CdE;
+   delete darcy;
+   delete idtcoeff;
+   delete dtcoeff;
+}
+
+Array<int> CoupledOperator::ConstructOffsets(const FiniteElementSpace *u_space,
+                                             const FiniteElementSpace *n_space, const FiniteElementSpace *E_space,
+                                             const FiniteElementSpace *B_space, const FiniteElementSpace *trace_space)
+{
+   Array<int> offsets((trace_space)?(6):(5));
+   int i = 0;
+   offsets[i++] = 0;
+   offsets[i++] = u_space->GetVSize();
+   offsets[i++] = n_space->GetVSize();
+   if (trace_space)
+   {
+      offsets[i++] = trace_space->GetVSize();
+   }
+   offsets[i++] = E_space->GetVSize();
+   offsets[i++] = B_space->GetVSize();
+   offsets.PartialSum();
+
+   return offsets;
+}
+
+void CoupledOperator::ImplicitSolve(const double dt, const Vector &x, Vector &y)
+{
+   const bool time_track = false;
+
+   BlockVector bx(const_cast<Vector&>(x), offsets);
+   BlockVector by(y, offsets);
+
+   int i = 0;
+   const Vector &un = bx.GetBlock(i++);
+   const Vector &nn = bx.GetBlock(i++);
+   if (tr_space) { i++; }
+   const Vector &En = bx.GetBlock(i++);
+   const Vector &Bn = bx.GetBlock(i++);
+
+   i = 2;
+   //Vector &u = by.GetBlock(i++);
+   //Vector &n = by.GetBlock(i++);
+   if (tr_space) { i++; }
+   Vector &E = by.GetBlock(i++);
+   Vector &B = by.GetBlock(i++);
+
+   //offsets
+
+   Array<int> X_offsets(3);
+   X_offsets[0] = 0;
+   if (tr_space)
+   {
+      X_offsets[1] = tr_space->GetVSize();
+   }
+   else
+   {
+      X_offsets[1] = darcy->Width();
+   }
+   X_offsets[2] = E_space->GetVSize();
+   X_offsets.PartialSum();
+
+   //solution & rhs vectors
+
+   BlockVector X(X_offsets), RHS(X_offsets);
+   BlockDiagonalPreconditioner bprec(X_offsets);
+   bprec.owns_blocks = true;
+
+   //plasma
+
+   LinearForm *g = lfs[0];
+   LinearForm *f = lfs[1];
+   LinearForm *h = lfs[2];
+
+   //set time
+
+   for (Coefficient *coeff : coeffs)
+   {
+      coeff->SetTime(t);
+   }
+
+   //assemble rhs
+
+   StopWatch chrono;
+   if (time_track)
+   {
+      chrono.Clear();
+      chrono.Start();
+   }
+
+   g->Assemble();
+   f->Assemble();
+   if (h) { h->Assemble(); }
+
+   //check if the operator has to be reassembled
+
+   bool reassemble = (idt != 1./dt);
+
+   if (reassemble)
+   {
+      idt = 1./dt;
+
+      //reset the operator
+
+      darcy->Update();
+
+      //assemble the system
+      darcy->Assemble();
+
+      if (Mu && tr_space)
+      {
+         Mu->Update();
+         Mu->Assemble();
+         //Mq0->Finalize();
+      }
+      if (Mn && tr_space)
+      {
+         Mn->Update();
+         Mn->Assemble();
+         //Mt0->Finalize();
+      }
+   }
+
+   if (Mu)
+   {
+      GridFunction u_h;
+      u_h.MakeRef(darcy->FluxFESpace(), const_cast<Vector&>(un), 0);
+      Mu->AddMult(u_h, *g, +1.);
+   }
+
+   if (Mn)
+   {
+      GridFunction p_h;
+      p_h.MakeRef(darcy->PotentialFESpace(), const_cast<Vector&>(nn), 0);
+      Mn->AddMult(p_h, *f, -1.);
+   }
+
+   //form the reduced system
+
+   OperatorHandle op_pl;
+   BlockVector darcy_x(const_cast<Vector&>(x), darcy->GetOffsets());
+   BlockVector darcy_rhs(g->GetData(), darcy->GetOffsets());
+   BlockVector X_pl;
+   BlockVector RHS_pl;
+   Array<int> tr_offsets(2);
+
+   if (tr_space)
+   {
+      tr_offsets[0] = 0;
+      tr_offsets[1] = tr_space->GetVSize();
+      X_pl.Update(X, tr_offsets);
+      RHS_pl.Update(RHS, tr_offsets);
+      if (h)
+      {
+         RHS_pl.Vector::operator=(*h);
+      }
+      else
+      {
+         RHS_pl = 0.;
+      }
+      darcy->FormLinearSystem(ess_u_tdofs_list, darcy_x, darcy_rhs,
+                              op_pl, X_pl, RHS_pl);
+   }
+   else
+   {
+      X_pl.Update(X, darcy->GetOffsets());
+      RHS_pl.Update(RHS, darcy->GetOffsets());
+      X_pl = darcy_x;
+      RHS_pl = darcy_rhs;
+      BlockVector darcy_x_tmp(X_pl, darcy->GetOffsets());
+      BlockVector darcy_rhs_tmp(RHS_pl, darcy->GetOffsets());
+      darcy->FormLinearSystem(ess_u_tdofs_list, darcy_x_tmp, darcy_rhs_tmp,
+                              op_pl, X_pl, RHS_pl);
+   }
+
+   if (time_track)
+   {
+      chrono.Stop();
+      std::cout << "Assembly took " << chrono.RealTime() << "s.\n";
+   }
+
+   if (tr_space)
+   {
+      bprec.SetDiagonalBlock(0, new DSmoother(*op_pl.As<SparseMatrix>()));
+   }
+   else
+   {
+      BlockDiagonalPreconditioner *darcy_prec = new BlockDiagonalPreconditioner(
+         darcy->GetOffsets());
+      darcy_prec->owns_blocks = true;;
+      darcy_prec->SetDiagonalBlock(0, new GSSmoother(Mu->SpMat()));
+      darcy_prec->SetDiagonalBlock(1, new DSmoother(Mn->SpMat()));
+      bprec.SetDiagonalBlock(0, darcy_prec);
+   }
+
+   //Maxwell
+
+   TransposeOperator Ct(CE);
+   ProductOperator CtCd(&Ct, CdE, false, false);
+   SumOperator MECtCd(ME, 1., &CtCd, dt*dt, false, false);
+
+   Vector &X_max = X.GetBlock(1);
+   X_max = En;
+
+   Vector &RHS_max = RHS.GetBlock(1);
+   ME->Mult(En, RHS_max);
+   //MECtCd.Mult(En, rhs);
+   CE->AddMultTranspose(Bn, RHS_max, dt);
+   //CtCd.AddMult(En, rhs, +dt*dt/2.);
+
+   //ME - dt*c2/2*Ct(Bn-dt*CE) = MEn + dt*c2/2CtBn
+   //(M + dt2*c2/2*Ct*C)E = MEn + dt*c2*CtBn
+   //ME - dt*c2*Ct(Bn-dt/2*CE-dt/2*CEn) = MEn
+   //(M + dt2*c2/2*Ct*C)E = MEn + dt*c2CtBn - dt2*c2/2*CtCEn
+   //-1/dt B - CE = 0
+
+   //ME->EliminateVDofsInRHS(ess_tdof_list, En, rhs);
+
+   ConstrainedOperator op_max(&MECtCd, ess_E_tdofs_list);
+
+   //op_max.EliminateRHS(En, RHS_max);
+
+   bprec.SetDiagonalBlock(1, new DSmoother(ME->SpMat()));
+
+   //coupling
+
+   /*const Mesh *mesh = n_space->GetMesh();
+   const int NE = mesh->GetNE();
+   for (int el = 0; el < NE; el++)
+   {
+
+   }*/
+
+   ReducedOperator bop(sigma, darcy, E_space, *op_pl.Ptr(), op_max);
+   if (tr_space)
+   {
+      Array<int> ess_tr_tdofs_list;//dummy
+      bop.SetEssentialTDOFs(ess_tr_tdofs_list, ess_E_tdofs_list);
+      bop.SetDarcyRHS(darcy_rhs);
+   }
+   else
+   {
+      bop.SetEssentialTDOFs(ess_u_tdofs_list, ess_E_tdofs_list);
+   }
+   bop.EliminateRHS(X, RHS);
+
+   //solve
+
+   GMRESSolver solver;
+   solver.SetMaxIter(1000);
+   solver.SetAbsTol(0.);
+   solver.SetRelTol(1e-6);
+   solver.SetOperator(bop);
+   solver.SetPreconditioner(bprec);
+   solver.SetPrintLevel(0);
+
+   NewtonSolver newton;
+   newton.SetMaxIter(1000);
+   newton.SetAbsTol(0.);
+   newton.SetRelTol(1e-5);
+   newton.SetOperator(bop);
+   newton.SetSolver(solver);
+   newton.SetPrintLevel(1);
+
+   if (time_track)
+   {
+      chrono.Clear();
+      chrono.Start();
+   }
+
+   newton.Mult(RHS, X);
+
+   if (time_track)
+   {
+      chrono.Stop();
+   }
+
+   if (newton.GetConverged())
+   {
+      std::cout << " converged in " << newton.GetNumIterations()
+                << " iterations with a residual norm of " << newton.GetFinalNorm()
+                << ".\n";
+   }
+   else
+   {
+      std::cout << " did not converge in " << newton.GetNumIterations()
+                << " iterations. Residual norm is " << newton.GetFinalNorm()
+                << ".\n";
+   }
+   if (time_track) { std::cout << "Solver took " << chrono.RealTime() << "s.\n"; }
+
+   //recover solution
+
+   BlockVector darcy_y(y, darcy->GetOffsets());
+   darcy_y = darcy_x;
+
+   if (tr_space)
+   {
+      darcy->RecoverFEMSolution(X_pl, darcy_rhs, darcy_y);
+      Vector &darcy_tr = by.GetBlock(2);
+      darcy_tr = X_pl;
+      darcy_tr -= bx.GetBlock(2);
+      darcy_tr *= idt;
+   }
+   else
+   {
+      darcy->RecoverFEMSolution(X_pl, RHS_pl, X_pl);
+      darcy_y = X_pl;
+   }
+
+   darcy_y -= darcy_x;
+   darcy_y *= idt;
+
+   E = X_max;
+
+   E -= En;
+   E *= idt;
+
+   CdE->Mult(En, B);
+   //CdE->AddMult(E, B);
+   //B *= -1./2.;
+   B.Neg();
+}
+CoupledOperator::ReducedOperator::ReducedOperator(Coefficient *sigma_,
+                                                  DarcyForm *darcy_, FiniteElementSpace *fes_E_, Operator &pl, Operator &max)
+   : sigma(sigma_), darcy(darcy_), fes_E(fes_E_)
+{
+   offsets.SetSize(3);
+   offsets[0] = 0;
+   offsets[1] = pl.Width();
+   offsets[2] = max.Width();
+   offsets.PartialSum();
+
+   width = height = offsets.Last();
+
+   if (darcy->GetHybridization())
+   {
+      offsets_x = offsets;
+   }
+   else
+   {
+      offsets_x.SetSize(4);
+      offsets_x[0] = 0;
+      offsets_x[1] = darcy->FluxFESpace()->GetVSize();
+      offsets_x[2] = darcy->PotentialFESpace()->GetVSize();
+      offsets_x[3] = fes_E->GetVSize();
+      offsets_x.PartialSum();
+   }
+
+   BlockOperator *bop = new BlockOperator(offsets);
+   bop->SetDiagonalBlock(0, &pl);
+   bop->SetDiagonalBlock(1, &max);
+
+   op.Reset(bop);
+}
+
+CoupledOperator::ReducedOperator::~ReducedOperator()
+{
+}
+
+void CoupledOperator::ReducedOperator::SetEssentialTDOFs(
+   const Array<int> &u_tdofs_list, const Array<int> &E_tdofs_list)
+{
+   ess_tdofs_list.DeleteAll();
+   ess_tdofs_list.Append(u_tdofs_list);
+   ess_tdofs_list.Append(E_tdofs_list);
+   const int size = ess_tdofs_list.Size();
+   for (int i = 0; i < E_tdofs_list.Size(); i++)
+   {
+      int &tdof = ess_tdofs_list[size - 1 - i];
+      if (tdof >= 0)
+      {
+         tdof += offsets[1];
+      }
+      else
+      {
+         tdof -= offsets[1];
+      }
+   }
+}
+
+void CoupledOperator::ReducedOperator::EliminateRHS(const Vector &x,
+                                                    Vector &b) const
+{
+   if (ess_tdofs_list.Size() <= 0) { return; }
+
+   Vector w(x.Size()), z(b.Size());
+
+   w = 0.;
+
+   for (int tdof : ess_tdofs_list)
+   {
+      w(tdof) = x(tdof);
+   }
+
+   MultUnconstrained(w, z);
+   b -= z;
+
+   for (int tdof : ess_tdofs_list)
+   {
+      b(tdof) = x(tdof);
+   }
+}
+
+void CoupledOperator::ReducedOperator::Mult(const Vector &x, Vector &y) const
+{
+   Vector z(x.Size());
+   z = x;
+
+   for (int tdof : ess_tdofs_list)
+   {
+      z(tdof) = 0.;
+   }
+
+   MultUnconstrained(z, y);
+
+   for (int tdof : ess_tdofs_list)
+   {
+      y(tdof) = x(tdof);
+   }
+}
+
+void CoupledOperator::ReducedOperator::MultUnconstrained(const Vector &x,
+                                                         Vector &y) const
+{
+   op->Mult(x, y);
+
+   const bool hybr = darcy->GetHybridization() != NULL;
+
+   BlockVector bx(const_cast<Vector&>(x), offsets_x);
+   BlockVector by(const_cast<Vector&>(y), offsets_x);
+   BlockVector darcy_x;
+
+   if (hybr)
+   {
+      darcy_x.Update(darcy->GetOffsets());
+      darcy->GetHybridization()->ComputeSolution(*darcy_rhs, x, darcy_x);
+      darcy_rhs->Vector::operator=(darcy_rhs_lin);
+   }
+
+   const Vector &xn = ((hybr)?(darcy_x):(bx)).GetBlock(1);
+   const Vector &xE = bx.GetBlock((hybr)?(1):(2));
+   Vector &yu = ((hybr)?(*darcy_rhs):(by)).GetBlock(0);
+   Vector &yE = by.GetBlock((hybr)?(1):(2));
+
+   Mesh *mesh = fes_E->GetMesh();
+   FiniteElementSpace *fes_u = darcy->FluxFESpace();
+   FiniteElementSpace *fes_n = darcy->PotentialFESpace();
+   Array<int> vdofs_u, dofs_n, vdofs_E;
+   DenseMatrix vshape_u, vshape_E;
+   Vector shape_u, shape_E, shape_n, n_z, E_z, E, bu_z, bE_z;
+
+   for (int z = 0; z < mesh->GetNE(); z++)
+   {
+      ElementTransformation *Tr = mesh->GetElementTransformation(z);
+      const FiniteElement *fe_u = fes_u->GetFE(z);
+      const FiniteElement *fe_n = fes_n->GetFE(z);
+      const FiniteElement *fe_E = fes_E->GetFE(z);
+      const int sdim = Tr->GetSpaceDim();
+      const int ndof_u = fe_u->GetDof();
+      const int ndof_n = fe_n->GetDof();
+
+      fes_u->GetElementVDofs(z, vdofs_u);
+      fes_n->GetElementDofs(z, dofs_n);
+      fes_E->GetElementVDofs(z, vdofs_E);
+
+      if (fe_u->GetRangeType() == FiniteElement::VECTOR)
+      {
+         vshape_u.SetSize(vdofs_u.Size(), sdim);
+      }
+      shape_u.SetSize(ndof_u);
+      shape_n.SetSize(ndof_n);
+      vshape_E.SetSize(vdofs_E.Size(), sdim);
+      shape_E.SetSize(vdofs_E.Size());
+      E.SetSize(sdim);
+
+      bu_z.SetSize(vdofs_u.Size());
+      bE_z.SetSize(vdofs_E.Size());
+      bu_z = 0.;
+      bE_z = 0.;
+
+      xn.GetSubVector(dofs_n, n_z);
+      xE.GetSubVector(vdofs_E, E_z);
+
+      const int order = std::max(fe_E->GetOrder(), fe_n->GetOrder()) * 2 + 1;
+      const IntegrationRule &ir = IntRules.Get(fe_n->GetGeomType(), order);
+      for (int q = 0; q < ir.GetNPoints(); q++)
+      {
+         const IntegrationPoint &ip = ir.IntPoint(q);
+         Tr->SetIntPoint(&ip);
+         fe_n->CalcShape(ip, shape_n);
+         const real_t n = n_z * shape_n;
+
+         fe_E->CalcVShape(*Tr, vshape_E);
+         vshape_E.MultTranspose(E_z, E);
+
+         real_t w = n * Tr->Weight();
+         if (sigma) { w *= sigma->Eval(*Tr, ip); }
+
+         if (fe_u->GetRangeType() == FiniteElement::VECTOR)
+         {
+            fe_u->CalcVShape(*Tr, vshape_u);
+            vshape_u.Mult(E, shape_u);
+            bu_z.Add(w, shape_u);
+         }
+         else
+         {
+            fe_u->CalcShape(ip, shape_u);
+            for (int d = 0; d < sdim; d++)
+               for (int i = 0; i < ndof_u; i++)
+               {
+                  bu_z(i+d*ndof_u) += w * E(d) * shape_u(i);
+               }
+         }
+         vshape_E.Mult(E, shape_E);
+         bE_z.Add(w, shape_E);
+      }
+
+      if (hybr) { bu_z.Neg(); }
+
+      yu.AddElementVector(vdofs_u, bu_z);
+      yE.AddElementVector(vdofs_E, bE_z);
+   }
+
+   if (hybr)
+   {
+      BlockVector darcy_Xrhs(darcy->GetOffsets());
+      add(darcy_rhs_lin, -1., *darcy_rhs, darcy_Xrhs);
+      darcy->GetHybridization()->ReduceRHS(darcy_Xrhs, by.GetBlock(0));
+   }
+}
+
+Operator &CoupledOperator::ReducedOperator::GetGradient(const Vector &x) const
+{
+   if (darcy->GetHybridization())
+   {
+      //TODO: coupling terms
+      return const_cast<Operator&>(*op);
+   }
+
+   grad.Clear();
+
+   FiniteElementSpace *fes_u = darcy->FluxFESpace();
+   FiniteElementSpace *fes_n = darcy->PotentialFESpace();
+
+   SparseMatrix *BEE, *BEu, *BnE, *Bnu;
+
+   BEE = new SparseMatrix(fes_E->GetVSize());
+   BEu = new SparseMatrix(fes_u->GetVSize(), fes_E->GetVSize());
+   BnE = new SparseMatrix(fes_E->GetVSize(), fes_n->GetVSize());
+   Bnu = new SparseMatrix(fes_u->GetVSize(), fes_n->GetVSize());
+
+   BlockVector bx(const_cast<Vector&>(x), offsets_x);
+
+   Mesh *mesh = fes_E->GetMesh();
+
+   Array<int> vdofs_u, dofs_n, vdofs_E;
+   DenseMatrix vshape_u, vshape_E;
+   DenseMatrix BEE_z, BEu_z, BnE_z, Bnu_z;
+   Vector shape_u, shape_E, shape_n, n_z, E_z, E;
+
+   for (int z = 0; z < mesh->GetNE(); z++)
+   {
+      ElementTransformation *Tr = mesh->GetElementTransformation(z);
+      const FiniteElement *fe_u = fes_u->GetFE(z);
+      const FiniteElement *fe_n = fes_n->GetFE(z);
+      const FiniteElement *fe_E = fes_E->GetFE(z);
+      const int sdim = Tr->GetSpaceDim();
+      const int ndof_u = fe_u->GetDof();
+      const int ndof_n = fe_n->GetDof();
+
+      fes_u->GetElementVDofs(z, vdofs_u);
+      fes_n->GetElementDofs(z, dofs_n);
+      fes_E->GetElementVDofs(z, vdofs_E);
+
+      if (fe_u->GetRangeType() == FiniteElement::VECTOR)
+      {
+         vshape_u.SetSize(vdofs_u.Size(), sdim);
+      }
+      shape_u.SetSize(ndof_u);
+      shape_n.SetSize(ndof_n);
+      vshape_E.SetSize(vdofs_E.Size(), sdim);
+      shape_E.SetSize(vdofs_E.Size());
+      E.SetSize(sdim);
+
+      BEE_z.SetSize(vdofs_E.Size());
+      BEu_z.SetSize(vdofs_u.Size(), vdofs_E.Size());
+      BnE_z.SetSize(vdofs_E.Size(), dofs_n.Size());
+      Bnu_z.SetSize(vdofs_u.Size(), dofs_n.Size());
+      BEE_z = 0.;
+      BEu_z = 0.;
+      BnE_z = 0.;
+      Bnu_z = 0.;
+
+      bx.GetBlock(1).GetSubVector(dofs_n, n_z);
+      bx.GetBlock(2).GetSubVector(vdofs_E, E_z);
+
+      const int order = std::max(fe_E->GetOrder(), fe_n->GetOrder()) * 2 + 1;
+      const IntegrationRule &ir = IntRules.Get(fe_n->GetGeomType(), order);
+      for (int q = 0; q < ir.GetNPoints(); q++)
+      {
+         const IntegrationPoint &ip = ir.IntPoint(q);
+         Tr->SetIntPoint(&ip);
+         fe_n->CalcShape(ip, shape_n);
+         const real_t n = n_z * shape_n;
+
+         fe_E->CalcVShape(*Tr, vshape_E);
+         vshape_E.MultTranspose(E_z, E);
+
+         real_t w = Tr->Weight();
+         if (sigma) { w *= sigma->Eval(*Tr, ip); }
+
+         if (fe_u->GetRangeType() == FiniteElement::VECTOR)
+         {
+            fe_u->CalcVShape(*Tr, vshape_u);
+            vshape_u.Mult(E, shape_u);
+            AddMult_a_VWt(w, shape_u, shape_n, Bnu_z);
+            AddMult_a_ABt(w * n, vshape_u, vshape_E, BEu_z);
+         }
+         else
+         {
+            fe_u->CalcShape(ip, shape_u);
+            for (int d = 0; d < sdim; d++)
+               for (int i = 0; i < ndof_u; i++)
+               {
+                  for (int j = 0; j < ndof_n; j++)
+                  {
+                     Bnu_z(i+d*ndof_u, j) += w * E(d) * shape_u(i) * shape_n(j);
+                  }
+
+                  for (int j = 0; j < vdofs_E.Size(); j++)
+                  {
+                     BEu_z(i+d*ndof_u, j) += w * n * shape_u(i) * vshape_E(j, d);
+                  }
+               }
+         }
+         vshape_E.Mult(E, shape_E);
+
+         AddMult_a_AAt(w * n, vshape_E, BEE_z);
+         AddMult_a_VWt(w, shape_E, shape_n, BnE_z);
+      }
+
+      BEE->AddSubMatrix(vdofs_E, vdofs_E, BEE_z);
+      BEu->AddSubMatrix(vdofs_u, vdofs_E, BEu_z);
+      BnE->AddSubMatrix(vdofs_E, dofs_n, BnE_z);
+      Bnu->AddSubMatrix(vdofs_u, dofs_n, Bnu_z);
+   }
+
+   BEE->Finalize();
+   BEu->Finalize();
+   BnE->Finalize();
+   Bnu->Finalize();
+
+   BlockOperator *bcouple = new BlockOperator(offsets_x);
+   bcouple->owns_blocks = true;
+   bcouple->SetBlock(2, 2, BEE);
+   bcouple->SetBlock(0, 2, BEu);
+   bcouple->SetBlock(2, 1, BnE);
+   bcouple->SetBlock(0, 1, Bnu);
+
+   grad.Reset(new SumOperator(op.Ptr(), 1., bcouple, 1., false, true));
+
+   if (ess_tdofs_list.Size() > 0)
+   {
+      grad.SetOperatorOwner(false);
+      grad.Reset(new ConstrainedOperator(grad.Ptr(), ess_tdofs_list));
+   }
+
+   return *grad;
+}
+}

examples/coupledop.hpp

@@ -0,0 +1,79 @@
+// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#ifndef MFEM_COUPLEDOP
+#define MFEM_COUPLEDOP
+
+#include "mfem.hpp"
+
+namespace mfem
+{
+class CoupledOperator : public TimeDependentOperator
+{
+   Array<int> ess_u_tdofs_list, ess_E_tdofs_list;
+   Coefficient *sigma;
+   const Array<LinearForm*> &lfs;
+   const Array<Coefficient*> &coeffs;
+   FiniteElementSpace *u_space, *n_space, *E_space, *B_space, *tr_space;
+   Array<int> offsets;
+   BilinearForm *ME{}, *Mu{}, *Mn{};
+   MixedBilinearForm *CE{}, *Du{};
+   DiscreteLinearOperator *CdE{};
+   DarcyForm *darcy{};
+   real_t idt{};
+   Coefficient *idtcoeff{}, *dtcoeff{};
+
+   class ReducedOperator : public Operator
+   {
+      Array<int> offsets, offsets_x;
+      Coefficient *sigma;
+      DarcyForm *darcy;
+      BlockVector *darcy_rhs{};
+      Vector darcy_rhs_lin;
+      FiniteElementSpace *fes_E;
+      OperatorHandle op;
+      Array<int> ess_tdofs_list;
+      mutable OperatorHandle grad;
+
+   public:
+      ReducedOperator(Coefficient *sigma, DarcyForm *darcy, FiniteElementSpace *fes_E,
+                      Operator &pl, Operator &max);
+      ~ReducedOperator();
+
+      void SetEssentialTDOFs(const Array<int> &u_tdofs_list,
+                             const Array<int> &E_tdofs_list);
+      void SetDarcyRHS(BlockVector &rhs) { darcy_rhs = &rhs; darcy_rhs_lin = rhs; }
+      void EliminateRHS(const Vector &x, Vector &b) const;
+
+      void Mult(const Vector &x, Vector &y) const override;
+      void MultUnconstrained(const Vector &x, Vector &y) const;
+      Operator& GetGradient(const Vector &x) const override;
+   };
+
+public:
+   CoupledOperator(const Array<int> &bdr_u_ess, const Array<int> &bdr_E_is_ess,
+                   Coefficient *sigma,
+                   const Array<LinearForm*> &lfs, const Array<Coefficient*> &coeffs,
+                   FiniteElementSpace *u_space, FiniteElementSpace *n_space,
+                   FiniteElementSpace *E_space, FiniteElementSpace *B_space,
+                   FiniteElementSpace *tr_space = NULL, real_t td = 0.5);
+   ~CoupledOperator();
+
+   static Array<int> ConstructOffsets(
+      const FiniteElementSpace *u_space, const FiniteElementSpace *n_space,
+      const FiniteElementSpace *E_space, const FiniteElementSpace *B_space,
+      const FiniteElementSpace *tr_space = NULL);
+
+   void ImplicitSolve(const double dt, const Vector &x, Vector &y) override;
+};
+}
+
+#endif

examples/darcyop.hpp

@@ -0,0 +1,226 @@
+// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#ifndef MFEM_DARCYOP
+#define MFEM_DARCYOP
+
+#include "mfem.hpp"
+#include "../general/socketstream.hpp"
+
+namespace mfem
+{
+
+class DarcyOperator : public TimeDependentOperator
+{
+public:
+   enum class SolverType
+   {
+      Default = 0,
+      LBFGS,
+      LBB,
+      Newton,
+      KINSol,
+   };
+
+private:
+   Array<int> offsets;
+   const Array<int> &ess_flux_tdofs_list;
+   DarcyForm *darcy;
+   LinearForm *g, *f, *h;
+#ifdef MFEM_USE_MPI
+   ParDarcyForm *pdarcy {};
+   ParLinearForm *pg{}, *pf{}, *ph{};
+#endif
+   const Array<Coefficient*> &coeffs;
+   SolverType solver_type;
+   bool btime_u, btime_p;
+   real_t rtol{1e-6}, atol{1e-10};
+   int max_iters{1000};
+
+   FiniteElementSpace *trace_space{};
+
+   real_t idt{};
+   std::unique_ptr<Coefficient> idtcoeff;
+   std::unique_ptr<BilinearForm> Mt0, Mq0;
+
+   std::string lsolver_str;
+   std::unique_ptr<Solver> prec, lin_prec;
+   std::string prec_str, lin_prec_str;
+   std::unique_ptr<IterativeSolver> solver;
+   std::string solver_str;
+   std::unique_ptr<IterativeSolverMonitor> monitor;
+   int monitor_step{-1};
+
+   mutable BlockVector x, rhs;
+
+   class SchurPreconditioner : public Solver
+   {
+      const DarcyForm *darcy;
+#ifdef MFEM_USE_MPI
+      const ParDarcyForm *pdarcy {};
+#endif
+      const Operator *op {};
+      bool nonlinear;
+
+      const char *prec_str;
+      mutable std::unique_ptr<BlockDiagonalPreconditioner> darcyPrec;
+      mutable std::unique_ptr<SparseMatrix> S;
+#ifdef MFEM_USE_MPI
+      mutable std::unique_ptr<HypreParMatrix> hS;
+#endif
+      mutable bool reconstruct {};
+
+      void Construct(const Vector &x) const;
+#ifdef MFEM_USE_MPI
+      void ConstructPar(const Vector &x) const;
+#endif
+
+   public:
+      SchurPreconditioner(const DarcyForm *darcy, bool nonlinear = false);
+#ifdef MFEM_USE_MPI
+      SchurPreconditioner(const ParDarcyForm *darcy, bool nonlinear = false);
+#endif
+
+      const char *GetString() const { return prec_str; }
+
+      void SetOperator(const Operator &op_) override
+      { op = &op_; reconstruct = true; }
+
+      void Mult(const Vector &x, Vector &y) const override;
+   };
+
+public:
+   class SolutionController : public IterativeSolverController
+   {
+   public:
+      enum class Type
+      {
+         Native,
+         Flux,
+         Potential
+      };
+
+   protected:
+      DarcyForm &darcy;
+      BlockVector &x;
+      const BlockVector &rhs;
+      Type type;
+      real_t rtol;
+      int it_prev{};
+      Vector sol_prev;
+
+      bool CheckSolution(const Vector &x, const Vector &y) const;
+      virtual void ReduceValues(real_t diff[], int num) const { }
+
+   public:
+      SolutionController(DarcyForm &darcy, BlockVector &x, const BlockVector &rhs,
+                         Type type, real_t rtol);
+
+      void MonitorSolution(int it, real_t norm, const Vector &x,
+                           bool final) override;
+
+      bool RequiresUpdatedSolution() const override { return true; }
+   };
+
+#ifdef MFEM_USE_MPI
+   class ParSolutionController : public SolutionController
+   {
+   protected:
+      ParDarcyForm &pdarcy;
+
+      void ReduceValues(real_t diff[], int num) const override;
+
+   public:
+      ParSolutionController(ParDarcyForm &pdarcy, BlockVector &x,
+                            const BlockVector &rhs, Type type, real_t rtol);
+
+      void MonitorSolution(int it, real_t norm, const Vector &x,
+                           bool final) override;
+   };
+#endif //MFEM_USE_MPI
+
+private:
+   SolutionController::Type sol_type{SolutionController::Type::Native};
+
+   class IterativeGLVis : public IterativeSolverMonitor
+   {
+   protected:
+      DarcyForm &darcy;
+      BlockVector &x;
+      const BlockVector &rhs;
+      int step;
+      bool save_files;
+
+      socketstream q_sock, t_sock;
+
+      virtual void StreamPreamble(socketstream &ss) { }
+      virtual std::string FormFilename(const char *base, int it,
+                                       const char *suff = "gf");
+   public:
+      IterativeGLVis(DarcyForm &darcy, BlockVector &x, const BlockVector &rhs,
+                     int step = 0, bool save_files = false);
+
+      void MonitorSolution(int it, real_t norm, const Vector &x,
+                           bool final) override;
+
+      bool RequiresUpdatedSolution() const override { return true; }
+   };
+
+#ifdef MFEM_USE_MPI
+   class ParIterativeGLVis : public IterativeGLVis
+   {
+      ParDarcyForm &pdarcy;
+
+      void StreamPreamble(socketstream &ss) override;
+      std::string FormFilename(const char *base, int it,
+                               const char *suff = "gf") override;
+   public:
+      ParIterativeGLVis(ParDarcyForm &pdarcy_, BlockVector &x, const BlockVector &rhs,
+                        int step = 0, bool save_files = false)
+         : IterativeGLVis(pdarcy_, x, rhs, step), pdarcy(pdarcy_) { }
+   };
+#endif //MFEM_USE_MPI
+
+   void SetupNonlinearSolver(real_t rtol, real_t atol, int iters);
+   void SetupLinearSolver(real_t rtol, real_t atol, int iters);
+
+public:
+   DarcyOperator(const Array<int> &ess_flux_tdofs_list, DarcyForm *darcy,
+                 LinearForm *g, LinearForm *f, LinearForm *h, const Array<Coefficient*> &coeffs,
+                 SolverType stype = SolverType::LBFGS,  bool bflux_u = true,
+                 bool btime_p = true);
+#ifdef MFEM_USE_MPI
+   DarcyOperator(const Array<int> &ess_flux_tdofs_list, ParDarcyForm *darcy,
+                 ParLinearForm *g, ParLinearForm *f, ParLinearForm *h,
+                 const Array<Coefficient*> &coeffs,
+                 SolverType stype = SolverType::LBFGS,  bool bflux_u = true,
+                 bool btime_p = true);
+#endif
+
+   ~DarcyOperator();
+
+   void SetTolerance(real_t rtol_, real_t atol_ = 0.) { rtol = rtol_; atol = atol_; }
+   void SetMaxIters(int iters_) { max_iters = iters_; }
+
+   void EnableSolutionController(SolutionController::Type type) { sol_type = type; }
+   void EnableIterationsVisualization(int vis_step = 0) { monitor_step = vis_step; }
+
+   static Array<int> ConstructOffsets(const DarcyForm &darcy);
+   inline const Array<int>& GetOffsets() const { return offsets; }
+
+   void ImplicitSolve(const real_t dt, const Vector &x, Vector &k) override;
+};
+
+void RandomizeMesh(Mesh &mesh, real_t dr);
+
+}
+
+#endif

examples/ex5-hdg.cpp

@@ -0,0 +1,605 @@
+//                                MFEM Example 5
+//
+// Compile with: make ex5
+//
+// Sample runs:  ex5 -m ../data/square-disc.mesh
+//               ex5 -m ../data/star.mesh
+//               ex5 -m ../data/star.mesh -pa
+//               ex5 -m ../data/beam-tet.mesh
+//               ex5 -m ../data/beam-hex.mesh
+//               ex5 -m ../data/beam-hex.mesh -pa
+//               ex5 -m ../data/escher.mesh
+//               ex5 -m ../data/fichera.mesh
+//
+// Device sample runs:
+//               ex5 -m ../data/star.mesh -pa -d cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-omp
+//               ex5 -m ../data/beam-hex.mesh -pa -d cuda
+//
+// Description:  This example code solves a simple 2D/3D mixed Darcy problem
+//               corresponding to the saddle point system
+//
+//                                 k*u + grad p = f
+//                                 - div u      = g
+//
+//               with natural boundary condition -p = <given pressure>.
+//               Here, we use a given exact solution (u,p) and compute the
+//               corresponding r.h.s. (f,g).  We discretize with Raviart-Thomas
+//               finite elements (velocity u) and piecewise discontinuous
+//               polynomials (pressure p). Alternatively, the piecewise discontinuous
+//               polynomials are used for both quantities.
+//
+//               The example demonstrates the use of the DarcyForm class, as
+//               well as hybridization of mixed systems and the collective saving
+//               of several grid functions in VisIt (visit.llnl.gov) and ParaView
+//               (paraview.org) formats.
+//
+//               We recommend viewing examples 1-4 before viewing this example.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+#include <algorithm>
+
+using namespace std;
+using namespace mfem;
+
+// Define the analytical solution and forcing terms / boundary conditions
+void uFun_ex(const Vector & x, Vector & u);
+real_t pFun_ex(const Vector & x);
+void fFun(const Vector & x, Vector & f);
+real_t gFun(const Vector & x);
+real_t f_natural(const Vector & x);
+
+int main(int argc, char *argv[])
+{
+   StopWatch chrono;
+
+   // 1. Parse command-line options.
+   const char *mesh_file = "";
+   int nx = 0;
+   int ny = 0;
+   int order = 1;
+   bool dg = false;
+   bool brt = false;
+   real_t td = 0.5;
+   bool hybridization = false;
+   bool reduction = false;
+   bool pa = false;
+   const char *device_config = "cpu";
+   bool visualization = 1;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&nx, "-nx", "--ncells-x",
+                  "Number of cells in x.");
+   args.AddOption(&ny, "-ny", "--ncells-y",
+                  "Number of cells in y.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&dg, "-dg", "--discontinuous", "-no-dg",
+                  "--no-discontinuous", "Enable DG elements for fluxes.");
+   args.AddOption(&brt, "-brt", "--broken-RT", "-no-brt",
+                  "--no-broken-RT", "Enable broken RT elements for fluxes.");
+   args.AddOption(&td, "-td", "--stab_diff",
+                  "Diffusion stabilization factor (1/2=default)");
+   args.AddOption(&hybridization, "-hb", "--hybridization", "-no-hb",
+                  "--no-hybridization", "Enable hybridization.");
+   args.AddOption(&reduction, "-rd", "--reduction", "-no-rd",
+                  "--no-reduction", "Enable reduction of DG flux.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
+   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
+   //    the same code.
+   if (ny <= 0)
+   {
+      ny = nx;
+   }
+
+   Mesh *mesh = NULL;
+   if (strlen(mesh_file) > 0)
+   {
+      mesh = new Mesh(mesh_file, 1, 1);
+   }
+   else
+   {
+      mesh = new Mesh(Mesh::MakeCartesian2D(nx, ny, Element::QUADRILATERAL));
+   }
+
+   int dim = mesh->Dimension();
+
+   // 4. Refine the mesh to increase the resolution. In this example we do
+   //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
+   //    largest number that gives a final mesh with no more than 10,000
+   //    elements.
+   if (strlen(mesh_file) > 0)
+   {
+      int ref_levels =
+         (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 5. Define a finite element space on the mesh. Here we use the
+   //    Raviart-Thomas finite elements of the specified order.
+   FiniteElementCollection *R_coll, *R_coll_dg = NULL;
+   if (dg)
+   {
+      // In the case of LDG formulation, we chose a closed basis as it
+      // is customary for HDG to match trace DOFs, but an open basis can
+      // be used instead.
+      R_coll = new L2_FECollection(order, dim, BasisType::GaussLobatto);
+   }
+   else if (brt)
+   {
+      R_coll = new BrokenRT_FECollection(order, dim);
+      R_coll_dg = new L2_FECollection(order+1, dim);
+   }
+   else
+   {
+      R_coll = new RT_FECollection(order, dim);
+   }
+   FiniteElementCollection *W_coll = new L2_FECollection(order, dim);
+
+   FiniteElementSpace *R_space = new FiniteElementSpace(mesh, R_coll,
+                                                        (dg)?(dim):(1));
+   FiniteElementSpace *R_space_dg = (R_coll_dg)?(new FiniteElementSpace(
+                                                    mesh, R_coll_dg, dim)):(NULL);
+   FiniteElementSpace *W_space = new FiniteElementSpace(mesh, W_coll);
+
+   DarcyForm *darcy = new DarcyForm(R_space, W_space);
+
+   // 6. Define the BlockStructure of the problem, i.e. define the array of
+   //    offsets for each variable. The last component of the Array is the sum
+   //    of the dimensions of each block.
+   const Array<int> &block_offsets = darcy->GetOffsets();
+
+   std::cout << "***********************************************************\n";
+   std::cout << "dim(R) = " << block_offsets[1] - block_offsets[0] << "\n";
+   std::cout << "dim(W) = " << block_offsets[2] - block_offsets[1] << "\n";
+   std::cout << "dim(R+W) = " << block_offsets.Last() << "\n";
+   std::cout << "***********************************************************\n";
+
+   // 7. Define the coefficients, analytical solution, and rhs of the PDE.
+   const double k = 1.0;
+   ConstantCoefficient kcoeff(k); //acoustic resistance
+   RatioCoefficient ikcoeff(1., kcoeff); //inverse acoustic resistance
+
+   VectorFunctionCoefficient fcoeff(dim, fFun); //velocity rhs
+   FunctionCoefficient fnatcoeff(f_natural); //boundary velocity rhs
+   FunctionCoefficient gcoeff(gFun); //pressure rhs
+
+   VectorFunctionCoefficient ucoeff(dim, uFun_ex); //velocity
+   FunctionCoefficient pcoeff(pFun_ex); //pressure
+
+   // 8. Allocate memory (x, rhs) for the analytical solution and the right hand
+   //    side.  Define the GridFunction u,p for the finite element solution and
+   //    linear forms fform and gform for the right hand side.  The data
+   //    allocated by x and rhs are passed as a reference to the grid functions
+   //    (u,p) and the linear forms (fform, gform).
+   MemoryType mt = device.GetMemoryType();
+   BlockVector x(block_offsets, mt), rhs(block_offsets, mt);
+
+   LinearForm *fform(new LinearForm);
+   fform->Update(R_space, rhs.GetBlock(0), 0);
+   if (dg)
+   {
+      fform->AddDomainIntegrator(new VectorDomainLFIntegrator(fcoeff));
+      fform->AddBdrFaceIntegrator(new VectorBoundaryFluxLFIntegrator(fnatcoeff));
+   }
+   else
+   {
+      fform->AddDomainIntegrator(new VectorFEDomainLFIntegrator(fcoeff));
+      if (brt)
+      {
+         fform->AddBdrFaceIntegrator(new VectorFEBoundaryFluxLFIntegrator(fnatcoeff));
+      }
+      else
+      {
+         fform->AddBoundaryIntegrator(new VectorFEBoundaryFluxLFIntegrator(fnatcoeff));
+      }
+   }
+   fform->Assemble();
+   fform->SyncAliasMemory(rhs);
+
+   LinearForm *gform(new LinearForm);
+   gform->Update(W_space, rhs.GetBlock(1), 0);
+   gform->AddDomainIntegrator(new DomainLFIntegrator(gcoeff));
+   gform->Assemble();
+   gform->SyncAliasMemory(rhs);
+
+   // 9. Assemble the finite element matrices for the Darcy operator
+   //
+   //                            D = [ M  B^T ]
+   //                                [ B   0  ]
+   //     where:
+   //
+   //     M = \int_\Omega k u_h \cdot v_h d\Omega   u_h, v_h \in R_h
+   //     B   = -\int_\Omega \div u_h q_h d\Omega   u_h \in R_h, q_h \in W_h
+   BilinearForm *mVarf = darcy->GetFluxMassForm();
+   MixedBilinearForm *bVarf = darcy->GetFluxDivForm();
+   BilinearForm *mtVarf = (dg)?(darcy->GetPotentialMassForm()):(NULL);
+
+   if (dg)
+   {
+      mVarf->AddDomainIntegrator(new VectorMassIntegrator(kcoeff));
+      bVarf->AddDomainIntegrator(new VectorDivergenceIntegrator());
+      bVarf->AddInteriorFaceIntegrator(new TransposeIntegrator(
+                                          new DGNormalTraceIntegrator(-1.)));
+      mtVarf->AddInteriorFaceIntegrator(new HDGDiffusionIntegrator(ikcoeff, td));
+   }
+   else
+   {
+      mVarf->AddDomainIntegrator(new VectorFEMassIntegrator(kcoeff));
+      bVarf->AddDomainIntegrator(new VectorFEDivergenceIntegrator);
+      if (brt)
+      {
+         bVarf->AddInteriorFaceIntegrator(new TransposeIntegrator(
+                                             new DGNormalTraceIntegrator(-1.)));
+      }
+   }
+
+   //set hybridization / assembly level
+
+   Array<int> ess_flux_tdofs_list;
+
+   FiniteElementCollection *trace_coll = NULL;
+   FiniteElementSpace *trace_space = NULL;
+
+   chrono.Clear();
+   chrono.Start();
+
+   if (hybridization)
+   {
+      trace_coll = new DG_Interface_FECollection(order, dim);
+      trace_space = new FiniteElementSpace(mesh, trace_coll);
+      darcy->EnableHybridization(trace_space,
+                                 new NormalTraceJumpIntegrator(),
+                                 ess_flux_tdofs_list);
+   }
+   else if (reduction && (dg || brt))
+   {
+      darcy->EnableFluxReduction();
+   }
+
+   if (pa) { darcy->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+
+   darcy->Assemble();
+
+   OperatorHandle pDarcyOp;
+   Vector X, B;
+   x = 0.;
+   darcy->FormLinearSystem(ess_flux_tdofs_list, x, rhs,
+                           pDarcyOp, X, B);
+
+   chrono.Stop();
+   std::cout << "Assembly took " << chrono.RealTime() << "s.\n";
+
+
+   int maxIter(1000);
+   real_t rtol(1.e-6);
+   real_t atol(1.e-10);
+
+   if (hybridization || (reduction && (dg || brt)))
+   {
+      // 10. Construct the preconditioner
+      GSSmoother prec(*pDarcyOp.As<SparseMatrix>());
+
+      // 11. Solve the linear system with GMRES.
+      //     Check the norm of the unpreconditioned residual.
+      chrono.Clear();
+      chrono.Start();
+      GMRESSolver solver;
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPreconditioner(prec);
+      solver.SetPrintLevel(1);
+
+      solver.Mult(B, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      chrono.Stop();
+
+      if (solver.GetConverged())
+      {
+         std::cout << "GMRES converged in " << solver.GetNumIterations()
+                   << " iterations with a residual norm of "
+                   << solver.GetFinalNorm() << ".\n";
+      }
+      else
+      {
+         std::cout << "GMRES did not converge in " << solver.GetNumIterations()
+                   << " iterations. Residual norm is " << solver.GetFinalNorm()
+                   << ".\n";
+      }
+      std::cout << "GMRES solver took " << chrono.RealTime() << "s.\n";
+   }
+   else
+   {
+      // 10. Construct the operators for preconditioner
+      //
+      //                 P = [ diag(M)         0         ]
+      //                     [  0       B diag(M)^-1 B^T ]
+      //
+      //     Here we use Symmetric Gauss-Seidel to approximate the inverse of the
+      //     pressure Schur Complement
+      SparseMatrix *MinvBt = NULL;
+      Vector Md(mVarf->Height());
+
+      BlockDiagonalPreconditioner darcyPrec(block_offsets);
+      Solver *invM, *invS;
+      SparseMatrix *S = NULL;
+
+      if (pa)
+      {
+         mVarf->AssembleDiagonal(Md);
+         auto Md_host = Md.HostRead();
+         Vector invMd(mVarf->Height());
+         for (int i=0; i<mVarf->Height(); ++i)
+         {
+            invMd(i) = 1.0 / Md_host[i];
+         }
+
+         Vector BMBt_diag(bVarf->Height());
+         bVarf->AssembleDiagonal_ADAt(invMd, BMBt_diag);
+
+         Array<int> ess_tdof_list;  // empty
+
+         invM = new OperatorJacobiSmoother(Md, ess_tdof_list);
+         invS = new OperatorJacobiSmoother(BMBt_diag, ess_tdof_list);
+      }
+      else
+      {
+         SparseMatrix &M(mVarf->SpMat());
+         M.GetDiag(Md);
+         Md.HostReadWrite();
+
+         SparseMatrix &B(bVarf->SpMat());
+         MinvBt = Transpose(B);
+
+         for (int i = 0; i < Md.Size(); i++)
+         {
+            MinvBt->ScaleRow(i, 1./Md(i));
+         }
+
+         S = Mult(B, *MinvBt);
+         if (mtVarf)
+         {
+            SparseMatrix &Mtm(mtVarf->SpMat());
+            SparseMatrix *Snew = Add(Mtm, *S);
+            delete S;
+            S = Snew;
+         }
+
+         invM = new DSmoother(M);
+
+#ifndef MFEM_USE_SUITESPARSE
+         invS = new GSSmoother(*S);
+#else
+         invS = new UMFPackSolver(*S);
+#endif
+      }
+
+      invM->iterative_mode = false;
+      invS->iterative_mode = false;
+
+      darcyPrec.SetDiagonalBlock(0, invM);
+      darcyPrec.SetDiagonalBlock(1, invS);
+
+      // 11. Solve the linear system with MINRES.
+      //     Check the norm of the unpreconditioned residual.
+
+      chrono.Clear();
+      chrono.Start();
+      MINRESSolver solver;
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPreconditioner(darcyPrec);
+      solver.SetPrintLevel(1);
+
+      solver.Mult(B, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      if (device.IsEnabled()) { x.HostRead(); }
+      chrono.Stop();
+
+      if (solver.GetConverged())
+      {
+         std::cout << "MINRES converged in " << solver.GetNumIterations()
+                   << " iterations with a residual norm of "
+                   << solver.GetFinalNorm() << ".\n";
+      }
+      else
+      {
+         std::cout << "MINRES did not converge in " << solver.GetNumIterations()
+                   << " iterations. Residual norm is " << solver.GetFinalNorm()
+                   << ".\n";
+      }
+      std::cout << "MINRES solver took " << chrono.RealTime() << "s.\n";
+
+      delete invM;
+      delete invS;
+      delete S;
+      delete MinvBt;
+   }
+
+   // 12. Create the grid functions u and p. Compute the L2 error norms.
+   GridFunction u, p;
+   if (R_space_dg)
+   {
+      GridFunction u_broken(R_space, x.GetBlock(0), 0);
+      VectorGridFunctionCoefficient coeff(&u_broken);
+      u.SetSpace(R_space_dg);
+      u.ProjectCoefficient(coeff);
+   }
+   else
+   {
+      u.MakeRef(R_space, x.GetBlock(0), 0);
+   }
+   p.MakeRef(W_space, x.GetBlock(1), 0);
+
+   int order_quad = max(2, 2*order+1);
+   const IntegrationRule *irs[Geometry::NumGeom];
+   for (int i=0; i < Geometry::NumGeom; ++i)
+   {
+      irs[i] = &(IntRules.Get(i, order_quad));
+   }
+
+   real_t err_u  = u.ComputeL2Error(ucoeff, irs);
+   real_t norm_u = ComputeLpNorm(2., ucoeff, *mesh, irs);
+   real_t err_p  = p.ComputeL2Error(pcoeff, irs);
+   real_t norm_p = ComputeLpNorm(2., pcoeff, *mesh, irs);
+
+   std::cout << "|| u_h - u_ex || / || u_ex || = " << err_u / norm_u << "\n";
+   std::cout << "|| p_h - p_ex || / || p_ex || = " << err_p / norm_p << "\n";
+
+   // 13. Save the mesh and the solution. This output can be viewed later using
+   //     GLVis: "glvis -m ex5.mesh -g sol_u.gf" or "glvis -m ex5.mesh -g
+   //     sol_p.gf".
+   {
+      ofstream mesh_ofs("ex5.mesh");
+      mesh_ofs.precision(8);
+      mesh->Print(mesh_ofs);
+
+      ofstream u_ofs("sol_u.gf");
+      u_ofs.precision(8);
+      u.Save(u_ofs);
+
+      ofstream p_ofs("sol_p.gf");
+      p_ofs.precision(8);
+      p.Save(p_ofs);
+   }
+
+   // 14. Save data in the VisIt format
+   VisItDataCollection visit_dc("Example5", mesh);
+   visit_dc.RegisterField("velocity", &u);
+   visit_dc.RegisterField("pressure", &p);
+   visit_dc.Save();
+
+   // 15. Save data in the ParaView format
+   ParaViewDataCollection paraview_dc("Example5", mesh);
+   paraview_dc.SetPrefixPath("ParaView");
+   paraview_dc.SetLevelsOfDetail(order);
+   paraview_dc.SetCycle(0);
+   paraview_dc.SetDataFormat(VTKFormat::BINARY);
+   paraview_dc.SetHighOrderOutput(true);
+   paraview_dc.SetTime(0.0); // set the time
+   paraview_dc.RegisterField("velocity",&u);
+   paraview_dc.RegisterField("pressure",&p);
+   paraview_dc.Save();
+
+   // 16. Send the solution by socket to a GLVis server.
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream u_sock(vishost, visport);
+      u_sock.precision(8);
+      u_sock << "solution\n" << *mesh << u << "window_title 'Velocity'" << endl;
+      u_sock << "keys Rljvvvvvmmc" << endl;
+      socketstream p_sock(vishost, visport);
+      p_sock.precision(8);
+      p_sock << "solution\n" << *mesh << p << "window_title 'Pressure'" << endl;
+      p_sock << "keys Rljmmc" << endl;
+   }
+
+   // 17. Free the used memory.
+   delete fform;
+   delete gform;
+   delete darcy;
+   delete W_space;
+   delete R_space;
+   delete R_space_dg;
+   delete trace_space;
+   delete W_coll;
+   delete R_coll;
+   delete R_coll_dg;
+   delete trace_coll;
+   delete mesh;
+
+   return 0;
+}
+
+
+void uFun_ex(const Vector & x, Vector & u)
+{
+   real_t xi(x(0));
+   real_t yi(x(1));
+   real_t zi(0.0);
+   if (x.Size() == 3)
+   {
+      zi = x(2);
+   }
+
+   u(0) = - exp(xi)*sin(yi)*cos(zi);
+   u(1) = - exp(xi)*cos(yi)*cos(zi);
+
+   if (x.Size() == 3)
+   {
+      u(2) = exp(xi)*sin(yi)*sin(zi);
+   }
+}
+
+// Change if needed
+real_t pFun_ex(const Vector & x)
+{
+   real_t xi(x(0));
+   real_t yi(x(1));
+   real_t zi(0.0);
+
+   if (x.Size() == 3)
+   {
+      zi = x(2);
+   }
+
+   return exp(xi)*sin(yi)*cos(zi);
+}
+
+void fFun(const Vector & x, Vector & f)
+{
+   f = 0.0;
+}
+
+real_t gFun(const Vector & x)
+{
+   if (x.Size() == 3)
+   {
+      return -pFun_ex(x);
+   }
+   else
+   {
+      return 0;
+   }
+}
+
+real_t f_natural(const Vector & x)
+{
+   return (-pFun_ex(x));
+}

examples/ex5-heat.cpp

@@ -0,0 +1,634 @@
+//                                MFEM Example 5
+//
+// Compile with: make ex5
+//
+// Sample runs:  ex5 -m ../data/square-disc.mesh
+//               ex5 -m ../data/star.mesh
+//               ex5 -m ../data/star.mesh -pa
+//               ex5 -m ../data/beam-tet.mesh
+//               ex5 -m ../data/beam-hex.mesh
+//               ex5 -m ../data/beam-hex.mesh -pa
+//               ex5 -m ../data/escher.mesh
+//               ex5 -m ../data/fichera.mesh
+//
+// Device sample runs:
+//               ex5 -m ../data/star.mesh -pa -d cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-omp
+//               ex5 -m ../data/beam-hex.mesh -pa -d cuda
+//
+// Description:  This example code solves a simple 2D/3D asymptotic heat diffusion
+//               problem in the mixed formulation corresponding to the system
+//
+//                                 k^-1.q + grad T =  f
+//                                  div q +    a*T = -g
+//
+//               with natural boundary condition q.n = 0, where n is the outer
+//               normal. The tensor k represents the heat conductivity, where its
+//               symmetric and antisymmetric parts can be adjusted. The scalar a
+//               is then the heat capacity, which can be zero, changing the problem
+//               to steady-state, indefinite, saddle-point. The r.h.s. is f = 0 and
+//               g = -a * <initial temperature> for the definite problem and
+//               g = -<initial temperature> for the indefinite one. As a reference,
+//               we use the exact solution (q,T) for the asymptote a -> infinity.
+//               We discretize with Raviart-Thomas finite elements (heat flux q)
+//               and piecewise discontinuous polynomials (temperature T). Alternatively,
+//               the piecewise discontinuous polynomials are used for both quantities.
+//
+//               The example demonstrates the use of the DarcyForm class, as
+//               well as hybridization of mixed systems and the collective saving
+//               of several grid functions in VisIt (visit.llnl.gov) and ParaView
+//               (paraview.org) formats.
+//
+//               We recommend viewing examples 1-4 before viewing this example.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+#include <algorithm>
+
+using namespace std;
+using namespace mfem;
+
+// Define the analytical solution and forcing terms / boundary conditions
+typedef std::function<real_t(const Vector &, real_t t)> TDFunc;
+typedef std::function<void(const Vector &, Vector &)> VecFunc;
+typedef std::function<void(const Vector &, DenseMatrix &)> MatFunc;
+
+TDFunc GetTFun(real_t t_0, real_t a, const MatFunc &kFun);
+VecFunc GetQFun(real_t t_0, real_t a, const MatFunc &kFun);
+MatFunc GetKFun(real_t k, real_t ks, real_t ka);
+
+int main(int argc, char *argv[])
+{
+   StopWatch chrono;
+
+   // 1. Parse command-line options.
+   const char *mesh_file = "";
+   int nx = 0;
+   int ny = 0;
+   int order = 1;
+   bool dg = false;
+   real_t ks = 1.;
+   real_t ka = 0.;
+   real_t a = 0.;
+   real_t td = 0.5;
+   bool hybridization = false;
+   bool pa = false;
+   const char *device_config = "cpu";
+   bool visualization = 1;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&nx, "-nx", "--ncells-x",
+                  "Number of cells in x.");
+   args.AddOption(&ny, "-ny", "--ncells-y",
+                  "Number of cells in y.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&dg, "-dg", "--discontinuous", "-no-dg",
+                  "--no-discontinuous", "Enable DG elements for fluxes.");
+   args.AddOption(&ks, "-ks", "--kappa_sym",
+                  "Symmetric anisotropy of the heat conductivity tensor");
+   args.AddOption(&ka, "-ka", "--kappa_anti",
+                  "Antisymmetric anisotropy of the heat conductivity tensor");
+   args.AddOption(&a, "-a", "--heat_capacity",
+                  "Heat capacity coefficient (0=indefinite problem)");
+   args.AddOption(&td, "-td", "--stab_diff",
+                  "Diffusion stabilization factor (1/2=default)");
+   args.AddOption(&hybridization, "-hb", "--hybridization", "-no-hb",
+                  "--no-hybridization", "Enable hybridization.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
+   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
+   //    the same code.
+   if (ny <= 0)
+   {
+      ny = nx;
+   }
+
+   Mesh *mesh = NULL;
+   if (strlen(mesh_file) > 0)
+   {
+      mesh = new Mesh(mesh_file, 1, 1);
+   }
+   else
+   {
+      mesh = new Mesh(Mesh::MakeCartesian2D(nx, ny, Element::QUADRILATERAL));
+   }
+
+   int dim = mesh->Dimension();
+
+   // 4. Refine the mesh to increase the resolution. In this example we do
+   //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
+   //    largest number that gives a final mesh with no more than 10,000
+   //    elements.
+   if (strlen(mesh_file) > 0)
+   {
+      int ref_levels =
+         (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 5. Define a finite element space on the mesh. Here we use the
+   //    Raviart-Thomas finite elements of the specified order.
+   FiniteElementCollection *V_coll;
+   if (dg)
+   {
+      // In the case of LDG formulation, we chose a closed basis as it
+      // is customary for HDG to match trace DOFs, but an open basis can
+      // be used instead.
+      V_coll = new L2_FECollection(order, dim, BasisType::GaussLobatto);
+   }
+   else
+   {
+      V_coll = new RT_FECollection(order, dim);
+   }
+   FiniteElementCollection *W_coll = new L2_FECollection(order, dim);
+
+   FiniteElementSpace *V_space = new FiniteElementSpace(mesh, V_coll,
+                                                        (dg)?(dim):(1));
+   FiniteElementSpace *W_space = new FiniteElementSpace(mesh, W_coll);
+
+   DarcyForm *darcy = new DarcyForm(V_space, W_space);
+
+   // 6. Define the BlockStructure of the problem, i.e. define the array of
+   //    offsets for each variable. The last component of the Array is the sum
+   //    of the dimensions of each block.
+   const Array<int> &block_offsets = darcy->GetOffsets();
+
+   std::cout << "***********************************************************\n";
+   std::cout << "dim(R) = " << block_offsets[1] - block_offsets[0] << "\n";
+   std::cout << "dim(W) = " << block_offsets[2] - block_offsets[1] << "\n";
+   std::cout << "dim(R+W) = " << block_offsets.Last() << "\n";
+   std::cout << "***********************************************************\n";
+
+   // 7. Define the coefficients, analytical solution, and rhs of the PDE.
+   const real_t t_0 = 1.; //base temperature
+   const real_t k = 1.; //base heat conductivity
+
+   ConstantCoefficient acoeff(a); //heat capacity
+
+   auto kFun = GetKFun(k, ks, ka);
+   MatrixFunctionCoefficient kcoeff(dim, kFun); //tensor conductivity
+   InverseMatrixCoefficient ikcoeff(kcoeff); //inverse tensor conductivity
+
+   auto tFun = GetTFun(t_0, a, kFun);
+   FunctionCoefficient tcoeff(tFun); //temperature
+   SumCoefficient gcoeff(0, tcoeff, 1., //boundary heat flux rhs
+                         -((a>0.)?(a):(1.)));//<-- due to symmetrization, the sign is opposite
+
+   auto qFun = GetQFun(t_0, a, kFun);
+   VectorFunctionCoefficient qcoeff(dim, qFun); //heat flux
+
+   // 8. Allocate memory (x, rhs) for the analytical solution and the right hand
+   //    side.  Define the GridFunction q,t for the finite element solution and
+   //    linear forms fform and gform for the right hand side.  The data
+   //    allocated by x and rhs are passed as a reference to the grid functions
+   //    (q,t) and the linear forms (fform, gform).
+   MemoryType mt = device.GetMemoryType();
+   BlockVector x(block_offsets, mt), rhs(block_offsets, mt);
+
+   LinearForm *fform(new LinearForm);
+   fform->Update(V_space, rhs.GetBlock(0), 0);
+   fform->Assemble();
+   fform->SyncAliasMemory(rhs);
+
+   LinearForm *gform(new LinearForm);
+   gform->Update(W_space, rhs.GetBlock(1), 0);
+   gform->AddDomainIntegrator(new DomainLFIntegrator(gcoeff));
+   /*Vector v ({-1., 0.});
+   VectorConstantCoefficient vc(v);
+   ConstantCoefficient one;
+   gform->AddBdrFaceIntegrator(new BoundaryFlowIntegrator(one, vc, 1.));*/
+   gform->Assemble();
+   gform->SyncAliasMemory(rhs);
+
+   // 9. Assemble the finite element matrices for the Darcy operator
+   //
+   //                            D = [ M  B^T ]
+   //                                [ B   0  ]
+   //     where:
+   //
+   //     M = \int_\Omega k u_h \cdot v_h d\Omega   q_h, v_h \in V_h
+   //     B   = -\int_\Omega \div u_h q_h d\Omega   q_h \in V_h, w_h \in W_h
+   BilinearForm *Mq = darcy->GetFluxMassForm();
+   MixedBilinearForm *B = darcy->GetFluxDivForm();
+   BilinearForm *Mt = (a > 0. || dg)?(darcy->GetPotentialMassForm()):(NULL);
+
+   if (dg)
+   {
+      Mq->AddDomainIntegrator(new VectorMassIntegrator(ikcoeff));
+      B->AddDomainIntegrator(new VectorDivergenceIntegrator());
+      B->AddInteriorFaceIntegrator(new TransposeIntegrator(
+                                      new DGNormalTraceIntegrator(-1.)));
+      if (td > 0.)
+      {
+         Mt->AddInteriorFaceIntegrator(new HDGDiffusionIntegrator(kcoeff, td));
+      }
+   }
+   else
+   {
+      Mq->AddDomainIntegrator(new VectorFEMassIntegrator(ikcoeff));
+      B->AddDomainIntegrator(new VectorFEDivergenceIntegrator());
+   }
+
+   if (Mt)
+   {
+      Mt->AddDomainIntegrator(new MassIntegrator(acoeff));
+   }
+
+   //set hybridization / assembly level
+
+   Array<int> ess_flux_tdofs_list;
+   /*Array<int> bdr_is_ess(mesh->bdr_attributes.Max());
+   bdr_is_ess = 0;
+   bdr_is_ess[3] = -1;
+   V_space->GetEssentialTrueDofs(bdr_is_ess, ess_flux_tdofs_list);*/
+
+   FiniteElementCollection *trace_coll = NULL;
+   FiniteElementSpace *trace_space = NULL;
+
+   chrono.Clear();
+   chrono.Start();
+
+   if (hybridization)
+   {
+      trace_coll = new DG_Interface_FECollection(order, dim);
+      trace_space = new FiniteElementSpace(mesh, trace_coll);
+      darcy->EnableHybridization(trace_space,
+                                 new NormalTraceJumpIntegrator(),
+                                 ess_flux_tdofs_list);
+   }
+
+   if (pa) { darcy->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+
+   darcy->Assemble();
+
+   OperatorHandle pDarcyOp;
+   Vector X, RHS;
+   //x = 1./ny;
+   darcy->FormLinearSystem(ess_flux_tdofs_list, x, rhs,
+                           pDarcyOp, X, RHS);
+
+   chrono.Stop();
+   std::cout << "Assembly took " << chrono.RealTime() << "s.\n";
+
+
+   int maxIter(1000);
+   real_t rtol(1.e-6);
+   real_t atol(1.e-10);
+
+   if (hybridization)
+   {
+      // 10. Construct the preconditioner
+      GSSmoother prec(*pDarcyOp.As<SparseMatrix>());
+
+      // 11. Solve the linear system with GMRES.
+      //     Check the norm of the unpreconditioned residual.
+      chrono.Clear();
+      chrono.Start();
+      GMRESSolver solver;
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPreconditioner(prec);
+      solver.SetPrintLevel(1);
+
+      solver.Mult(RHS, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      chrono.Stop();
+
+      if (solver.GetConverged())
+      {
+         std::cout << "GMRES converged in " << solver.GetNumIterations()
+                   << " iterations with a residual norm of "
+                   << solver.GetFinalNorm() << ".\n";
+      }
+      else
+      {
+         std::cout << "GMRES did not converge in " << solver.GetNumIterations()
+                   << " iterations. Residual norm is " << solver.GetFinalNorm()
+                   << ".\n";
+      }
+      std::cout << "GMRES solver took " << chrono.RealTime() << "s.\n";
+   }
+   else
+   {
+      // 10. Construct the operators for preconditioner
+      //
+      //                 P = [ diag(M)         0         ]
+      //                     [  0       B diag(M)^-1 B^T ]
+      //
+      //     Here we use Symmetric Gauss-Seidel to approximate the inverse of the
+      //     temperature Schur Complement
+      SparseMatrix *MinvBt = NULL;
+      Vector Md(Mq->Height());
+
+      BlockDiagonalPreconditioner darcyPrec(block_offsets);
+      Solver *invM, *invS;
+      SparseMatrix *S = NULL;
+
+      if (pa)
+      {
+         Mq->AssembleDiagonal(Md);
+         auto Md_host = Md.HostRead();
+         Vector invMd(Mq->Height());
+         for (int i=0; i<Mq->Height(); ++i)
+         {
+            invMd(i) = 1.0 / Md_host[i];
+         }
+
+         Vector BMBt_diag(B->Height());
+         B->AssembleDiagonal_ADAt(invMd, BMBt_diag);
+
+         Array<int> ess_tdof_list;  // empty
+
+         invM = new OperatorJacobiSmoother(Md, ess_tdof_list);
+         invS = new OperatorJacobiSmoother(BMBt_diag, ess_tdof_list);
+      }
+      else
+      {
+         SparseMatrix &Mqm(Mq->SpMat());
+         Mqm.GetDiag(Md);
+         Md.HostReadWrite();
+
+         SparseMatrix &Bm(B->SpMat());
+         MinvBt = Transpose(Bm);
+
+         for (int i = 0; i < Md.Size(); i++)
+         {
+            MinvBt->ScaleRow(i, 1./Md(i));
+         }
+
+         S = Mult(Bm, *MinvBt);
+         if (Mt)
+         {
+            SparseMatrix &Mtm(Mt->SpMat());
+            SparseMatrix *Snew = Add(Mtm, *S);
+            delete S;
+            S = Snew;
+         }
+
+         invM = new DSmoother(Mqm);
+
+#ifndef MFEM_USE_SUITESPARSE
+         invS = new GSSmoother(*S);
+#else
+         invS = new UMFPackSolver(*S);
+#endif
+      }
+
+      invM->iterative_mode = false;
+      invS->iterative_mode = false;
+
+      darcyPrec.SetDiagonalBlock(0, invM);
+      darcyPrec.SetDiagonalBlock(1, invS);
+
+      // 11. Solve the linear system with MINRES.
+      //     Check the norm of the unpreconditioned residual.
+
+      chrono.Clear();
+      chrono.Start();
+      MINRESSolver solver;
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPreconditioner(darcyPrec);
+      solver.SetPrintLevel(1);
+
+      solver.Mult(RHS, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      if (device.IsEnabled()) { x.HostRead(); }
+      chrono.Stop();
+
+      if (solver.GetConverged())
+      {
+         std::cout << "MINRES converged in " << solver.GetNumIterations()
+                   << " iterations with a residual norm of "
+                   << solver.GetFinalNorm() << ".\n";
+      }
+      else
+      {
+         std::cout << "MINRES did not converge in " << solver.GetNumIterations()
+                   << " iterations. Residual norm is " << solver.GetFinalNorm()
+                   << ".\n";
+      }
+      std::cout << "MINRES solver took " << chrono.RealTime() << "s.\n";
+
+      delete invM;
+      delete invS;
+      delete S;
+      //delete Bt;
+      delete MinvBt;
+   }
+
+   // 12. Create the grid functions q and t. Compute the L2 error norms.
+   GridFunction q, t;
+   q.MakeRef(V_space, x.GetBlock(0), 0);
+   t.MakeRef(W_space, x.GetBlock(1), 0);
+
+   int order_quad = max(2, 2*order+1);
+   const IntegrationRule *irs[Geometry::NumGeom];
+   for (int i=0; i < Geometry::NumGeom; ++i)
+   {
+      irs[i] = &(IntRules.Get(i, order_quad));
+   }
+
+   qcoeff.SetTime(1.);
+   tcoeff.SetTime(1.);
+
+   real_t err_q  = q.ComputeL2Error(qcoeff, irs);
+   real_t norm_q = ComputeLpNorm(2., qcoeff, *mesh, irs);
+   real_t err_t  = t.ComputeL2Error(tcoeff, irs);
+   real_t norm_t = ComputeLpNorm(2., tcoeff, *mesh, irs);
+
+   std::cout << "|| q_h - q_ex || / || q_ex || = " << err_q / norm_q << "\n";
+   std::cout << "|| t_h - t_ex || / || t_ex || = " << err_t / norm_t << "\n";
+
+   // 13. Save the mesh and the solution. This output can be viewed later using
+   //     GLVis: "glvis -m ex5.mesh -g sol_q.gf" or "glvis -m ex5.mesh -g
+   //     sol_t.gf".
+   {
+      ofstream mesh_ofs("ex5.mesh");
+      mesh_ofs.precision(8);
+      mesh->Print(mesh_ofs);
+
+      ofstream q_ofs("sol_q.gf");
+      q_ofs.precision(8);
+      q.Save(q_ofs);
+
+      ofstream t_ofs("sol_t.gf");
+      t_ofs.precision(8);
+      t.Save(t_ofs);
+   }
+
+   // 14. Save data in the VisIt format
+   VisItDataCollection visit_dc("Example5", mesh);
+   visit_dc.RegisterField("heat flux", &q);
+   visit_dc.RegisterField("temperature", &t);
+   visit_dc.Save();
+
+   // 15. Save data in the ParaView format
+   ParaViewDataCollection paraview_dc("Example5", mesh);
+   paraview_dc.SetPrefixPath("ParaView");
+   paraview_dc.SetLevelsOfDetail(order);
+   paraview_dc.SetCycle(0);
+   paraview_dc.SetDataFormat(VTKFormat::BINARY);
+   paraview_dc.SetHighOrderOutput(true);
+   paraview_dc.SetTime(0.0); // set the time
+   paraview_dc.RegisterField("heat flux",&q);
+   paraview_dc.RegisterField("temperature",&t);
+   paraview_dc.Save();
+
+   // 16. Send the solution by socket to a GLVis server.
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream q_sock(vishost, visport);
+      q_sock.precision(8);
+      q_sock << "solution\n" << *mesh << q << "window_title 'Heat flux'" << endl;
+      q_sock << "keys Rljvvvvvmmc" << endl;
+      socketstream t_sock(vishost, visport);
+      t_sock.precision(8);
+      t_sock << "solution\n" << *mesh << t << "window_title 'Temperature'" << endl;
+      t_sock << "keys Rljmmc" << endl;
+   }
+
+   // 17. Free the used memory.
+   delete fform;
+   delete gform;
+   //delete Mq;
+   //delete B;
+   delete darcy;
+   delete W_space;
+   delete V_space;
+   delete trace_space;
+   delete W_coll;
+   delete V_coll;
+   delete trace_coll;
+   delete mesh;
+
+   return 0;
+}
+
+TDFunc GetTFun(real_t t_0, real_t a, const MatFunc &kFun)
+{
+   return [=](const Vector &x, real_t t) -> real_t
+   {
+      const int ndim = x.Size();
+      real_t t0 = t_0 * sin(M_PI*x(0)) * sin(M_PI*x(1));
+      if (ndim > 2)
+      {
+         t0 *= sin(M_PI*x(2));
+      }
+
+      if (a <= 0.) { return t0; }
+
+      Vector ddT((ndim<=2)?(2):(4));
+      ddT(0) = -t_0 * M_PI*M_PI * sin(M_PI*x(0)) * sin(M_PI*x(1));//xx,yy
+      ddT(1) = +t_0 * M_PI*M_PI * cos(M_PI*x(0)) * cos(M_PI*x(1));//xy
+      if (ndim > 2)
+      {
+         ddT(0) *= sin(M_PI*x(2));//xx,yy,zz
+         ddT(1) *= sin(M_PI*x(2));//xy
+         ddT(2) = +t_0 * M_PI*M_PI * cos(M_PI*x(0)) * sin(M_PI*x(1)) * cos(M_PI*x(
+                                                                              2));//xz
+         ddT(3) = +t_0 * M_PI*M_PI * sin(M_PI*x(0)) * cos(M_PI*x(1)) * cos(M_PI*x(
+                                                                              2));//yz
+
+      }
+
+      DenseMatrix kappa;
+      kFun(x, kappa);
+
+      real_t div = -(kappa(0,0) + kappa(1,1)) * ddT(0) - (kappa(0,1) + kappa(1,0)) * ddT(1);
+      if (ndim > 2)
+      {
+         div += -kappa(2,2) * ddT(0) - (kappa(0,2) + kappa(2,0)) * ddT(2) - (kappa(1,
+                                                                                   2) + kappa(2,1)) * ddT(3);
+      }
+      return t0 - div / a * t;
+   };
+}
+
+VecFunc GetQFun(real_t t_0, real_t a, const MatFunc &kFun)
+{
+   return [=](const Vector &x, Vector &v)
+   {
+      const int vdim = x.Size();
+      v.SetSize(vdim);
+
+      Vector gT(vdim);
+      gT = 0.;
+      gT(0) = t_0 * M_PI * cos(M_PI*x(0)) * sin(M_PI*x(1));
+      gT(1) = t_0 * M_PI * sin(M_PI*x(0)) * cos(M_PI*x(1));
+      if (vdim > 2)
+      {
+         gT(0) *= sin(M_PI*x(2));
+         gT(1) *= sin(M_PI*x(2));
+         gT(2) = t_0 * M_PI * sin(M_PI*x(0)) * sin(M_PI*x(1)) * cos(M_PI*x(2));
+      }
+
+      DenseMatrix kappa;
+      kFun(x, kappa);
+
+      if (vdim <= 2)
+      {
+         v(0) = -kappa(0,0) * gT(0) -kappa(0,1) * gT(1);
+         v(1) = -kappa(1,0) * gT(0) -kappa(1,1) * gT(1);
+      }
+      else
+      {
+         kappa.Mult(gT, v);
+         v.Neg();
+      }
+   };
+}
+
+MatFunc GetKFun(real_t k, real_t ks, real_t ka)
+{
+   return [=](const Vector &x, DenseMatrix &kappa)
+   {
+      const int ndim = x.Size();
+      kappa.Diag(k, ndim);
+      kappa(0,0) *= ks;
+      kappa(0,1) = +ka * k;
+      kappa(1,0) = -ka * k;
+      if (ndim > 2)
+      {
+         kappa(0,2) = +ka * k;
+         kappa(2,0) = -ka * k;
+      }
+   };
+}
+
+

examples/ex5-max.cpp

@@ -0,0 +1,543 @@
+//                                MFEM Example 5
+//
+// Compile with: make ex5
+//
+// Sample runs:  ex5 -m ../data/square-disc.mesh
+//               ex5 -m ../data/star.mesh
+//               ex5 -m ../data/star.mesh -pa
+//               ex5 -m ../data/beam-tet.mesh
+//               ex5 -m ../data/beam-hex.mesh
+//               ex5 -m ../data/beam-hex.mesh -pa
+//               ex5 -m ../data/escher.mesh
+//               ex5 -m ../data/fichera.mesh
+//
+// Device sample runs:
+//               ex5 -m ../data/star.mesh -pa -d cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-omp
+//               ex5 -m ../data/beam-hex.mesh -pa -d cuda
+//
+// Description:  This example code solves a simple 2D mixed electromagnetic
+//               diffusion problem corresponding to the mixed system
+//
+//                                 sigma E - curl B = f
+//                                  curl E +      B = g
+//
+//               with essential boundary condition E x n = <given tangential field>.
+//               Here, we use a given exact solution (E,B) and compute the
+//               corresponding r.h.s. (f,g).  We discretize with Nedelec
+//               finite elements (electric field E) and piecewise discontinuous
+//               integral polynomials (magnetic field B).
+//
+//               The example demonstrates the use of the DarcyForm class, as
+//               well as the collective saving of several grid functions in
+//               VisIt (visit.llnl.gov) and ParaView (paraview.org) formats.
+//
+//               We recommend viewing examples 1-4 before viewing this example.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+#include <algorithm>
+
+using namespace std;
+using namespace mfem;
+
+// Define the analytical solution and forcing terms / boundary conditions
+void EFun_ex(const Vector & x, Vector & E);
+real_t BFun_ex(const Vector & x);
+void fFun(const Vector & x, Vector & f);
+real_t gFun(const Vector & x);
+real_t freq = 1.0, kappa;
+
+int main(int argc, char *argv[])
+{
+   StopWatch chrono;
+
+   // 1. Parse command-line options.
+   const char *mesh_file = "";
+   int nx = 0;
+   int ny = 0;
+   int order = 1;
+   bool hybridization = false;
+   bool pa = false;
+   const char *device_config = "cpu";
+   bool visualization = 1;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&nx, "-nx", "--ncells-x",
+                  "Number of cells in x.");
+   args.AddOption(&ny, "-ny", "--ncells-y",
+                  "Number of cells in y.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&freq, "-f", "--frequency", "Set the frequency for the exact"
+                  " solution.");
+   args.AddOption(&hybridization, "-hb", "--hybridization", "-no-hb",
+                  "--no-hybridization", "Enable hybridization.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+   kappa = freq * M_PI;
+
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
+   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
+   //    the same code.
+   if (ny <= 0)
+   {
+      ny = nx;
+   }
+
+   Mesh *mesh = NULL;
+   if (strlen(mesh_file) > 0)
+   {
+      mesh = new Mesh(mesh_file, 1, 1);
+   }
+   else
+   {
+      mesh = new Mesh(Mesh::MakeCartesian2D(nx, ny, Element::QUADRILATERAL));
+   }
+
+   int dim = mesh->Dimension();
+
+   // 4. Refine the mesh to increase the resolution. In this example we do
+   //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
+   //    largest number that gives a final mesh with no more than 10,000
+   //    elements.
+   if (strlen(mesh_file) > 0)
+   {
+      int ref_levels =
+         (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 5. Define a finite element space on the mesh. Here we use the
+   //    Raviart-Thomas finite elements of the specified order.
+   FiniteElementCollection *R_coll(new ND_FECollection(order+1, dim));
+   FiniteElementCollection *W_coll(new L2_FECollection(order, dim, 0,
+                                                       FiniteElement::INTEGRAL));
+
+   FiniteElementSpace *R_space = new FiniteElementSpace(mesh, R_coll);
+   FiniteElementSpace *W_space = new FiniteElementSpace(mesh, W_coll);
+
+   DarcyForm *darcy = new DarcyForm(R_space, W_space);
+
+   // 6. Define the BlockStructure of the problem, i.e. define the array of
+   //    offsets for each variable. The last component of the Array is the sum
+   //    of the dimensions of each block.
+   const Array<int> &block_offsets = darcy->GetOffsets();
+
+   std::cout << "***********************************************************\n";
+   std::cout << "dim(R) = " << block_offsets[1] - block_offsets[0] << "\n";
+   std::cout << "dim(W) = " << block_offsets[2] - block_offsets[1] << "\n";
+   std::cout << "dim(R+W) = " << block_offsets.Last() << "\n";
+   std::cout << "***********************************************************\n";
+
+   // 7. Define the coefficients, analytical solution, and rhs of the PDE.
+   ConstantCoefficient muinvsqrt(1.0);
+   ConstantCoefficient sigma(1.0);
+
+   VectorFunctionCoefficient fcoeff(dim, fFun);
+   FunctionCoefficient gcoeff(gFun);
+
+   VectorFunctionCoefficient Ecoeff(dim, EFun_ex);
+   FunctionCoefficient Bcoeff(BFun_ex);
+
+   // 8. Allocate memory (x, rhs) for the analytical solution and the right hand
+   //    side.  Define the GridFunction E,B for the finite element solution and
+   //    linear forms fform and gform for the right hand side.  The data
+   //    allocated by x and rhs are passed as a reference to the grid functions
+   //    (E,B) and the linear forms (fform, gform).
+   MemoryType mt = device.GetMemoryType();
+   BlockVector x(block_offsets, mt), rhs(block_offsets, mt);
+
+   LinearForm *fform(new LinearForm);
+   fform->Update(R_space, rhs.GetBlock(0), 0);
+   fform->AddDomainIntegrator(new VectorFEDomainLFIntegrator(fcoeff));
+   fform->Assemble();
+   fform->SyncAliasMemory(rhs);
+
+   LinearForm *gform(new LinearForm);
+   gform->Update(W_space, rhs.GetBlock(1), 0);
+   gform->AddDomainIntegrator(new DomainLFIntegrator(gcoeff));
+   gform->Assemble();
+   gform->SyncAliasMemory(rhs);
+
+   // 9. Assemble the finite element matrices for the Darcy operator
+   //
+   //                            D = [ M  C^T ]
+   //                                [ C   0  ]
+   //     where:
+   //
+   //     M = \int_\Omega \sigma E_h \cdot v_h d\Omega   E_h, v_h \in R_h
+   //     C   = \int_\Omega \curl E_h q_h d\Omega   E_h \in R_h, q_h \in W_h
+   //BilinearForm *mEVarf(new BilinearForm(R_space));
+   //MixedBilinearForm *cVarf(new MixedBilinearForm(R_space, W_space));
+   BilinearForm *mEVarf = darcy->GetFluxMassForm();
+   MixedBilinearForm *cVarf = darcy->GetFluxDivForm();
+   BilinearForm *mBVarf = darcy->GetPotentialMassForm();
+
+   //if (pa) { mEVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   mEVarf->AddDomainIntegrator(new VectorFEMassIntegrator(sigma));
+   //mEVarf->Assemble();
+   //if (!pa) { mEVarf->Finalize(); }
+
+   //if (pa) { cVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   cVarf->AddDomainIntegrator(new MixedScalarCurlIntegrator(muinvsqrt));
+   //cVarf->Assemble();
+   //if (!pa) { cVarf->Finalize(); }
+
+   mBVarf->AddDomainIntegrator(new MassIntegrator());
+
+   //set essential boundary condition
+
+   GridFunction E, B;
+   E.MakeRef(R_space, x.GetBlock(0), 0);
+   B.MakeRef(W_space, x.GetBlock(1), 0);
+
+   Array<int> ess_flux_tdofs_list;
+   if (mesh->bdr_attributes.Size())
+   {
+      Array<int> ess_bdr(mesh->bdr_attributes.Max());
+      ess_bdr = 1;
+      R_space->GetEssentialTrueDofs(ess_bdr, ess_flux_tdofs_list);
+      E.ProjectBdrCoefficientTangent(Ecoeff, ess_bdr);
+   }
+
+   //set hybridization / assembly level
+
+   FiniteElementCollection *trace_coll = NULL;
+   FiniteElementSpace *trace_space = NULL;
+
+   chrono.Clear();
+   chrono.Start();
+
+   if (hybridization)
+   {
+      trace_coll = new ND_Trace_FECollection(order+1, dim);
+      trace_space = new FiniteElementSpace(mesh, trace_coll);
+      darcy->EnableHybridization(trace_space,
+                                 new TangentTraceJumpIntegrator(),
+                                 ess_flux_tdofs_list);
+   }
+
+   if (pa) { darcy->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+
+   darcy->Assemble();
+   //if (!pa) { darcy->Finalize(); }
+
+   OperatorHandle pDarcyOp;
+   Vector X, RHS;
+
+   //darcy->FormSystemMatrix(ess_flux_tdofs_list, pDarcyOp);
+   darcy->FormLinearSystem(ess_flux_tdofs_list, x, rhs,
+                           pDarcyOp, X, RHS);
+
+   chrono.Stop();
+   std::cout << "Assembly took " << chrono.RealTime() << "s.\n";
+
+
+   int maxIter(1000);
+   real_t rtol(1.e-6);
+   real_t atol(1.e-10);
+
+   if (hybridization)
+   {
+      // 10. Construct the preconditioner
+      GSSmoother prec(*pDarcyOp.As<SparseMatrix>());
+
+      // 11. Solve the linear system with GMRES.
+      //     Check the norm of the unpreconditioned residual.
+      chrono.Clear();
+      chrono.Start();
+      GMRESSolver solver;
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPreconditioner(prec);
+      solver.SetPrintLevel(1);
+
+      solver.Mult(RHS, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      chrono.Stop();
+
+      if (solver.GetConverged())
+      {
+         std::cout << "GMRES converged in " << solver.GetNumIterations()
+                   << " iterations with a residual norm of "
+                   << solver.GetFinalNorm() << ".\n";
+      }
+      else
+      {
+         std::cout << "GMRES did not converge in " << solver.GetNumIterations()
+                   << " iterations. Residual norm is " << solver.GetFinalNorm()
+                   << ".\n";
+      }
+      std::cout << "GMRES solver took " << chrono.RealTime() << "s.\n";
+   }
+   else
+   {
+      // 10. Construct the operators for preconditioner
+      //
+      //                 P = [ diag(M)         0         ]
+      //                     [  0       C diag(M)^-1 C^T ]
+      //
+      //     Here we use Symmetric Gauss-Seidel to approximate the inverse of the
+      //     magnetic field Schur Complement
+      SparseMatrix *MinvBt = NULL;
+      Vector Md(mEVarf->Height());
+
+      BlockDiagonalPreconditioner darcyPrec(block_offsets);
+      Solver *invM, *invS;
+      SparseMatrix *S = NULL;
+
+      if (pa)
+      {
+         mEVarf->AssembleDiagonal(Md);
+         auto Md_host = Md.HostRead();
+         Vector invMd(mEVarf->Height());
+         for (int i=0; i<mEVarf->Height(); ++i)
+         {
+            invMd(i) = 1.0 / Md_host[i];
+         }
+
+         Vector BMBt_diag(cVarf->Height());
+         cVarf->AssembleDiagonal_ADAt(invMd, BMBt_diag);
+
+         Array<int> ess_tdof_list;  // empty
+
+         invM = new OperatorJacobiSmoother(Md, ess_tdof_list);
+         invS = new OperatorJacobiSmoother(BMBt_diag, ess_tdof_list);
+      }
+      else
+      {
+         SparseMatrix &M(mEVarf->SpMat());
+         M.GetDiag(Md);
+         Md.HostReadWrite();
+
+         SparseMatrix &C(cVarf->SpMat());
+         MinvBt = Transpose(C);
+
+         for (int i = 0; i < Md.Size(); i++)
+         {
+            MinvBt->ScaleRow(i, 1./Md(i));
+         }
+
+         S = Mult(C, *MinvBt);
+         if (mBVarf)
+         {
+            SparseMatrix &Mtm(mBVarf->SpMat());
+            SparseMatrix *Snew = Add(Mtm, *S);
+            delete S;
+            S = Snew;
+         }
+
+         invM = new DSmoother(M);
+
+#ifndef MFEM_USE_SUITESPARSE
+         invS = new GSSmoother(*S);
+#else
+         invS = new UMFPackSolver(*S);
+#endif
+      }
+
+      invM->iterative_mode = false;
+      invS->iterative_mode = false;
+
+      darcyPrec.SetDiagonalBlock(0, invM);
+      darcyPrec.SetDiagonalBlock(1, invS);
+
+      // 11. Solve the linear system with MINRES.
+      //     Check the norm of the unpreconditioned residual.
+
+      chrono.Clear();
+      chrono.Start();
+      FGMRESSolver solver;
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPreconditioner(darcyPrec);
+      solver.SetPrintLevel(1);
+
+      solver.Mult(RHS, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      if (device.IsEnabled()) { x.HostRead(); }
+      chrono.Stop();
+
+      if (solver.GetConverged())
+      {
+         std::cout << "GMRES converged in " << solver.GetNumIterations()
+                   << " iterations with a residual norm of "
+                   << solver.GetFinalNorm() << ".\n";
+      }
+      else
+      {
+         std::cout << "GMRES did not converge in " << solver.GetNumIterations()
+                   << " iterations. Residual norm is " << solver.GetFinalNorm()
+                   << ".\n";
+      }
+      std::cout << "MINRES solver took " << chrono.RealTime() << "s.\n";
+
+      delete invM;
+      delete invS;
+      delete S;
+      //delete Bt;
+      delete MinvBt;
+   }
+
+   // 12. Create the grid functions E and B. Compute the L2 error norms.
+
+   int order_quad = max(2, 2*order+1);
+   const IntegrationRule *irs[Geometry::NumGeom];
+   for (int i=0; i < Geometry::NumGeom; ++i)
+   {
+      irs[i] = &(IntRules.Get(i, order_quad));
+   }
+
+   real_t err_E  = E.ComputeL2Error(Ecoeff, irs);
+   real_t norm_E = ComputeLpNorm(2., Ecoeff, *mesh, irs);
+   real_t err_B  = B.ComputeL2Error(Bcoeff, irs);
+   real_t norm_B = ComputeLpNorm(2., Bcoeff, *mesh, irs);
+
+   std::cout << "|| E_h - E_ex || / || E_ex || = " << err_E / norm_E << "\n";
+   std::cout << "|| B_h - B_ex || / || B_ex || = " << err_B / norm_B << "\n";
+
+   // 13. Save the mesh and the solution. This output can be viewed later using
+   //     GLVis: "glvis -m ex5.mesh -g sol_u.gf" or "glvis -m ex5.mesh -g
+   //     sol_p.gf".
+   {
+      ofstream mesh_ofs("ex5.mesh");
+      mesh_ofs.precision(8);
+      mesh->Print(mesh_ofs);
+
+      ofstream E_ofs("sol_E.gf");
+      E_ofs.precision(8);
+      E.Save(E_ofs);
+
+      ofstream B_ofs("sol_B.gf");
+      B_ofs.precision(8);
+      B.Save(B_ofs);
+   }
+
+   // 14. Save data in the VisIt format
+   VisItDataCollection visit_dc("Example5", mesh);
+   visit_dc.RegisterField("electric field", &E);
+   visit_dc.RegisterField("magnetic field", &B);
+   visit_dc.Save();
+
+   // 15. Save data in the ParaView format
+   ParaViewDataCollection paraview_dc("Example5", mesh);
+   paraview_dc.SetPrefixPath("ParaView");
+   paraview_dc.SetLevelsOfDetail(order);
+   paraview_dc.SetCycle(0);
+   paraview_dc.SetDataFormat(VTKFormat::BINARY);
+   paraview_dc.SetHighOrderOutput(true);
+   paraview_dc.SetTime(0.0); // set the time
+   paraview_dc.RegisterField("electric field",&E);
+   paraview_dc.RegisterField("magnetic field",&B);
+   paraview_dc.Save();
+
+
+   // 16. Send the solution by socket to a GLVis server.
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream E_sock(vishost, visport);
+      E_sock.precision(8);
+      E_sock << "solution\n" << *mesh << E << "window_title 'Electric field'" << endl;
+      E_sock << "keys Rljvvvvvmmc" << endl;
+      socketstream B_sock(vishost, visport);
+      B_sock.precision(8);
+      B_sock << "solution\n" << *mesh << B << "window_title 'Magnetic field'" << endl;
+      B_sock << "keys Rljmmc" << endl;
+   }
+
+   // 17. Free the used memory.
+   delete fform;
+   delete gform;
+   //delete mEVarf;
+   //delete cVarf;
+   delete darcy;
+   delete W_space;
+   delete R_space;
+   delete trace_space;
+   delete W_coll;
+   delete R_coll;
+   delete trace_coll;
+   delete mesh;
+
+   return 0;
+}
+
+
+void EFun_ex(const Vector & x, Vector & E)
+{
+   const int dim = x.Size();
+
+   if (dim == 3)
+   {
+      E(0) = sin(kappa * x(1));
+      E(1) = sin(kappa * x(2));
+      E(2) = sin(kappa * x(0));
+   }
+   else
+   {
+      E(0) = sin(kappa * x(1));
+      E(1) = sin(kappa * x(0));
+      if (x.Size() == 3) { E(2) = 0.0; }
+   }
+}
+
+real_t BFun_ex(const Vector & x)
+{
+   return kappa * (-cos(kappa * x(0)) + cos(kappa * x(1)));
+}
+
+void fFun(const Vector & x, Vector & f)
+{
+   const int dim = x.Size();
+
+   if (dim == 3)
+   {
+      f(0) = (1. + kappa * kappa) * sin(kappa * x(1));
+      f(1) = (1. + kappa * kappa) * sin(kappa * x(2));
+      f(2) = (1. + kappa * kappa) * sin(kappa * x(0));
+   }
+   else
+   {
+      f(0) = (1. + kappa * kappa) * sin(kappa * x(1));
+      f(1) = (1. + kappa * kappa) * sin(kappa * x(0));
+      if (x.Size() == 3) { f(2) = 0.0; }
+   }
+}
+
+real_t gFun(const Vector & x)
+{
+   return 0.;
+}

examples/ex5-scatter.cpp

@@ -0,0 +1,938 @@
+//                                MFEM Example 5
+//
+// Compile with: make ex5
+//
+// Sample runs:  ex5 -m ../data/square-disc.mesh
+//               ex5 -m ../data/star.mesh
+//               ex5 -m ../data/star.mesh -pa
+//               ex5 -m ../data/beam-tet.mesh
+//               ex5 -m ../data/beam-hex.mesh
+//               ex5 -m ../data/beam-hex.mesh -pa
+//               ex5 -m ../data/escher.mesh
+//               ex5 -m ../data/fichera.mesh
+//
+// Device sample runs:
+//               ex5 -m ../data/star.mesh -pa -d cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-omp
+//               ex5 -m ../data/beam-hex.mesh -pa -d cuda
+//
+// Description:  This example code solves a simple 2D coupled Maxwell + compression
+//               wave interaction problem in the mixed formulation corresponding to
+//               the system
+//
+//                                 du/dt + grad n =  sigma0 * n * E
+//                                 div u +  dn/dt = 0
+//                                 dE/dt - curl B = -sigma0 * n * E
+//                                 dB/dt + curl E = 0
+//
+//               with natural boundary condition n = <given density> and/or
+//               essential (RT) / natural (DG) boundary condition u.n = <given
+//               velocity>. Similarly, essential boundary condition Exnxn =
+//               <given electric field> can be set or natural boundary condition
+//               for the magnetic field. Multiple problems are offered:
+//               1) material wave - compression wave in medium (left u b.c.)
+//               2) Maxwell - electromagnetic wave (left E b.c.)
+//               3) excitation - electromagnetic wave exciting the medium (left
+//                               E b.c.)
+//               4) scaterring - interaction of electromagnetic and compression
+//                               Gaussian beams (bottom u and left E b.c.)
+//               The waves are harmonic in time with the given frequency. We
+//               discretize the problem with normally continuous or broken
+//               Raviart-Thomas, or piecewise discontinuous finite elements the
+//               velocity u; piecewise discontinuous polynomials the density n;
+//               tangentially continuous Nedelec the electric field; and
+//               piecewise discountinuous polynomials the magnetic field B.
+//
+//               The example demonstrates the use of the DarcyForm class, as
+//               well as hybridization of mixed systems and the collective saving
+//               of several grid functions in VisIt (visit.llnl.gov) and ParaView
+//               (paraview.org) formats.
+//
+//               We recommend viewing examples 1-4 before viewing this example.
+
+#include "mfem.hpp"
+#include "coupledop.hpp"
+#include <fstream>
+#include <iostream>
+#include <algorithm>
+
+using namespace std;
+using namespace mfem;
+
+// Define the analytical solution and forcing terms / boundary conditions
+typedef std::function<real_t(const Vector &, real_t)> TFunc;
+typedef std::function<void(const Vector &, Vector &)> VecFunc;
+typedef std::function<void(const Vector &, real_t, Vector &)> VecTFunc;
+typedef std::function<real_t(real_t f, const Vector &x)> KFunc;
+
+enum Problem
+{
+   MaterialWave = 1,
+   Maxwell,
+   Excitation,
+   Scattering,
+};
+
+constexpr real_t epsilon = numeric_limits<real_t>::epsilon();
+
+TFunc GetSigFun(Problem prob, real_t f, real_t s0);
+TFunc GetNFun(Problem prob, real_t t_0, real_t k, real_t c);
+VecTFunc GetUFun(Problem prob, real_t f, real_t a0);
+VecTFunc GetEFun(Problem prob, real_t f);
+TFunc GetFFun(Problem prob, real_t t_0, real_t k, real_t c);
+
+int main(int argc, char *argv[])
+{
+   StopWatch chrono;
+
+   // 1. Parse command-line options.
+   const char *mesh_file = "";
+   int nx = 0;
+   int ny = 0;
+   real_t sx = 1.;
+   real_t sy = 1.;
+   int order = 1;
+   bool dg = false;
+   bool brt = false;
+   int iproblem = Problem::MaterialWave;
+   real_t tf = 1.;
+   int nt = 0;
+   int ode = 1;
+   real_t k = 1.;
+   real_t c = 1.;
+   real_t freq = 1.;
+   real_t s0 = 1.;
+   real_t a0 = 1e-3;
+   real_t td = 0.5;
+   bool bc_neumann = false;
+   //bool reduction = false;
+   bool hybridization = false;
+   /*bool nonlinear = false;
+   bool nonlinear_conv = false;
+   bool nonlinear_diff = false;
+   int hdg_scheme = 1;
+   int solver_type = (int)DarcyOperator::SolverType::Default;
+   bool pa = false;*/
+   const char *device_config = "cpu";
+   bool mfem = false;
+   bool visit = false;
+   bool paraview = false;
+   bool visualization = true;
+   bool analytic = false;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&nx, "-nx", "--ncells-x",
+                  "Number of cells in x.");
+   args.AddOption(&ny, "-ny", "--ncells-y",
+                  "Number of cells in y.");
+   args.AddOption(&sx, "-sx", "--size-x",
+                  "Size along x axis.");
+   args.AddOption(&sy, "-sy", "--size-y",
+                  "Size along y axis.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&dg, "-dg", "--discontinuous", "-no-dg",
+                  "--no-discontinuous", "Enable DG elements for fluxes.");
+   args.AddOption(&brt, "-brt", "--broken-RT", "-no-brt",
+                  "--no-broken-RT", "Enable broken RT elements for fluxes.");
+   args.AddOption(&iproblem, "-p", "--problem",
+                  "Problem to solve:\n\t\t"
+                  "1=dumping\n\t\t"
+                  "2=Maxwell\n\t\t");
+   args.AddOption(&tf, "-tf", "--time-final",
+                  "Final time.");
+   args.AddOption(&nt, "-nt", "--ntimesteps",
+                  "Number of time steps.");
+   args.AddOption(&ode, "-ode", "--ode-solver",
+                  "ODE time solver (1=Bacward Euler, 2=RK23L, 3=RK23A, 4=RK34).");
+   args.AddOption(&k, "-k", "--kappa",
+                  "Heat conductivity");
+   args.AddOption(&c, "-c", "--velocity",
+                  "Convection velocity");
+   args.AddOption(&freq, "-f", "--frequency",
+                  "Harmonic frequency");
+   args.AddOption(&s0, "-s0", "--sigma0",
+                  "Coupling factor");
+   args.AddOption(&a0, "-a0", "--amplitude0",
+                  "Amplitude factor");
+   args.AddOption(&td, "-td", "--stab_diff",
+                  "Diffusion stabilization factor (1/2=default)");
+   args.AddOption(&bc_neumann, "-bcn", "--bc-neumann", "-no-bcn",
+                  "--no-bc-neumann", "Enable Neumann outflow boundary condition.");
+   //args.AddOption(&reduction, "-rd", "--reduction", "-no-rd",
+   //               "--no-reduction", "Enable reduction.");
+   args.AddOption(&hybridization, "-hb", "--hybridization", "-no-hb",
+                  "--no-hybridization", "Enable hybridization.");
+   /*args.AddOption(&nonlinear, "-nl", "--nonlinear", "-no-nl",
+                  "--no-nonlinear", "Enable non-linear regime.");
+   args.AddOption(&nonlinear_conv, "-nlc", "--nonlinear-convection", "-no-nlc",
+                  "--no-nonlinear-convection", "Enable non-linear convection regime.");
+   args.AddOption(&nonlinear_diff, "-nld", "--nonlinear-diffusion", "-no-nld",
+                  "--no-nonlinear-diffusion", "Enable non-linear diffusion regime.");
+   args.AddOption(&hdg_scheme, "-hdg", "--hdg_scheme",
+                  "HDG scheme (1=HDG-I, 2=HDG-II, 3=Rusanov, 4=Godunov).");
+   args.AddOption(&solver_type, "-nls", "--nonlinear-solver",
+                  "Nonlinear solver type (1=LBFGS, 2=LBB, 3=Newton, 4=KINSol).");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");*/
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&mfem, "-mfem", "--mfem", "-no-mfem",
+                  "--no-mfem",
+                  "Enable or disable MFEM output.");
+   args.AddOption(&visit, "-visit", "--visit", "-no-visit",
+                  "--no-visit",
+                  "Enable or disable Visit output.");
+   args.AddOption(&paraview, "-paraview", "--paraview", "-no-paraview",
+                  "--no-paraview",
+                  "Enable or disable ParaView output.");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.AddOption(&analytic, "-anal", "--analytic", "-no-anal",
+                  "--no-analytic",
+                  "Enable or disable analytic solution.");
+
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+
+   // Set the problem options
+   Problem problem = (Problem)iproblem;
+   bool btime = false;
+   switch (problem)
+   {
+      case Problem::MaterialWave:
+      case Problem::Maxwell:
+      case Problem::Excitation:
+      case Problem::Scattering:
+         btime = true;
+         break;
+      default:
+         cerr << "Unknown problem" << endl;
+         return 1;
+   }
+
+   /*if (bnldiff && reduction)
+   {
+      cerr << "Reduction is not possible with non-linear diffusion" << endl;
+      return 1;
+   }
+
+   if (!bconv && !bnlconv && upwinded)
+   {
+      cerr << "Upwinded scheme cannot work without advection" << endl;
+      return 1;
+   }
+
+   if (bnlconv && !nonlinear)
+   {
+      cerr << "Nonlinear convection can only work in the nonlinear regime" << endl;
+      return 1;
+   }*/
+
+   if (btime && nt <= 0)
+   {
+      cerr << "You must specify the number of time steps for time evolving problems"
+           << endl;
+      return 1;
+   }
+
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
+   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
+   //    the same code.
+   if (ny <= 0)
+   {
+      ny = nx;
+   }
+
+   Mesh *mesh = NULL;
+   if (strlen(mesh_file) > 0)
+   {
+      mesh = new Mesh(mesh_file, 1, 1);
+   }
+   else
+   {
+      mesh = new Mesh(Mesh::MakeCartesian2D(nx, ny, Element::QUADRILATERAL, false,
+                                            sx, sy));
+   }
+
+   int dim = mesh->Dimension();
+
+   // Mark boundary conditions
+   Array<int> bdr_u_is_dirichlet(mesh->bdr_attributes.Max());
+   Array<int> bdr_u_is_neumann(bdr_u_is_dirichlet.Size());
+   Array<int> bdr_E_is_neumann(bdr_u_is_dirichlet.Size());
+   bdr_u_is_dirichlet = 0;
+   bdr_u_is_neumann = 0;
+   bdr_E_is_neumann = 0;
+
+   switch (problem)
+   {
+      case Problem::MaterialWave:
+         bdr_u_is_neumann[3] = -1;//inflow
+         if (bc_neumann)
+         {
+            bdr_u_is_neumann[0] = -1;//outflow
+            bdr_u_is_neumann[2] = -1;//outflow
+         }
+         break;
+      case Problem::Maxwell:
+      case Problem::Excitation:
+         bdr_u_is_dirichlet = -1;
+         bdr_u_is_neumann[3] = -1;
+         bdr_E_is_neumann[3] = -1;//inflow
+         if (bc_neumann)
+         {
+            bdr_E_is_neumann[0] = -1;//outflow
+            bdr_E_is_neumann[2] = -1;//outflow
+         }
+         break;
+      case Problem::Scattering:
+         bdr_u_is_dirichlet = -1;
+         bdr_u_is_neumann[0] = -1;//inflow
+         bdr_E_is_neumann[3] = -1;//inflow
+         if (bc_neumann)
+         {
+            bdr_u_is_neumann[1] = -1;//outflow
+            bdr_u_is_neumann[3] = -1;//outflow
+            bdr_E_is_neumann[0] = -1;//outflow
+            bdr_E_is_neumann[2] = -1;//outflow
+         }
+         break;
+   }
+
+   // 4. Refine the mesh to increase the resolution. In this example we do
+   //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
+   //    largest number that gives a final mesh with no more than 10,000
+   //    elements.
+   if (strlen(mesh_file) > 0)
+   {
+      int ref_levels =
+         (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 5. Define a finite element space on the mesh. Here we use the
+   //    Raviart-Thomas finite elements of the specified order.
+   FiniteElementCollection *V_coll, *V_coll_dg = NULL;
+   if (dg)
+   {
+      // In the case of LDG formulation, we chose a closed basis as it
+      // is customary for HDG to match trace DOFs, but an open basis can
+      // be used instead.
+      V_coll = new L2_FECollection(order, dim, BasisType::GaussLobatto);
+   }
+   else if (brt)
+   {
+      V_coll = new BrokenRT_FECollection(order, dim);
+      V_coll_dg = new L2_FECollection(order+1, dim);
+   }
+   else
+   {
+      V_coll = new RT_FECollection(order, dim);
+   }
+   FiniteElementCollection *W_coll = new L2_FECollection(order, dim,
+                                                         BasisType::GaussLobatto);
+   FiniteElementCollection *E_coll = new ND_FECollection(order, dim);
+   FiniteElementCollection *B_coll = new L2_FECollection(order, dim, 0,
+                                                         FiniteElement::INTEGRAL);
+
+   FiniteElementSpace *V_space = new FiniteElementSpace(mesh, V_coll,
+                                                        (dg)?(dim):(1));
+   FiniteElementSpace *V_space_dg = (V_coll_dg)?(new FiniteElementSpace(
+                                                    mesh, V_coll_dg, dim)):(NULL);
+   FiniteElementSpace *W_space = new FiniteElementSpace(mesh, W_coll);
+   FiniteElementSpace *E_space = new FiniteElementSpace(mesh, E_coll);
+   FiniteElementSpace *B_space = new FiniteElementSpace(mesh, B_coll);
+
+   FiniteElementCollection *trace_coll = NULL;
+   FiniteElementSpace *trace_space = NULL;
+
+   if (hybridization)
+   {
+      trace_coll = new DG_Interface_FECollection(order, dim);
+      trace_space = new FiniteElementSpace(mesh, trace_coll);
+   }
+
+   // 6. Define the coefficients, analytical solution, and rhs of the PDE.
+   const real_t t_0 = 1.; //base density
+
+   ConstantCoefficient kcoeff(k); //conductivity
+   ConstantCoefficient ikcoeff(1./k); //inverse conductivity
+
+   auto sigFun = GetSigFun(problem, freq, s0);
+   FunctionCoefficient sigcoeff(sigFun); //coupling
+
+   auto nFun = GetNFun(problem, t_0, k, c);
+   FunctionCoefficient ncoeff(nFun); //density
+   SumCoefficient gcoeff(0., ncoeff, 1., -1.); //boundary velocity rhs
+   ProductCoefficient ghcoeff(0.5, gcoeff);
+
+   auto fFun = GetFFun(problem, t_0, k, c);
+   FunctionCoefficient fcoeff(fFun); //density rhs
+
+   auto uFun = GetUFun(problem, freq, a0);
+   VectorFunctionCoefficient ucoeff(dim, uFun); //velocity
+   ConstantCoefficient one;
+
+   auto Efun = GetEFun(problem, freq);
+   VectorFunctionCoefficient Ecoeff(dim, Efun); //electric field
+
+   // 7. Assemble the finite element matrices for the Darcy operator
+   //
+   //                            D = [ M  B^T ]
+   //                                [ B   0  ]
+   //     where:
+   //
+   //     M = \int_\Omega k u_h \cdot v_h d\Omega   u_h, v_h \in V_h
+   //     B   = -\int_\Omega \div u_h u_h d\Omega   u_h \in V_h, w_h \in W_h
+
+   // 8. Define the BlockStructure of the problem, i.e. define the array of
+   //    offsets for each variable. The last component of the Array is the sum
+   //    of the dimensions of each block.
+   const Array<int> block_offsets(CoupledOperator::ConstructOffsets(V_space,
+                                                                    W_space, E_space, B_space, trace_space));
+
+   std::cout << "***********************************************************\n";
+   std::cout << "dim(V) = " << block_offsets[1] - block_offsets[0] << "\n";
+   std::cout << "dim(W) = " << block_offsets[2] - block_offsets[1] << "\n";
+   if (hybridization)
+   {
+      std::cout << "dim(M) = " << block_offsets[3] - block_offsets[2] << "\n";
+      std::cout << "dim(E) = " << block_offsets[4] - block_offsets[3] << "\n";
+      std::cout << "dim(B) = " << block_offsets[5] - block_offsets[4] << "\n";
+      std::cout << "dim(V+W+M+E+B) = " << block_offsets.Last() << "\n";
+   }
+   else
+   {
+      std::cout << "dim(E) = " << block_offsets[3] - block_offsets[2] << "\n";
+      std::cout << "dim(B) = " << block_offsets[4] - block_offsets[3] << "\n";
+      std::cout << "dim(V+W+E+B) = " << block_offsets.Last() << "\n";
+   }
+   std::cout << "***********************************************************\n";
+
+   // 9. Allocate memory (x, rhs) for the analytical solution and the right hand
+   //    side.  Define the GridFunction q,t for the finite element solution and
+   //    linear forms fform and gform for the right hand side.  The data
+   //    allocated by x and rhs are passed as a reference to the grid functions
+   //    (q,t) and the linear forms (fform, gform).
+   MemoryType mt = device.GetMemoryType();
+   BlockVector x(block_offsets, mt), rhs(block_offsets, mt);
+
+   x = 0.;
+   GridFunction u_h, n_h, tr_h, E_h, B_h;
+   int i = 0;
+   u_h.MakeRef(V_space, x.GetBlock(i++), 0);
+   n_h.MakeRef(W_space, x.GetBlock(i++), 0);
+   if (trace_space)
+   {
+      tr_h.MakeRef(trace_space, x.GetBlock(i++), 0);
+   }
+   E_h.MakeRef(E_space, x.GetBlock(i++), 0);
+   B_h.MakeRef(B_space, x.GetBlock(i++), 0);
+
+   if (btime)
+   {
+      n_h.ProjectCoefficient(ncoeff); //initial condition
+   }
+
+   if (!dg && !brt)
+   {
+      u_h.ProjectBdrCoefficientNormal(ucoeff,
+                                      bdr_u_is_neumann);   //essential Neumann BC
+   }
+
+   LinearForm *gform(new LinearForm);
+   gform->Update(V_space, rhs.GetBlock(0), 0);
+   if (dg)
+   {
+      gform->AddBdrFaceIntegrator(new VectorBoundaryFluxLFIntegrator(gcoeff),
+                                  bdr_u_is_dirichlet);
+      if (!hybridization)
+      {
+         gform->AddBdrFaceIntegrator(new VectorBoundaryFluxLFIntegrator(
+                                        gcoeff, 0.5), bdr_u_is_neumann);
+      }
+   }
+   else
+   {
+      if (brt)
+      {
+         gform->AddBdrFaceIntegrator(new VectorFEBoundaryFluxLFIntegrator(gcoeff),
+                                     bdr_u_is_dirichlet);
+         if (!hybridization)
+         {
+            gform->AddBdrFaceIntegrator(new VectorFEBoundaryFluxLFIntegrator(
+                                           ghcoeff), bdr_u_is_neumann);
+         }
+      }
+      else
+      {
+         gform->AddBoundaryIntegrator(new VectorFEBoundaryFluxLFIntegrator(gcoeff),
+                                      bdr_u_is_dirichlet);
+      }
+   }
+
+   LinearForm *fform(new LinearForm);
+   fform->Update(W_space, rhs.GetBlock(1), 0);
+   fform->AddDomainIntegrator(new DomainLFIntegrator(fcoeff));
+
+   //Neumann
+   if (!hybridization && (dg || brt))
+   {
+      fform->AddBdrFaceIntegrator(new BoundaryFlowIntegrator(one, ucoeff, +1., 0.),
+                                  bdr_u_is_neumann);
+   }
+
+   //prepare (reduced) solution and rhs vectors
+
+   LinearForm *hform = NULL;
+
+   //Neumann BC for the hybridized system
+
+   if (hybridization)
+   {
+      hform = new LinearForm();
+      hform->Update(trace_space, rhs.GetBlock(2), 0);
+      //note that Neumann BC must be applied only for the velocity
+      //and not the total flux for stability reasons
+      hform->AddBoundaryIntegrator(new BoundaryNormalLFIntegrator(ucoeff, 2),
+                                   bdr_u_is_neumann);
+   }
+
+   //construct the operator
+
+   Array<LinearForm*> lfs({gform, fform, hform, (LinearForm*)NULL, (LinearForm*)NULL});
+
+   Array<Coefficient*> coeffs({(Coefficient*)&gcoeff,
+                               (Coefficient*)&fcoeff,
+                               (Coefficient*)&ucoeff});
+
+   CoupledOperator op(bdr_u_is_neumann, bdr_E_is_neumann, &sigcoeff, lfs, coeffs,
+                      V_space, W_space, E_space, B_space, trace_space, td);
+
+   //construct the time solver
+
+   ODESolver *ode_solver;
+
+   switch (ode)
+   {
+      case 1: ode_solver = new BackwardEulerSolver(); break;
+      case 2: ode_solver = new SDIRK23Solver(2); break;
+      case 3: ode_solver = new SDIRK23Solver(); break;
+      case 4: ode_solver = new SDIRK34Solver(); break;
+      default:
+         MFEM_ABORT("Unknown solver");
+         return 1;
+   }
+
+   ode_solver->Init(op);
+
+   //iterate in time
+
+   if (!btime) { nt = 1; }
+
+   const real_t dt = tf / nt; //time step
+
+   for (int ti = 0; ti < nt; ti++)
+   {
+      //set current time
+
+      real_t t = tf * ti / nt;
+
+      if (!dg && !brt)
+      {
+         ucoeff.SetTime(t);
+         u_h.ProjectBdrCoefficientNormal(ucoeff,
+                                         bdr_u_is_neumann);   //essential Neumann BC
+      }
+
+      Ecoeff.SetTime(t);
+      E_h.ProjectBdrCoefficientTangent(Ecoeff, bdr_E_is_neumann);
+
+      //perform time step
+
+      real_t dt_ = dt;//<---ignore time step changes
+      ode_solver->Step(x, t, dt_);
+
+      // 12. Compute the L2 error norms.
+
+      int order_quad = max(2, 2*order+1);
+      const IntegrationRule *irs[Geometry::NumGeom];
+      for (int i=0; i < Geometry::NumGeom; ++i)
+      {
+         irs[i] = &(IntRules.Get(i, order_quad));
+      }
+
+      real_t err_u  = u_h.ComputeL2Error(ucoeff, irs);
+      real_t norm_u = ComputeLpNorm(2., ucoeff, *mesh, irs);
+      real_t err_n  = n_h.ComputeL2Error(ncoeff, irs);
+      real_t norm_n = ComputeLpNorm(2., ncoeff, *mesh, irs);
+
+      if (btime)
+      {
+         cout << "iter:\t" << ti
+              << "\ttime:\t" << t
+              << "\tq_err:\t" << err_u / norm_u
+              << "\tt_err:\t" << err_n / norm_n
+              << endl;
+      }
+      else
+      {
+         cout << "|| u_h - u_ex || / || u_ex || = " << err_u / norm_u << "\n";
+         cout << "|| n_h - n_ex || / || n_ex || = " << err_n / norm_n << "\n";
+      }
+
+      // Project the broken space
+
+      GridFunction u_v;
+      if (V_space_dg)
+      {
+         VectorGridFunctionCoefficient coeff(&u_h);
+         u_v.SetSpace(V_space_dg);
+         u_v.ProjectCoefficient(coeff);
+      }
+      else
+      {
+         u_v.MakeRef(V_space, u_h, 0);
+      }
+
+      // Project the analytic solution
+
+      static GridFunction u_a, n_a, c_gf;
+
+      u_a.SetSpace(V_space);
+      u_a.ProjectCoefficient(ucoeff);
+
+      n_a.SetSpace(W_space);
+      n_a.ProjectCoefficient(ncoeff);
+
+      // 13. Save the mesh and the solution. This output can be viewed later using
+      //     GLVis: "glvis -m ex5.mesh -g sol_q.gf" or "glvis -m ex5.mesh -g
+      //     sol_t.gf".
+      if (mfem)
+      {
+         stringstream ss;
+         ss.str("");
+         ss << "mesh";
+         if (btime) { ss << "_" << ti; }
+         ss << ".mesh";
+         ofstream mesh_ofs(ss.str());
+         mesh_ofs.precision(8);
+         mesh->Print(mesh_ofs);
+
+         ss.str("");
+         ss << "sol_u";
+         if (btime) { ss << "_" << ti; }
+         ss << ".gf";
+         ofstream u_ofs(ss.str());
+         u_ofs.precision(8);
+         u_v.Save(u_ofs);
+
+         ss.str("");
+         ss << "sol_n";
+         if (btime) { ss << "_" << ti; }
+         ss << ".gf";
+         ofstream n_ofs(ss.str());
+         n_ofs.precision(8);
+         n_h.Save(n_ofs);
+
+         ss.str("");
+         ss << "sol_E";
+         if (btime) { ss << "_" << ti; }
+         ss << ".gf";
+         ofstream E_ofs(ss.str());
+         E_ofs.precision(8);
+         E_h.Save(E_ofs);
+
+         ss.str("");
+         ss << "sol_B";
+         if (btime) { ss << "_" << ti; }
+         ss << ".gf";
+         ofstream B_ofs(ss.str());
+         B_ofs.precision(8);
+         B_h.Save(B_ofs);
+      }
+
+      // 14. Save data in the VisIt format
+      if (visit)
+      {
+         static VisItDataCollection visit_dc("Example5", mesh);
+         if (ti == 0)
+         {
+            visit_dc.RegisterField("velocity", &u_h);
+            visit_dc.RegisterField("density", &n_h);
+            if (analytic)
+            {
+               visit_dc.RegisterField("velocity analytic", &u_a);
+               visit_dc.RegisterField("density analytic", &n_a);
+            }
+         }
+         visit_dc.SetCycle(ti);
+         visit_dc.SetTime(t); // set the time
+         visit_dc.Save();
+      }
+
+      // 15. Save data in the ParaView format
+      if (paraview)
+      {
+         static ParaViewDataCollection paraview_dc("Example5", mesh);
+         if (ti == 0)
+         {
+            paraview_dc.SetPrefixPath("ParaView");
+            paraview_dc.SetLevelsOfDetail(order);
+            paraview_dc.SetDataFormat(VTKFormat::BINARY);
+            paraview_dc.SetHighOrderOutput(true);
+            paraview_dc.RegisterField("velocity",&u_h);
+            paraview_dc.RegisterField("density",&n_h);
+            if (analytic)
+            {
+               paraview_dc.RegisterField("velocity analytic", &u_a);
+               paraview_dc.RegisterField("density analytic", &n_a);
+            }
+         }
+         paraview_dc.SetCycle(ti);
+         paraview_dc.SetTime(t); // set the time
+         paraview_dc.Save();
+      }
+
+      // 16. Send the solution by socket to a GLVis server.
+      if (visualization)
+      {
+         const char vishost[] = "localhost";
+         const int  visport   = 19916;
+         static socketstream u_sock(vishost, visport);
+         u_sock.precision(8);
+         u_sock << "solution\n" << *mesh << u_v << endl;
+         if (ti == 0)
+         {
+            u_sock << "window_title 'Velocity'" << endl;
+            u_sock << "keys Rljvvvvvmmc" << endl;
+         }
+         static socketstream n_sock(vishost, visport);
+         n_sock.precision(8);
+         n_sock << "solution\n" << *mesh << n_h << endl;
+         if (ti == 0)
+         {
+            n_sock << "window_title 'Density'" << endl;
+            n_sock << "keys Rljmmc" << endl;
+         }
+         static socketstream E_sock(vishost, visport);
+         E_sock.precision(8);
+         E_sock << "solution\n" << *mesh << E_h << endl;
+         if (ti == 0)
+         {
+            E_sock << "window_title 'Electric field'" << endl;
+            E_sock << "keys Rljvvvvvmmc" << endl;
+         }
+         static socketstream B_sock(vishost, visport);
+         B_sock.precision(8);
+         B_sock << "solution\n" << *mesh << B_h << endl;
+         if (ti == 0)
+         {
+            B_sock << "window_title 'Magnetic field'" << endl;
+            B_sock << "keys Rljmmc" << endl;
+         }
+         if (analytic)
+         {
+            static socketstream qa_sock(vishost, visport);
+            qa_sock.precision(8);
+            qa_sock << "solution\n" << *mesh << u_a << endl;
+            if (ti == 0)
+            {
+               qa_sock << "window_title 'Velocity analytic'" << endl;
+               qa_sock << "keys Rljvvvvvmmc" << endl;
+            }
+            static socketstream ta_sock(vishost, visport);
+            ta_sock.precision(8);
+            ta_sock << "solution\n" << *mesh << n_a << endl;
+            if (ti == 0)
+            {
+               ta_sock << "window_title 'Density analytic'" << endl;
+               ta_sock << "keys Rljmmc" << endl;
+            }
+         }
+      }
+   }
+
+   // 17. Free the used memory.
+
+   delete ode_solver;
+   delete fform;
+   delete gform;
+   delete hform;
+   delete W_space;
+   delete V_space;
+   delete V_space_dg;
+   delete E_space;
+   delete B_space;
+   delete trace_space;
+   delete W_coll;
+   delete V_coll;
+   delete V_coll_dg;
+   delete E_coll;
+   delete B_coll;
+   delete trace_coll;
+   delete mesh;
+
+   return 0;
+}
+
+TFunc GetSigFun(Problem prob, real_t f, real_t s0)
+{
+   switch (prob)
+   {
+      case Problem::MaterialWave:
+      case Problem::Maxwell:
+         return [=](const Vector &x, real_t) -> real_t
+         {
+            return 0.;
+         };
+      case Problem::Excitation:
+      case Problem::Scattering:
+         return [=](const Vector &x, real_t) -> real_t
+         {
+            constexpr real_t x0 = 0.5;
+            constexpr real_t y0 = 0.5;
+            constexpr real_t w = 0.5;
+            const real_t r = hypot(x(0) - x0, x(1) - y0) / w;
+            return exp(-r*r) * s0;
+         };
+   }
+   return TFunc();
+}
+
+TFunc GetNFun(Problem prob, real_t t_0, real_t k, real_t c)
+{
+   switch (prob)
+   {
+      case Problem::MaterialWave:
+      case Problem::Maxwell:
+      case Problem::Scattering:
+         return [=](const Vector &x, real_t) -> real_t
+         {
+            return 0.;
+         };
+      case Problem::Excitation:
+         return [=](const Vector &x, real_t) -> real_t
+         {
+            return 1.;
+         };
+   }
+   return TFunc();
+}
+
+VecTFunc GetUFun(Problem prob, real_t f, real_t a0)
+{
+   switch (prob)
+   {
+      case Problem::MaterialWave:
+         return [=](const Vector &x, real_t t, Vector &v)
+         {
+            const int vdim = x.Size();
+            v.SetSize(vdim);
+
+            v = 0.;
+            constexpr real_t w = 0.25;
+            constexpr real_t y0 = 0.5;
+            const real_t dy = (x(1) - y0) / w;
+            v(0) = exp(-dy*dy) * sin(M_PI * f * t) * cos(M_PI * x(0));
+         };
+      case Problem::Maxwell:
+      case Problem::Excitation:
+         return [=](const Vector &x, real_t t, Vector &v)
+         {
+            const int vdim = x.Size();
+            v.SetSize(vdim);
+            v = 0.;
+         };
+      case Problem::Scattering:
+         return [=](const Vector &x, real_t t, Vector &v)
+         {
+            const int vdim = x.Size();
+            v.SetSize(vdim);
+
+            v = 0.;
+            constexpr real_t w = 0.15;
+            constexpr real_t r0 = 0.5;
+            const real_t r = x(0) - r0;
+            const real_t rw = r / w;
+            constexpr real_t zR = 0.5;
+            constexpr real_t z0 = 0.5;
+            const real_t dz = x(1) - z0;
+            const real_t R = dz / (dz*dz + zR*zR);
+            v(1) = exp(-rw*rw) * sin(M_PI * (f * t - r*r / R)) * cos(M_PI * x(1)) * a0;
+         };
+   }
+   return VecTFunc();
+}
+
+VecTFunc GetEFun(Problem prob, real_t f)
+{
+   switch (prob)
+   {
+      case Problem::MaterialWave:
+      case Problem::Maxwell:
+      case Problem::Excitation:
+         return [=](const Vector &x, real_t t, Vector &v)
+         {
+            const int vdim = x.Size();
+            v.SetSize(vdim);
+
+            v = 0.;
+            constexpr real_t w = 0.25;
+            constexpr real_t y0 = 0.5;
+            const real_t dy = (x(1) - y0) / w;
+            v(1) = exp(-dy*dy) * sin(M_PI * f * t) * cos(M_PI * x(0));
+         };
+      case Problem::Scattering:
+         return [=](const Vector &x, real_t t, Vector &v)
+         {
+            const int vdim = x.Size();
+            v.SetSize(vdim);
+
+            v = 0.;
+            constexpr real_t w = 0.15;
+            const real_t r = x(1) - 0.5;
+            const real_t rw = r / w;
+            constexpr real_t zR = 0.5;
+            constexpr real_t z0 = 0.5;
+            const real_t dz = x(0) - z0;
+            const real_t R = dz / (dz*dz + zR*zR);
+            v(1) = exp(-rw*rw) * sin(M_PI * (f * t - r*r / R)) * cos(M_PI * x(0));
+         };
+   }
+   return VecTFunc();
+}
+
+TFunc GetFFun(Problem prob, real_t t_0, real_t k, real_t c)
+{
+   switch (prob)
+   {
+      case Problem::MaterialWave:
+      case Problem::Maxwell:
+      case Problem::Excitation:
+      case Problem::Scattering:
+         return [=](const Vector &x, real_t) -> real_t
+         {
+            return 0.;
+         };
+   }
+   return TFunc();
+}

examples/ex5.cpp

@@ -29,9 +29,10 @@
 //               finite elements (velocity u) and piecewise discontinuous
 //               polynomials (pressure p).
 //
-//               The example demonstrates the use of the BlockOperator class, as
-//               well as the collective saving of several grid functions in
-//               VisIt (visit.llnl.gov) and ParaView (paraview.org) formats.
+//               The example demonstrates the use of the DarcyForm class, as
+//               well as hybridization of mixed systems and the collective saving
+//               of several grid functions in VisIt (visit.llnl.gov) and ParaView
+//               (paraview.org) formats.
 //
 //               We recommend viewing examples 1-4 before viewing this example.
 
@@ -55,8 +56,11 @@ int main(int argc, char *argv[])
    StopWatch chrono;
 
    // 1. Parse command-line options.
-   const char *mesh_file = "../data/star.mesh";
+   const char *mesh_file = "";
+   int nx = 0;
+   int ny = 0;
    int order = 1;
+   bool hybridization = false;
    bool pa = false;
    const char *device_config = "cpu";
    bool visualization = 1;
@@ -64,8 +68,14 @@ int main(int argc, char *argv[])
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
                   "Mesh file to use.");
+   args.AddOption(&nx, "-nx", "--ncells-x",
+                  "Number of cells in x.");
+   args.AddOption(&ny, "-ny", "--ncells-y",
+                  "Number of cells in y.");
    args.AddOption(&order, "-o", "--order",
                   "Finite element order (polynomial degree).");
+   args.AddOption(&hybridization, "-hb", "--hybridization", "-no-hb",
+                  "--no-hybridization", "Enable hybridization.");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                   "--no-partial-assembly", "Enable Partial Assembly.");
    args.AddOption(&device_config, "-d", "--device",
@@ -89,13 +99,28 @@ int main(int argc, char *argv[])
    // 3. Read the mesh from the given mesh file. We can handle triangular,
    //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
    //    the same code.
-   Mesh *mesh = new Mesh(mesh_file, 1, 1);
+   if (ny <= 0)
+   {
+      ny = nx;
+   }
+
+   Mesh *mesh = NULL;
+   if (strlen(mesh_file) > 0)
+   {
+      mesh = new Mesh(mesh_file, 1, 1);
+   }
+   else
+   {
+      mesh = new Mesh(Mesh::MakeCartesian2D(nx, ny, Element::QUADRILATERAL));
+   }
+
    int dim = mesh->Dimension();
 
    // 4. Refine the mesh to increase the resolution. In this example we do
    //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
    //    largest number that gives a final mesh with no more than 10,000
    //    elements.
+   if (strlen(mesh_file) > 0)
    {
       int ref_levels =
          (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
@@ -107,20 +132,23 @@ int main(int argc, char *argv[])
 
    // 5. Define a finite element space on the mesh. Here we use the
    //    Raviart-Thomas finite elements of the specified order.
-   FiniteElementCollection *hdiv_coll(new RT_FECollection(order, dim));
-   FiniteElementCollection *l2_coll(new L2_FECollection(order, dim));
+   FiniteElementCollection *R_coll(new RT_FECollection(order, dim));
+   FiniteElementCollection *W_coll(new L2_FECollection(order, dim));
 
-   FiniteElementSpace *R_space = new FiniteElementSpace(mesh, hdiv_coll);
-   FiniteElementSpace *W_space = new FiniteElementSpace(mesh, l2_coll);
+   FiniteElementSpace *R_space = new FiniteElementSpace(mesh, R_coll);
+   FiniteElementSpace *W_space = new FiniteElementSpace(mesh, W_coll);
+
+   DarcyForm *darcy = new DarcyForm(R_space, W_space, false);
 
    // 6. Define the BlockStructure of the problem, i.e. define the array of
    //    offsets for each variable. The last component of the Array is the sum
    //    of the dimensions of each block.
-   Array<int> block_offsets(3); // number of variables + 1
+   const Array<int> &block_offsets = darcy->GetOffsets();
+   /*(3); // number of variables + 1
    block_offsets[0] = 0;
    block_offsets[1] = R_space->GetVSize();
    block_offsets[2] = W_space->GetVSize();
-   block_offsets.PartialSum();
+   block_offsets.PartialSum();*/
 
    std::cout << "***********************************************************\n";
    std::cout << "dim(R) = " << block_offsets[1] - block_offsets[0] << "\n";
@@ -129,7 +157,8 @@ int main(int argc, char *argv[])
    std::cout << "***********************************************************\n";
 
    // 7. Define the coefficients, analytical solution, and rhs of the PDE.
-   ConstantCoefficient k(1.0);
+   const double k = 1.0;
+   ConstantCoefficient kcoeff(k);
 
    VectorFunctionCoefficient fcoeff(dim, fFun);
    FunctionCoefficient fnatcoeff(f_natural);
@@ -167,24 +196,55 @@ int main(int argc, char *argv[])
    //
    //     M = \int_\Omega k u_h \cdot v_h d\Omega   u_h, v_h \in R_h
    //     B   = -\int_\Omega \div u_h q_h d\Omega   u_h \in R_h, q_h \in W_h
-   BilinearForm *mVarf(new BilinearForm(R_space));
-   MixedBilinearForm *bVarf(new MixedBilinearForm(R_space, W_space));
+   //BilinearForm *mVarf(new BilinearForm(R_space));
+   //MixedBilinearForm *bVarf(new MixedBilinearForm(R_space, W_space));
+   BilinearForm *mVarf = darcy->GetFluxMassForm();
+   MixedBilinearForm *bVarf = darcy->GetFluxDivForm();
 
-   if (pa) { mVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
-   mVarf->AddDomainIntegrator(new VectorFEMassIntegrator(k));
-   mVarf->Assemble();
-   if (!pa) { mVarf->Finalize(); }
+   //if (pa) { mVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   mVarf->AddDomainIntegrator(new VectorFEMassIntegrator(kcoeff));
+   //mVarf->Assemble();
+   //if (!pa) { mVarf->Finalize(); }
 
-   if (pa) { bVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
-   bVarf->AddDomainIntegrator(new VectorFEDivergenceIntegrator);
-   bVarf->Assemble();
-   if (!pa) { bVarf->Finalize(); }
+   //if (pa) { bVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   ConstantCoefficient cdiv(-1.);
+   bVarf->AddDomainIntegrator(new VectorFEDivergenceIntegrator(cdiv));
+   //bVarf->Assemble();
+   //if (!pa) { bVarf->Finalize(); }
 
-   BlockOperator darcyOp(block_offsets);
+   //set hybridization / assembly level
 
-   TransposeOperator *Bt = NULL;
+   Array<int> ess_flux_tdofs_list;
+   /*Array<int> bdr_is_ess(mesh->bdr_attributes.Max());
+   bdr_is_ess = 0;
+   bdr_is_ess[3] = -1;
+   R_space->GetEssentialTrueDofs(bdr_is_ess, ess_flux_tdofs_list);*/
 
-   if (pa)
+   FiniteElementCollection *trace_coll = NULL;
+   FiniteElementSpace *trace_space = NULL;
+
+   chrono.Clear();
+   chrono.Start();
+
+   if (hybridization)
+   {
+      trace_coll = new DG_Interface_FECollection(order, dim);
+      trace_space = new FiniteElementSpace(mesh, trace_coll);
+      darcy->EnableHybridization(trace_space,
+                                 new NormalTraceJumpIntegrator(),
+                                 ess_flux_tdofs_list);
+   }
+
+   if (pa) { darcy->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+
+   darcy->Assemble();
+   //if (!pa) { darcy->Finalize(); }
+
+   //BlockOperator darcyOp(block_offsets);
+
+   //TransposeOperator *Bt = NULL;
+
+   /*if (pa)
    {
       Bt = new TransposeOperator(bVarf);
 
@@ -202,104 +262,163 @@ int main(int argc, char *argv[])
       darcyOp.SetBlock(0,0, &M);
       darcyOp.SetBlock(0,1, Bt);
       darcyOp.SetBlock(1,0, &B);
-   }
+   }*/
 
-   // 10. Construct the operators for preconditioner
-   //
-   //                 P = [ diag(M)         0         ]
-   //                     [  0       B diag(M)^-1 B^T ]
-   //
-   //     Here we use Symmetric Gauss-Seidel to approximate the inverse of the
-   //     pressure Schur Complement
-   SparseMatrix *MinvBt = NULL;
-   Vector Md(mVarf->Height());
+   OperatorHandle pDarcyOp;
+   Vector X, B;
+   x = 0.;
+   //darcy->FormSystemMatrix(ess_flux_tdofs_list, pDarcyOp);
+   darcy->FormLinearSystem(ess_flux_tdofs_list, x, rhs,
+                           pDarcyOp, X, B);
 
-   BlockDiagonalPreconditioner darcyPrec(block_offsets);
-   Solver *invM, *invS;
-   SparseMatrix *S = NULL;
+   chrono.Stop();
+   std::cout << "Assembly took " << chrono.RealTime() << "s.\n";
 
-   if (pa)
-   {
-      mVarf->AssembleDiagonal(Md);
-      auto Md_host = Md.HostRead();
-      Vector invMd(mVarf->Height());
-      for (int i=0; i<mVarf->Height(); ++i)
-      {
-         invMd(i) = 1.0 / Md_host[i];
-      }
 
-      Vector BMBt_diag(bVarf->Height());
-      bVarf->AssembleDiagonal_ADAt(invMd, BMBt_diag);
-
-      Array<int> ess_tdof_list;  // empty
-
-      invM = new OperatorJacobiSmoother(Md, ess_tdof_list);
-      invS = new OperatorJacobiSmoother(BMBt_diag, ess_tdof_list);
-   }
-   else
-   {
-      SparseMatrix &M(mVarf->SpMat());
-      M.GetDiag(Md);
-      Md.HostReadWrite();
-
-      SparseMatrix &B(bVarf->SpMat());
-      MinvBt = Transpose(B);
-
-      for (int i = 0; i < Md.Size(); i++)
-      {
-         MinvBt->ScaleRow(i, 1./Md(i));
-      }
-
-      S = Mult(B, *MinvBt);
-
-      invM = new DSmoother(M);
-
-#ifndef MFEM_USE_SUITESPARSE
-      invS = new GSSmoother(*S);
-#else
-      invS = new UMFPackSolver(*S);
-#endif
-   }
-
-   invM->iterative_mode = false;
-   invS->iterative_mode = false;
-
-   darcyPrec.SetDiagonalBlock(0, invM);
-   darcyPrec.SetDiagonalBlock(1, invS);
-
-   // 11. Solve the linear system with MINRES.
-   //     Check the norm of the unpreconditioned residual.
    int maxIter(1000);
    real_t rtol(1.e-6);
    real_t atol(1.e-10);
 
-   chrono.Clear();
-   chrono.Start();
-   MINRESSolver solver;
-   solver.SetAbsTol(atol);
-   solver.SetRelTol(rtol);
-   solver.SetMaxIter(maxIter);
-   solver.SetOperator(darcyOp);
-   solver.SetPreconditioner(darcyPrec);
-   solver.SetPrintLevel(1);
-   x = 0.0;
-   solver.Mult(rhs, x);
-   if (device.IsEnabled()) { x.HostRead(); }
-   chrono.Stop();
-
-   if (solver.GetConverged())
+   if (hybridization)
    {
-      std::cout << "MINRES converged in " << solver.GetNumIterations()
-                << " iterations with a residual norm of "
-                << solver.GetFinalNorm() << ".\n";
+      // 10. Construct the preconditioner
+      GSSmoother prec(*pDarcyOp.As<SparseMatrix>());
+
+      // 11. Solve the linear system with GMRES.
+      //     Check the norm of the unpreconditioned residual.
+      chrono.Clear();
+      chrono.Start();
+      GMRESSolver solver;
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPreconditioner(prec);
+      solver.SetPrintLevel(1);
+
+      solver.Mult(B, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      chrono.Stop();
+
+      if (solver.GetConverged())
+      {
+         std::cout << "GMRES converged in " << solver.GetNumIterations()
+                   << " iterations with a residual norm of "
+                   << solver.GetFinalNorm() << ".\n";
+      }
+      else
+      {
+         std::cout << "GMRES did not converge in " << solver.GetNumIterations()
+                   << " iterations. Residual norm is " << solver.GetFinalNorm()
+                   << ".\n";
+      }
+      std::cout << "GMRES solver took " << chrono.RealTime() << "s.\n";
    }
    else
    {
-      std::cout << "MINRES did not converge in " << solver.GetNumIterations()
-                << " iterations. Residual norm is " << solver.GetFinalNorm()
-                << ".\n";
+      // 10. Construct the operators for preconditioner
+      //
+      //                 P = [ diag(M)         0         ]
+      //                     [  0       B diag(M)^-1 B^T ]
+      //
+      //     Here we use Symmetric Gauss-Seidel to approximate the inverse of the
+      //     pressure Schur Complement
+      SparseMatrix *MinvBt = NULL;
+      Vector Md(mVarf->Height());
+
+      BlockDiagonalPreconditioner darcyPrec(block_offsets);
+      Solver *invM, *invS;
+      SparseMatrix *S = NULL;
+
+      if (pa)
+      {
+         mVarf->AssembleDiagonal(Md);
+         auto Md_host = Md.HostRead();
+         Vector invMd(mVarf->Height());
+         for (int i=0; i<mVarf->Height(); ++i)
+         {
+            invMd(i) = 1.0 / Md_host[i];
+         }
+
+         Vector BMBt_diag(bVarf->Height());
+         bVarf->AssembleDiagonal_ADAt(invMd, BMBt_diag);
+
+         Array<int> ess_tdof_list;  // empty
+
+         invM = new OperatorJacobiSmoother(Md, ess_tdof_list);
+         invS = new OperatorJacobiSmoother(BMBt_diag, ess_tdof_list);
+      }
+      else
+      {
+         SparseMatrix &M(mVarf->SpMat());
+         M.GetDiag(Md);
+         Md.HostReadWrite();
+
+         SparseMatrix &B(bVarf->SpMat());
+         MinvBt = Transpose(B);
+
+         for (int i = 0; i < Md.Size(); i++)
+         {
+            MinvBt->ScaleRow(i, 1./Md(i));
+         }
+
+         S = Mult(B, *MinvBt);
+
+         invM = new DSmoother(M);
+
+#ifndef MFEM_USE_SUITESPARSE
+         invS = new GSSmoother(*S);
+#else
+         invS = new UMFPackSolver(*S);
+#endif
+      }
+
+      invM->iterative_mode = false;
+      invS->iterative_mode = false;
+
+      darcyPrec.SetDiagonalBlock(0, invM);
+      darcyPrec.SetDiagonalBlock(1, invS);
+
+      // 11. Solve the linear system with MINRES.
+      //     Check the norm of the unpreconditioned residual.
+
+      chrono.Clear();
+      chrono.Start();
+      MINRESSolver solver;
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPreconditioner(darcyPrec);
+      solver.SetPrintLevel(1);
+
+      solver.Mult(B, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      if (device.IsEnabled()) { x.HostRead(); }
+      chrono.Stop();
+
+      if (solver.GetConverged())
+      {
+         std::cout << "MINRES converged in " << solver.GetNumIterations()
+                   << " iterations with a residual norm of "
+                   << solver.GetFinalNorm() << ".\n";
+      }
+      else
+      {
+         std::cout << "MINRES did not converge in " << solver.GetNumIterations()
+                   << " iterations. Residual norm is " << solver.GetFinalNorm()
+                   << ".\n";
+      }
+      std::cout << "MINRES solver took " << chrono.RealTime() << "s.\n";
+
+      delete invM;
+      delete invS;
+      delete S;
+      //delete Bt;
+      delete MinvBt;
    }
-   std::cout << "MINRES solver took " << chrono.RealTime() << "s.\n";
 
    // 12. Create the grid functions u and p. Compute the L2 error norms.
    GridFunction u, p;
@@ -364,25 +483,25 @@ int main(int argc, char *argv[])
       socketstream u_sock(vishost, visport);
       u_sock.precision(8);
       u_sock << "solution\n" << *mesh << u << "window_title 'Velocity'" << endl;
+      u_sock << "keys Rljvvvvvmmc" << endl;
       socketstream p_sock(vishost, visport);
       p_sock.precision(8);
       p_sock << "solution\n" << *mesh << p << "window_title 'Pressure'" << endl;
+      p_sock << "keys Rljmmc" << endl;
    }
 
    // 17. Free the used memory.
    delete fform;
    delete gform;
-   delete invM;
-   delete invS;
-   delete S;
-   delete Bt;
-   delete MinvBt;
-   delete mVarf;
-   delete bVarf;
+   //delete mVarf;
+   //delete bVarf;
+   delete darcy;
    delete W_space;
    delete R_space;
-   delete l2_coll;
-   delete hdiv_coll;
+   delete trace_space;
+   delete W_coll;
+   delete R_coll;
+   delete trace_coll;
    delete mesh;
 
    return 0;

examples/ex5p-hdg.cpp

@@ -0,0 +1,655 @@
+//                                MFEM Example 5
+//
+// Compile with: make ex5
+//
+// Sample runs:  ex5 -m ../data/square-disc.mesh
+//               ex5 -m ../data/star.mesh
+//               ex5 -m ../data/star.mesh -pa
+//               ex5 -m ../data/beam-tet.mesh
+//               ex5 -m ../data/beam-hex.mesh
+//               ex5 -m ../data/beam-hex.mesh -pa
+//               ex5 -m ../data/escher.mesh
+//               ex5 -m ../data/fichera.mesh
+//
+// Device sample runs:
+//               ex5 -m ../data/star.mesh -pa -d cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-omp
+//               ex5 -m ../data/beam-hex.mesh -pa -d cuda
+//
+// Description:  This example code solves a simple 2D/3D mixed Darcy problem
+//               corresponding to the saddle point system
+//
+//                                 k*u + grad p = f
+//                                 - div u      = g
+//
+//               with natural boundary condition -p = <given pressure>.
+//               Here, we use a given exact solution (u,p) and compute the
+//               corresponding r.h.s. (f,g).  We discretize with Raviart-Thomas
+//               finite elements (velocity u) and piecewise discontinuous
+//               polynomials (pressure p). Alternatively, the piecewise discontinuous
+//               polynomials are used for both quantities.
+//
+//               The example demonstrates the use of the DarcyForm class, as
+//               well as hybridization of mixed systems and the collective saving
+//               of several grid functions in VisIt (visit.llnl.gov) and ParaView
+//               (paraview.org) formats.
+//
+//               We recommend viewing examples 1-4 before viewing this example.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+#include <algorithm>
+
+using namespace std;
+using namespace mfem;
+
+// Define the analytical solution and forcing terms / boundary conditions
+void uFun_ex(const Vector & x, Vector & u);
+real_t pFun_ex(const Vector & x);
+void fFun(const Vector & x, Vector & f);
+real_t gFun(const Vector & x);
+real_t f_natural(const Vector & x);
+
+int main(int argc, char *argv[])
+{
+   StopWatch chrono;
+
+   // 1. Initialize MPI and HYPRE.
+   Mpi::Init(argc, argv);
+   int num_procs = Mpi::WorldSize();
+   int myid = Mpi::WorldRank();
+   Hypre::Init();
+   bool verbose = (myid == 0);
+
+   // 2. Parse command-line options.
+   const char *mesh_file = "";
+   int nx = 0;
+   int ny = 0;
+   int ref_levels = -1;
+   int order = 1;
+   bool dg = false;
+   real_t td = 0.5;
+   bool hybridization = false;
+   bool reduction = false;
+   bool pa = false;
+   const char *device_config = "cpu";
+   bool visualization = 1;
+   bool par_format = false;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&ref_levels, "-r", "--refine",
+                  "Number of times to refine the mesh uniformly.");
+   args.AddOption(&nx, "-nx", "--ncells-x",
+                  "Number of cells in x.");
+   args.AddOption(&ny, "-ny", "--ncells-y",
+                  "Number of cells in y.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&dg, "-dg", "--discontinuous", "-no-dg",
+                  "--no-discontinuous", "Enable DG elements for fluxes.");
+   args.AddOption(&td, "-td", "--stab_diff",
+                  "Diffusion stabilization factor (1/2=default)");
+   args.AddOption(&hybridization, "-hb", "--hybridization", "-no-hb",
+                  "--no-hybridization", "Enable hybridization.");
+   args.AddOption(&reduction, "-rd", "--reduction", "-no-rd",
+                  "--no-reduction", "Enable reduction of DG flux.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.AddOption(&par_format, "-pf", "--parallel-format", "-sf",
+                  "--serial-format",
+                  "Format to use when saving the results for VisIt.");
+   args.Parse();
+   if (!args.Good())
+   {
+      if (verbose)
+      {
+         args.PrintUsage(cout);
+      }
+      return 1;
+   }
+   if (verbose)
+   {
+      args.PrintOptions(cout);
+   }
+
+   // 3. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   if (myid == 0) { device.Print(); }
+
+   // 4. Read the (serial) mesh from the given mesh file on all processors.  We
+   //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
+   //    and volume meshes with the same code.
+   if (ny <= 0)
+   {
+      ny = nx;
+   }
+
+   Mesh *mesh = NULL;
+   if (strlen(mesh_file) > 0)
+   {
+      mesh = new Mesh(mesh_file, 1, 1);
+   }
+   else
+   {
+      mesh = new Mesh(Mesh::MakeCartesian2D(nx, ny, Element::QUADRILATERAL));
+   }
+
+   int dim = mesh->Dimension();
+
+   // 5. Refine the serial mesh on all processors to increase the resolution. In
+   //    this example we do 'ref_levels' of uniform refinement. We choose
+   //    'ref_levels' to be the largest number that gives a final mesh with no
+   //    more than 10,000 elements, unless the user specifies it as input.
+   if (strlen(mesh_file) > 0)
+   {
+      if (ref_levels == -1)
+      {
+         ref_levels = (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
+      }
+
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
+   //    this mesh further in parallel to increase the resolution. Once the
+   //    parallel mesh is defined, the serial mesh can be deleted.
+   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
+   delete mesh;
+   /*{
+      int par_ref_levels = 2;
+      for (int l = 0; l < par_ref_levels; l++)
+      {
+         pmesh->UniformRefinement();
+      }
+   }*/
+
+   // 7. Define a finite element space on the mesh. Here we use the
+   //    Raviart-Thomas finite elements of the specified order.
+   FiniteElementCollection *R_coll;
+   if (dg)
+   {
+      // In the case of LDG formulation, we chose a closed basis as it
+      // is customary for HDG to match trace DOFs, but an open basis can
+      // be used instead.
+      R_coll = new L2_FECollection(order, dim, BasisType::GaussLobatto);
+   }
+   else
+   {
+      R_coll = new RT_FECollection(order, dim);
+   }
+   FiniteElementCollection *W_coll = new L2_FECollection(order, dim);
+
+   ParFiniteElementSpace *R_space = new ParFiniteElementSpace(pmesh, R_coll,
+                                                              (dg)?(dim):(1));
+   ParFiniteElementSpace *W_space = new ParFiniteElementSpace(pmesh, W_coll);
+
+   ParDarcyForm *darcy = new ParDarcyForm(R_space, W_space);
+
+   HYPRE_BigInt dimR = R_space->GlobalTrueVSize();
+   HYPRE_BigInt dimW = W_space->GlobalTrueVSize();
+
+   if (verbose)
+   {
+      std::cout << "***********************************************************\n";
+      std::cout << "dim(R) = " << dimR << "\n";
+      std::cout << "dim(W) = " << dimW << "\n";
+      std::cout << "dim(R+W) = " << dimR + dimR << "\n";
+      std::cout << "***********************************************************\n";
+   }
+
+   // 8. Define the two BlockStructure of the problem.  block_offsets is used
+   //    for Vector based on dof (like ParGridFunction or ParLinearForm),
+   //    block_trueOffstes is used for Vector based on trueDof (HypreParVector
+   //    for the rhs and solution of the linear system).  The offsets computed
+   //    here are local to the processor.
+
+   const Array<int> &block_offsets = darcy->GetOffsets();
+   const Array<int> &block_trueOffsets = darcy->GetTrueOffsets();
+
+   // 9. Define the coefficients, analytical solution, and rhs of the PDE.
+   const double k = 1.0;
+   ConstantCoefficient kcoeff(k); //acoustic resistance
+   RatioCoefficient ikcoeff(1., kcoeff); //inverse acoustic resistance
+
+   VectorFunctionCoefficient fcoeff(dim, fFun); //velocity rhs
+   FunctionCoefficient fnatcoeff(f_natural); //boundary velocity rhs
+   FunctionCoefficient gcoeff(gFun); //pressure rhs
+
+   VectorFunctionCoefficient ucoeff(dim, uFun_ex); //velocity
+   FunctionCoefficient pcoeff(pFun_ex); //pressure
+
+   // 10. Define the parallel grid function and parallel linear forms, solution
+   //     vector and rhs.
+   MemoryType mt = device.GetMemoryType();
+   BlockVector x(block_offsets, mt), rhs(block_offsets, mt);
+
+   ParLinearForm *fform(new ParLinearForm);
+   fform->Update(R_space, rhs.GetBlock(0), 0);
+   if (dg)
+   {
+      fform->AddDomainIntegrator(new VectorDomainLFIntegrator(fcoeff));
+      fform->AddBdrFaceIntegrator(new VectorBoundaryFluxLFIntegrator(fnatcoeff));
+   }
+   else
+   {
+      fform->AddDomainIntegrator(new VectorFEDomainLFIntegrator(fcoeff));
+      fform->AddBoundaryIntegrator(new VectorFEBoundaryFluxLFIntegrator(fnatcoeff));
+   }
+   fform->Assemble();
+   fform->SyncAliasMemory(rhs);
+
+   ParLinearForm *gform(new ParLinearForm);
+   gform->Update(W_space, rhs.GetBlock(1), 0);
+   gform->AddDomainIntegrator(new DomainLFIntegrator(gcoeff));
+   gform->Assemble();
+   gform->SyncAliasMemory(rhs);
+
+   // 11. Assemble the finite element matrices for the Darcy operator
+   //
+   //                            D = [ M  B^T ]
+   //                                [ B   0  ]
+   //     where:
+   //
+   //     M = \int_\Omega k u_h \cdot v_h d\Omega   u_h, v_h \in R_h
+   //     B   = -\int_\Omega \div u_h q_h d\Omega   u_h \in R_h, q_h \in W_h
+   ParBilinearForm *mVarf = darcy->GetParFluxMassForm();
+   ParMixedBilinearForm *bVarf = darcy->GetParFluxDivForm();
+   ParBilinearForm *mtVarf = (dg)?(darcy->GetParPotentialMassForm()):(NULL);
+
+   if (dg)
+   {
+      mVarf->AddDomainIntegrator(new VectorMassIntegrator(kcoeff));
+      bVarf->AddDomainIntegrator(new VectorDivergenceIntegrator());
+      bVarf->AddInteriorFaceIntegrator(new TransposeIntegrator(
+                                          new DGNormalTraceIntegrator(-1.)));
+      mtVarf->AddInteriorFaceIntegrator(new HDGDiffusionIntegrator(ikcoeff, td));
+   }
+   else
+   {
+      mVarf->AddDomainIntegrator(new VectorFEMassIntegrator(kcoeff));
+      bVarf->AddDomainIntegrator(new VectorFEDivergenceIntegrator);
+   }
+
+   //set hybridization / assembly level
+
+   Array<int> ess_flux_tdofs_list;
+
+   FiniteElementCollection *trace_coll = NULL;
+   ParFiniteElementSpace *trace_space = NULL;
+
+   chrono.Clear();
+   chrono.Start();
+
+   if (hybridization)
+   {
+      trace_coll = new DG_Interface_FECollection(order, dim);
+      trace_space = new ParFiniteElementSpace(pmesh, trace_coll);
+      darcy->EnableHybridization(trace_space,
+                                 new NormalTraceJumpIntegrator(),
+                                 ess_flux_tdofs_list);
+   }
+   else if (reduction && dg)
+   {
+      darcy->EnableFluxReduction();
+   }
+
+   if (pa) { darcy->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+
+   darcy->Assemble();
+
+   OperatorHandle pDarcyOp;
+   Vector X, B;
+   x = 0.;
+   darcy->FormLinearSystem(ess_flux_tdofs_list, x, rhs,
+                           pDarcyOp, X, B);
+
+   chrono.Stop();
+   if (verbose)
+   {
+      std::cout << "Assembly took " << chrono.RealTime() << "s.\n";
+   }
+
+
+   int maxIter(1000);
+   real_t rtol(1.e-6);
+   real_t atol(1.e-10);
+
+   if (hybridization || (reduction && dg))
+   {
+      // 12. Construct the preconditioner
+      HypreBoomerAMG prec;
+
+      // 13. Solve the linear system with GMRES.
+      //     Check the norm of the unpreconditioned residual.
+      chrono.Clear();
+      chrono.Start();
+      GMRESSolver solver(MPI_COMM_WORLD);
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetPreconditioner(prec);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPrintLevel(verbose);
+
+      solver.Mult(B, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      chrono.Stop();
+
+      if (verbose)
+      {
+         if (solver.GetConverged())
+         {
+            std::cout << "GMRES converged in " << solver.GetNumIterations()
+                      << " iterations with a residual norm of "
+                      << solver.GetFinalNorm() << ".\n";
+         }
+         else
+         {
+            std::cout << "GMRES did not converge in " << solver.GetNumIterations()
+                      << " iterations. Residual norm is " << solver.GetFinalNorm()
+                      << ".\n";
+         }
+         std::cout << "GMRES solver took " << chrono.RealTime() << "s.\n";
+      }
+   }
+   else
+   {
+      // 12. Construct the operators for preconditioner
+      //
+      //                 P = [ diag(M)         0         ]
+      //                     [  0       B diag(M)^-1 B^T ]
+      //
+      //     Here we use Symmetric Gauss-Seidel to approximate the inverse of the
+      //     pressure Schur Complement
+      HypreParMatrix *MinvBt = NULL;
+      HypreParVector *Md = NULL;
+      HypreParMatrix *S = NULL;
+      Solver *invM, *invS;
+
+      if (pa)
+      {
+         Vector Md(R_space->GetTrueVSize());
+         mVarf->AssembleDiagonal(Md);
+         auto Md_host = Md.HostRead();
+         Vector invMd(Md.Size());
+         for (int i=0; i<Md.Size(); ++i)
+         {
+            invMd(i) = 1.0 / Md_host[i];
+         }
+
+         Vector BMBt_diag(W_space->GetTrueVSize());
+         bVarf->AssembleDiagonal_ADAt(invMd, BMBt_diag);
+
+         Array<int> ess_tdof_list;  // empty
+
+         invM = new OperatorJacobiSmoother(Md, ess_tdof_list);
+         invS = new OperatorJacobiSmoother(BMBt_diag, ess_tdof_list);
+      }
+      else
+      {
+         HypreParMatrix &M = *mVarf->ParallelAssembleInternal();
+         Md = new HypreParVector(MPI_COMM_WORLD, M.GetGlobalNumRows(),
+                                 M.GetRowStarts());
+         M.GetDiag(*Md);
+
+         HypreParMatrix &B = *bVarf->ParallelAssembleInternal();
+         MinvBt = B.Transpose();
+         MinvBt->InvScaleRows(*Md);
+         S = ParMult(&B, MinvBt);
+
+         if (mtVarf)
+         {
+            HypreParMatrix &Mt = *mtVarf->ParallelAssembleInternal();
+            HypreParMatrix *Snew = ParAdd(&Mt, S);
+            delete S;
+            S = Snew;
+         }
+
+         invM = new HypreDiagScale(M);
+         invS = new HypreBoomerAMG(*S);
+      }
+
+      invM->iterative_mode = false;
+      invS->iterative_mode = false;
+
+      BlockDiagonalPreconditioner darcyPrec(block_trueOffsets);
+      darcyPrec.SetDiagonalBlock(0, invM);
+      darcyPrec.SetDiagonalBlock(1, invS);
+
+      // 13. Solve the linear system with MINRES.
+      //     Check the norm of the unpreconditioned residual.
+
+      chrono.Clear();
+      chrono.Start();
+      MINRESSolver solver(MPI_COMM_WORLD);
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPreconditioner(darcyPrec);
+      solver.SetPrintLevel(verbose);
+
+      solver.Mult(B, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      if (device.IsEnabled()) { x.HostRead(); }
+      chrono.Stop();
+
+      if (verbose)
+      {
+         if (solver.GetConverged())
+         {
+            std::cout << "MINRES converged in " << solver.GetNumIterations()
+                      << " iterations with a residual norm of "
+                      << solver.GetFinalNorm() << ".\n";
+         }
+         else
+         {
+            std::cout << "MINRES did not converge in " << solver.GetNumIterations()
+                      << " iterations. Residual norm is " << solver.GetFinalNorm()
+                      << ".\n";
+         }
+         std::cout << "MINRES solver took " << chrono.RealTime() << "s.\n";
+      }
+
+      delete invM;
+      delete invS;
+      delete S;
+      delete Md;
+      delete MinvBt;
+   }
+
+   // 14. Extract the parallel grid function corresponding to the finite element
+   //     approximation X. This is the local solution on each processor. Compute
+   //     L2 error norms.
+   ParGridFunction u, p;
+   u.MakeRef(R_space, x.GetBlock(0), 0);
+   p.MakeRef(W_space, x.GetBlock(1), 0);
+
+   int order_quad = max(2, 2*order+1);
+   const IntegrationRule *irs[Geometry::NumGeom];
+   for (int i=0; i < Geometry::NumGeom; ++i)
+   {
+      irs[i] = &(IntRules.Get(i, order_quad));
+   }
+
+   real_t err_u  = u.ComputeL2Error(ucoeff, irs);
+   real_t norm_u = ComputeGlobalLpNorm(2., ucoeff, *pmesh, irs);
+   real_t err_p  = p.ComputeL2Error(pcoeff, irs);
+   real_t norm_p = ComputeGlobalLpNorm(2., pcoeff, *pmesh, irs);
+
+   if (verbose)
+   {
+      std::cout << "|| u_h - u_ex || / || u_ex || = " << err_u / norm_u << "\n";
+      std::cout << "|| p_h - p_ex || / || p_ex || = " << err_p / norm_p << "\n";
+   }
+
+   // 15. Save the refined mesh and the solution in parallel. This output can be
+   //     viewed later using GLVis: "glvis -np <np> -m mesh -g sol_*".
+   {
+      ostringstream mesh_name, u_name, p_name;
+      mesh_name << "mesh." << setfill('0') << setw(6) << myid;
+      u_name << "sol_u." << setfill('0') << setw(6) << myid;
+      p_name << "sol_p." << setfill('0') << setw(6) << myid;
+
+      ofstream mesh_ofs(mesh_name.str().c_str());
+      mesh_ofs.precision(8);
+      pmesh->Print(mesh_ofs);
+
+      ofstream u_ofs(u_name.str().c_str());
+      u_ofs.precision(8);
+      u.Save(u_ofs);
+
+      ofstream p_ofs(p_name.str().c_str());
+      p_ofs.precision(8);
+      p.Save(p_ofs);
+   }
+
+   // 16. Save data in the VisIt format
+   VisItDataCollection visit_dc("Example5-Parallel", pmesh);
+   visit_dc.RegisterField("velocity", &u);
+   visit_dc.RegisterField("pressure", &p);
+   visit_dc.SetFormat(!par_format ?
+                      DataCollection::SERIAL_FORMAT :
+                      DataCollection::PARALLEL_FORMAT);
+   visit_dc.Save();
+
+   // 17. Save data in the ParaView format
+   ParaViewDataCollection paraview_dc("Example5P", pmesh);
+   paraview_dc.SetPrefixPath("ParaView");
+   paraview_dc.SetLevelsOfDetail(order);
+   paraview_dc.SetDataFormat(VTKFormat::BINARY);
+   paraview_dc.SetHighOrderOutput(true);
+   paraview_dc.SetCycle(0);
+   paraview_dc.SetTime(0.0); // set the time
+   paraview_dc.RegisterField("velocity",&u);
+   paraview_dc.RegisterField("pressure",&p);
+   paraview_dc.Save();
+
+   // 18. Optionally output a BP (binary pack) file using ADIOS2. This can be
+   //     visualized with the ParaView VTX reader.
+#ifdef MFEM_USE_ADIOS2
+   if (adios2)
+   {
+      std::string postfix(mesh_file);
+      postfix.erase(0, std::string("../data/").size() );
+      postfix += "_o" + std::to_string(order);
+      const std::string collection_name = "ex5-p_" + postfix + ".bp";
+
+      ADIOS2DataCollection adios2_dc(MPI_COMM_WORLD, collection_name, pmesh);
+      adios2_dc.SetLevelsOfDetail(1);
+      adios2_dc.SetCycle(1);
+      adios2_dc.SetTime(0.0);
+      adios2_dc.RegisterField("velocity",&u);
+      adios2_dc.RegisterField("pressure",&p);
+      adios2_dc.Save();
+   }
+#endif
+
+   // 19. Send the solution by socket to a GLVis server.
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream u_sock(vishost, visport);
+      u_sock << "parallel " << num_procs << " " << myid << "\n";
+      u_sock.precision(8);
+      u_sock << "solution\n" << *pmesh << u << "window_title 'Velocity'"
+             << endl;
+      u_sock << "keys Rljvvvvvmmc" << endl;
+      // Make sure all ranks have sent their 'u' solution before initiating
+      // another set of GLVis connections (one from each rank):
+      MPI_Barrier(pmesh->GetComm());
+      socketstream p_sock(vishost, visport);
+      p_sock << "parallel " << num_procs << " " << myid << "\n";
+      p_sock.precision(8);
+      p_sock << "solution\n" << *pmesh << p << "window_title 'Pressure'"
+             << endl;
+      p_sock << "keys Rljmmc" << endl;
+   }
+
+   // 20. Free the used memory.
+   delete fform;
+   delete gform;
+   delete darcy;
+   delete W_space;
+   delete R_space;
+   delete trace_space;
+   delete W_coll;
+   delete R_coll;
+   delete trace_coll;
+   delete pmesh;
+
+   return 0;
+}
+
+
+void uFun_ex(const Vector & x, Vector & u)
+{
+   real_t xi(x(0));
+   real_t yi(x(1));
+   real_t zi(0.0);
+   if (x.Size() == 3)
+   {
+      zi = x(2);
+   }
+
+   u(0) = - exp(xi)*sin(yi)*cos(zi);
+   u(1) = - exp(xi)*cos(yi)*cos(zi);
+
+   if (x.Size() == 3)
+   {
+      u(2) = exp(xi)*sin(yi)*sin(zi);
+   }
+}
+
+// Change if needed
+real_t pFun_ex(const Vector & x)
+{
+   real_t xi(x(0));
+   real_t yi(x(1));
+   real_t zi(0.0);
+
+   if (x.Size() == 3)
+   {
+      zi = x(2);
+   }
+
+   return exp(xi)*sin(yi)*cos(zi);
+}
+
+void fFun(const Vector & x, Vector & f)
+{
+   f = 0.0;
+}
+
+real_t gFun(const Vector & x)
+{
+   if (x.Size() == 3)
+   {
+      return -pFun_ex(x);
+   }
+   else
+   {
+      return 0;
+   }
+}
+
+real_t f_natural(const Vector & x)
+{
+   return (-pFun_ex(x));
+}

examples/makefile

@@ -20,10 +20,10 @@ CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
 
-SEQ_EXAMPLES = ex0 ex1 ex2 ex3 ex4 ex5 ex6 ex7 ex8 ex9 ex10 ex14 ex15 ex16 \
+SEQ_EXAMPLES = ex0 ex1 ex2 ex3 ex4 ex5 ex5-max ex5-hdg ex5-heat ex6 ex7 ex8 ex9 ex10 ex14 ex15 ex16 \
    ex17 ex18 ex19 ex20 ex21 ex22 ex23 ex24 ex25 ex26 ex27 ex28 ex29 ex30 \
    ex31 ex33 ex34 ex36 ex37 ex38 ex39 ex40
-PAR_EXAMPLES = ex0p ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex8p ex9p ex10p ex11p \
+PAR_EXAMPLES = ex0p ex1p ex2p ex3p ex4p ex5p ex5p-hdg ex6p ex7p ex8p ex9p ex10p ex11p \
    ex12p ex13p ex14p ex15p ex16p ex17p ex18p ex19p ex20p ex21p ex22p ex24p \
    ex25p ex26p ex27p ex28p ex29p ex30p ex31p ex32p ex33p ex34p ex35p ex36p \
    ex37p ex39p ex40p
@@ -80,10 +80,14 @@ SUBDIRS_TPRINT = $(addsuffix /test-print,$(SUBDIRS))
 
 # Remove built-in rule
 %: %.cpp
+%.o: %.cpp
 
 # Replace the default implicit rule for *.cpp files
-%: $(SRC)%.cpp $(MFEM_LIB_FILE) $(CONFIG_MK)
-	$(MFEM_CXX) $(MFEM_FLAGS) $< -o $@ $(MFEM_LIBS)
+%.o: $(SRC)%.cpp $(MFEM_LIB_FILE) $(CONFIG_MK)
+	$(MFEM_CXX) $(MFEM_FLAGS) $< -c -o $@ $(MFEM_LIBS)
+
+%: $(SRC)%.o $(MFEM_LIB_FILE) $(CONFIG_MK)
+	$(MFEM_CXX) $(MFEM_FLAGS) $(filter %.o, $^) -o $@ $(MFEM_LIBS)
 
 all: $(EXAMPLES) $(SUBDIRS_ALL)
 
@@ -94,6 +98,11 @@ $(SUBDIRS_TPRINT):
 	@$(MAKE) -C $(@D) $(@F)
 
 # Additional dependencies
+ex5-nguyen: darcyop.o
+ex5p-nguyen: darcyop.o
+ex5-plasma: darcyop.o
+ex5-aniso: darcyop.o
+ex5-scatter: coupledop.o
 ex18: $(SRC)ex18.hpp
 ex33: $(SRC)ex33.hpp
 ex37: $(SRC)ex37.hpp

examples/regress_test/p1_o2_dg_hb_nl.txt

@@ -0,0 +1,117 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 0
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --hybridization
+   --nonlinear
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00966076s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.0169918s.
+Preconditioner took 4.6463e-05s.
+LBFGS iteration 0 : ||r|| = 1.46578
+LBFGS iteration 1 : ||r|| = 2.01258, ||r||/||r_0|| = 1.37304
+LBFGS iteration 2 : ||r|| = 2.41053, ||r||/||r_0|| = 1.64454
+LBFGS iteration 3 : ||r|| = 4.48418, ||r||/||r_0|| = 3.05924
+LBFGS iteration 4 : ||r|| = 2.44484, ||r||/||r_0|| = 1.66794
+LBFGS iteration 5 : ||r|| = 0.996497, ||r||/||r_0|| = 0.679841
+LBFGS iteration 6 : ||r|| = 0.913284, ||r||/||r_0|| = 0.62307
+LBFGS iteration 7 : ||r|| = 1.03122, ||r||/||r_0|| = 0.703531
+LBFGS iteration 8 : ||r|| = 2.21746, ||r||/||r_0|| = 1.51282
+LBFGS iteration 9 : ||r|| = 0.769563, ||r||/||r_0|| = 0.525019
+LBFGS iteration 10 : ||r|| = 0.607547, ||r||/||r_0|| = 0.414487
+LBFGS iteration 11 : ||r|| = 0.759198, ||r||/||r_0|| = 0.517948
+LBFGS iteration 12 : ||r|| = 1.45778, ||r||/||r_0|| = 0.994541
+LBFGS iteration 13 : ||r|| = 0.563251, ||r||/||r_0|| = 0.384267
+LBFGS iteration 14 : ||r|| = 0.428853, ||r||/||r_0|| = 0.292576
+LBFGS iteration 15 : ||r|| = 0.441501, ||r||/||r_0|| = 0.301206
+LBFGS iteration 16 : ||r|| = 1.38991, ||r||/||r_0|| = 0.948236
+LBFGS iteration 17 : ||r|| = 0.272828, ||r||/||r_0|| = 0.186132
+LBFGS iteration 18 : ||r|| = 0.165047, ||r||/||r_0|| = 0.1126
+LBFGS iteration 19 : ||r|| = 0.151715, ||r||/||r_0|| = 0.103504
+LBFGS iteration 20 : ||r|| = 0.331738, ||r||/||r_0|| = 0.226322
+LBFGS iteration 21 : ||r|| = 0.106159, ||r||/||r_0|| = 0.0724251
+LBFGS iteration 22 : ||r|| = 0.0594514, ||r||/||r_0|| = 0.0405595
+LBFGS iteration 23 : ||r|| = 0.0596277, ||r||/||r_0|| = 0.0406798
+LBFGS iteration 24 : ||r|| = 0.171595, ||r||/||r_0|| = 0.117067
+LBFGS iteration 25 : ||r|| = 0.0533591, ||r||/||r_0|| = 0.0364032
+LBFGS iteration 26 : ||r|| = 0.0273665, ||r||/||r_0|| = 0.0186703
+LBFGS iteration 27 : ||r|| = 0.0191679, ||r||/||r_0|| = 0.013077
+LBFGS iteration 28 : ||r|| = 0.0555099, ||r||/||r_0|| = 0.0378705
+LBFGS iteration 29 : ||r|| = 0.0141599, ||r||/||r_0|| = 0.00966033
+LBFGS iteration 30 : ||r|| = 0.0077165, ||r||/||r_0|| = 0.00526443
+LBFGS iteration 31 : ||r|| = 0.00710641, ||r||/||r_0|| = 0.00484821
+LBFGS iteration 32 : ||r|| = 0.00727829, ||r||/||r_0|| = 0.00496547
+LBFGS iteration 33 : ||r|| = 0.0154916, ||r||/||r_0|| = 0.0105689
+LBFGS iteration 34 : ||r|| = 0.00322952, ||r||/||r_0|| = 0.00220328
+LBFGS iteration 35 : ||r|| = 0.00266012, ||r||/||r_0|| = 0.00181482
+LBFGS iteration 36 : ||r|| = 0.0029587, ||r||/||r_0|| = 0.00201852
+LBFGS iteration 37 : ||r|| = 0.00287213, ||r||/||r_0|| = 0.00195945
+LBFGS iteration 38 : ||r|| = 0.00598566, ||r||/||r_0|| = 0.0040836
+LBFGS iteration 39 : ||r|| = 0.000777973, ||r||/||r_0|| = 0.000530757
+LBFGS iteration 40 : ||r|| = 0.000622731, ||r||/||r_0|| = 0.000424846
+LBFGS iteration 41 : ||r|| = 0.00101354, ||r||/||r_0|| = 0.00069147
+LBFGS iteration 42 : ||r|| = 0.000778935, ||r||/||r_0|| = 0.000531413
+LBFGS iteration 43 : ||r|| = 0.000322145, ||r||/||r_0|| = 0.000219777
+LBFGS iteration 44 : ||r|| = 0.000233689, ||r||/||r_0|| = 0.000159429
+LBFGS iteration 45 : ||r|| = 0.000266598, ||r||/||r_0|| = 0.000181881
+LBFGS iteration 46 : ||r|| = 0.000378973, ||r||/||r_0|| = 0.000258547
+LBFGS iteration 47 : ||r|| = 0.000330508, ||r||/||r_0|| = 0.000225483
+LBFGS iteration 48 : ||r|| = 0.000147423, ||r||/||r_0|| = 0.000100576
+LBFGS iteration 49 : ||r|| = 0.000150309, ||r||/||r_0|| = 0.000102545
+LBFGS iteration 50 : ||r|| = 0.000206405, ||r||/||r_0|| = 0.000140816
+LBFGS iteration 51 : ||r|| = 0.000214436, ||r||/||r_0|| = 0.000146295
+LBFGS iteration 52 : ||r|| = 0.000140579, ||r||/||r_0|| = 9.59076e-05
+LBFGS iteration 53 : ||r|| = 0.000143331, ||r||/||r_0|| = 9.77847e-05
+LBFGS iteration 54 : ||r|| = 0.000184619, ||r||/||r_0|| = 0.000125952
+LBFGS iteration 55 : ||r|| = 8.66031e-05, ||r||/||r_0|| = 5.90832e-05
+LBFGS iteration 56 : ||r|| = 7.3517e-05, ||r||/||r_0|| = 5.01555e-05
+LBFGS iteration 57 : ||r|| = 8.2379e-05, ||r||/||r_0|| = 5.62014e-05
+LBFGS iteration 58 : ||r|| = 0.000205661, ||r||/||r_0|| = 0.000140308
+LBFGS iteration 59 : ||r|| = 6.82689e-05, ||r||/||r_0|| = 4.65751e-05
+LBFGS iteration 60 : ||r|| = 4.65785e-05, ||r||/||r_0|| = 3.17773e-05
+LBFGS iteration 61 : ||r|| = 5.19221e-05, ||r||/||r_0|| = 3.54229e-05
+LBFGS iteration 62 : ||r|| = 0.000121276, ||r||/||r_0|| = 8.27379e-05
+LBFGS iteration 63 : ||r|| = 5.40902e-05, ||r||/||r_0|| = 3.69019e-05
+LBFGS iteration 64 : ||r|| = 3.67227e-05, ||r||/||r_0|| = 2.50533e-05
+LBFGS iteration 65 : ||r|| = 4.11639e-05, ||r||/||r_0|| = 2.80833e-05
+LBFGS iteration 66 : ||r|| = 3.78694e-05, ||r||/||r_0|| = 2.58357e-05
+LBFGS iteration 67 : ||r|| = 0.000192235, ||r||/||r_0|| = 0.000131148
+LBFGS iteration 68 : ||r|| = 1.88491e-05, ||r||/||r_0|| = 1.28594e-05
+LBFGS iteration 69 : ||r|| = 1.37588e-05, ||r||/||r_0|| = 9.38668e-06
+LBFGS iteration 70 : ||r|| = 8.26133e-06, ||r||/||r_0|| = 5.63613e-06
+LBFGS iteration 71 : ||r|| = 1.65205e-05, ||r||/||r_0|| = 1.12708e-05
+LBFGS iteration 72 : ||r|| = 3.0717e-06, ||r||/||r_0|| = 2.09561e-06
+LBFGS iteration 73 : ||r|| = 1.85004e-06, ||r||/||r_0|| = 1.26215e-06
+LBFGS iteration 74 : ||r|| = 1.77343e-06, ||r||/||r_0|| = 1.20989e-06
+LBFGS iteration 75 : ||r|| = 2.89294e-06, ||r||/||r_0|| = 1.97365e-06
+LBFGS iteration 76 : ||r|| = 1.11005e-06, ||r||/||r_0|| = 7.57313e-07
+LBFGS/Newton+GMRES converged in 76 iterations with a residual norm of 1.11005e-06.
+solver took 3.89622s.
+|| q_h - q_ex || / || q_ex || = 0.000247123
+|| t_h - t_ex || / || t_ex || = 0.000241696

examples/regress_test/p1_o2_dg_hb_nl_newton.txt

@@ -0,0 +1,49 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --no-broken-RT
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.014452s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.00999689s.
+Preconditioner took 2.2244e-05s.
+Newton iteration  0 : ||r|| = 1.46578
+Newton iteration  1 : ||r|| = 6.21893e-08, ||r||/||r_0|| = 4.24274e-08
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 6.21893e-08.
+solver took 0.306186s.
+|| q_h - q_ex || / || q_ex || = 0.000247131
+|| t_h - t_ex || / || t_ex || = 0.000241709

examples/regress_test/p1_o2_dg_hb_nl_nld.txt

@@ -0,0 +1,124 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --no-broken-RT
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.030215s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.00968131s.
+Preconditioner took 6.1074e-05s.
+LBFGS iteration 0 : ||r|| = 1.46578
+LBFGS iteration 1 : ||r|| = 2.01258, ||r||/||r_0|| = 1.37304
+LBFGS iteration 2 : ||r|| = 2.41053, ||r||/||r_0|| = 1.64454
+LBFGS iteration 3 : ||r|| = 4.48418, ||r||/||r_0|| = 3.05924
+LBFGS iteration 4 : ||r|| = 2.44484, ||r||/||r_0|| = 1.66794
+LBFGS iteration 5 : ||r|| = 0.996497, ||r||/||r_0|| = 0.679841
+LBFGS iteration 6 : ||r|| = 0.913284, ||r||/||r_0|| = 0.62307
+LBFGS iteration 7 : ||r|| = 1.03122, ||r||/||r_0|| = 0.703531
+LBFGS iteration 8 : ||r|| = 2.21745, ||r||/||r_0|| = 1.51281
+LBFGS iteration 9 : ||r|| = 0.769554, ||r||/||r_0|| = 0.525013
+LBFGS iteration 10 : ||r|| = 0.607543, ||r||/||r_0|| = 0.414484
+LBFGS iteration 11 : ||r|| = 0.759138, ||r||/||r_0|| = 0.517907
+LBFGS iteration 12 : ||r|| = 1.4581, ||r||/||r_0|| = 0.994757
+LBFGS iteration 13 : ||r|| = 0.563222, ||r||/||r_0|| = 0.384247
+LBFGS iteration 14 : ||r|| = 0.428817, ||r||/||r_0|| = 0.292552
+LBFGS iteration 15 : ||r|| = 0.44147, ||r||/||r_0|| = 0.301185
+LBFGS iteration 16 : ||r|| = 1.39, ||r||/||r_0|| = 0.9483
+LBFGS iteration 17 : ||r|| = 0.272891, ||r||/||r_0|| = 0.186175
+LBFGS iteration 18 : ||r|| = 0.165054, ||r||/||r_0|| = 0.112605
+LBFGS iteration 19 : ||r|| = 0.151718, ||r||/||r_0|| = 0.103506
+LBFGS iteration 20 : ||r|| = 0.331585, ||r||/||r_0|| = 0.226217
+LBFGS iteration 21 : ||r|| = 0.106143, ||r||/||r_0|| = 0.0724142
+LBFGS iteration 22 : ||r|| = 0.0594506, ||r||/||r_0|| = 0.040559
+LBFGS iteration 23 : ||r|| = 0.0596312, ||r||/||r_0|| = 0.0406822
+LBFGS iteration 24 : ||r|| = 0.171728, ||r||/||r_0|| = 0.117158
+LBFGS iteration 25 : ||r|| = 0.0533533, ||r||/||r_0|| = 0.0363992
+LBFGS iteration 26 : ||r|| = 0.0273829, ||r||/||r_0|| = 0.0186814
+LBFGS iteration 27 : ||r|| = 0.0191745, ||r||/||r_0|| = 0.0130814
+LBFGS iteration 28 : ||r|| = 0.0553769, ||r||/||r_0|| = 0.0377798
+LBFGS iteration 29 : ||r|| = 0.0141317, ||r||/||r_0|| = 0.00964105
+LBFGS iteration 30 : ||r|| = 0.00770544, ||r||/||r_0|| = 0.00525689
+LBFGS iteration 31 : ||r|| = 0.00709767, ||r||/||r_0|| = 0.00484225
+LBFGS iteration 32 : ||r|| = 0.00732886, ||r||/||r_0|| = 0.00499997
+LBFGS iteration 33 : ||r|| = 0.0153653, ||r||/||r_0|| = 0.0104827
+LBFGS iteration 34 : ||r|| = 0.00322618, ||r||/||r_0|| = 0.002201
+LBFGS iteration 35 : ||r|| = 0.00265732, ||r||/||r_0|| = 0.0018129
+LBFGS iteration 36 : ||r|| = 0.00296415, ||r||/||r_0|| = 0.00202224
+LBFGS iteration 37 : ||r|| = 0.00285425, ||r||/||r_0|| = 0.00194726
+LBFGS iteration 38 : ||r|| = 0.00619247, ||r||/||r_0|| = 0.00422469
+LBFGS iteration 39 : ||r|| = 0.000777538, ||r||/||r_0|| = 0.00053046
+LBFGS iteration 40 : ||r|| = 0.000623058, ||r||/||r_0|| = 0.000425069
+LBFGS iteration 41 : ||r|| = 0.00101854, ||r||/||r_0|| = 0.000694876
+LBFGS iteration 42 : ||r|| = 0.000787498, ||r||/||r_0|| = 0.000537255
+LBFGS iteration 43 : ||r|| = 0.000321394, ||r||/||r_0|| = 0.000219265
+LBFGS iteration 44 : ||r|| = 0.000233725, ||r||/||r_0|| = 0.000159455
+LBFGS iteration 45 : ||r|| = 0.000266519, ||r||/||r_0|| = 0.000181828
+LBFGS iteration 46 : ||r|| = 0.000373324, ||r||/||r_0|| = 0.000254693
+LBFGS iteration 47 : ||r|| = 0.000342686, ||r||/||r_0|| = 0.000233791
+LBFGS iteration 48 : ||r|| = 0.00014717, ||r||/||r_0|| = 0.000100404
+LBFGS iteration 49 : ||r|| = 0.000149241, ||r||/||r_0|| = 0.000101817
+LBFGS iteration 50 : ||r|| = 0.000200512, ||r||/||r_0|| = 0.000136795
+LBFGS iteration 51 : ||r|| = 0.000247279, ||r||/||r_0|| = 0.000168701
+LBFGS iteration 52 : ||r|| = 0.000138893, ||r||/||r_0|| = 9.47569e-05
+LBFGS iteration 53 : ||r|| = 0.000129112, ||r||/||r_0|| = 8.80841e-05
+LBFGS iteration 54 : ||r|| = 0.000175704, ||r||/||r_0|| = 0.000119871
+LBFGS iteration 55 : ||r|| = 7.87371e-05, ||r||/||r_0|| = 5.37169e-05
+LBFGS iteration 56 : ||r|| = 7.30606e-05, ||r||/||r_0|| = 4.98442e-05
+LBFGS iteration 57 : ||r|| = 9.5593e-05, ||r||/||r_0|| = 6.52164e-05
+LBFGS iteration 58 : ||r|| = 0.000134289, ||r||/||r_0|| = 9.16163e-05
+LBFGS iteration 59 : ||r|| = 6.66397e-05, ||r||/||r_0|| = 4.54636e-05
+LBFGS iteration 60 : ||r|| = 5.38465e-05, ||r||/||r_0|| = 3.67357e-05
+LBFGS iteration 61 : ||r|| = 5.8085e-05, ||r||/||r_0|| = 3.96274e-05
+LBFGS iteration 62 : ||r|| = 8.23697e-05, ||r||/||r_0|| = 5.61951e-05
+LBFGS iteration 63 : ||r|| = 4.59471e-05, ||r||/||r_0|| = 3.13465e-05
+LBFGS iteration 64 : ||r|| = 4.2169e-05, ||r||/||r_0|| = 2.8769e-05
+LBFGS iteration 65 : ||r|| = 4.36386e-05, ||r||/||r_0|| = 2.97715e-05
+LBFGS iteration 66 : ||r|| = 0.000102276, ||r||/||r_0|| = 6.97757e-05
+LBFGS iteration 67 : ||r|| = 2.55284e-05, ||r||/||r_0|| = 1.74162e-05
+LBFGS iteration 68 : ||r|| = 1.74439e-05, ||r||/||r_0|| = 1.19008e-05
+LBFGS iteration 69 : ||r|| = 1.55022e-05, ||r||/||r_0|| = 1.05761e-05
+LBFGS iteration 70 : ||r|| = 2.78517e-05, ||r||/||r_0|| = 1.90012e-05
+LBFGS iteration 71 : ||r|| = 8.23786e-06, ||r||/||r_0|| = 5.62012e-06
+LBFGS iteration 72 : ||r|| = 3.15803e-06, ||r||/||r_0|| = 2.1545e-06
+LBFGS iteration 73 : ||r|| = 2.32222e-06, ||r||/||r_0|| = 1.58429e-06
+LBFGS iteration 74 : ||r|| = 2.23543e-06, ||r||/||r_0|| = 1.52508e-06
+LBFGS iteration 75 : ||r|| = 6.48079e-06, ||r||/||r_0|| = 4.42139e-06
+LBFGS iteration 76 : ||r|| = 1.24673e-06, ||r||/||r_0|| = 8.50556e-07
+LBFGS/Newton+GMRES converged in 76 iterations with a residual norm of 1.24673e-06.
+solver took 6.42006s.
+|| q_h - q_ex || / || q_ex || = 0.000247126
+|| t_h - t_ex || / || t_ex || = 0.0002417

examples/regress_test/p1_o2_dg_hb_nl_nld_newton.txt

@@ -0,0 +1,49 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --no-broken-RT
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00849795s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.0105149s.
+Preconditioner took 2.9135e-05s.
+Newton iteration  0 : ||r|| = 1.46578
+Newton iteration  1 : ||r|| = 6.21638e-08, ||r||/||r_0|| = 4.241e-08
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 6.21638e-08.
+solver took 0.353555s.
+|| q_h - q_ex || / || q_ex || = 0.000247131
+|| t_h - t_ex || / || t_ex || = 0.000241709

examples/regress_test/p1_o2_dg_hb_nld.txt

@@ -0,0 +1,124 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --no-broken-RT
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0070498s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.0383239s.
+Preconditioner took 5.6454e-05s.
+LBFGS iteration 0 : ||r|| = 1.46578
+LBFGS iteration 1 : ||r|| = 2.01258, ||r||/||r_0|| = 1.37304
+LBFGS iteration 2 : ||r|| = 2.41053, ||r||/||r_0|| = 1.64454
+LBFGS iteration 3 : ||r|| = 4.48418, ||r||/||r_0|| = 3.05924
+LBFGS iteration 4 : ||r|| = 2.44484, ||r||/||r_0|| = 1.66794
+LBFGS iteration 5 : ||r|| = 0.996497, ||r||/||r_0|| = 0.679841
+LBFGS iteration 6 : ||r|| = 0.913284, ||r||/||r_0|| = 0.62307
+LBFGS iteration 7 : ||r|| = 1.03122, ||r||/||r_0|| = 0.703531
+LBFGS iteration 8 : ||r|| = 2.21745, ||r||/||r_0|| = 1.51281
+LBFGS iteration 9 : ||r|| = 0.769554, ||r||/||r_0|| = 0.525013
+LBFGS iteration 10 : ||r|| = 0.607543, ||r||/||r_0|| = 0.414484
+LBFGS iteration 11 : ||r|| = 0.759138, ||r||/||r_0|| = 0.517907
+LBFGS iteration 12 : ||r|| = 1.4581, ||r||/||r_0|| = 0.994757
+LBFGS iteration 13 : ||r|| = 0.563222, ||r||/||r_0|| = 0.384247
+LBFGS iteration 14 : ||r|| = 0.428817, ||r||/||r_0|| = 0.292552
+LBFGS iteration 15 : ||r|| = 0.44147, ||r||/||r_0|| = 0.301185
+LBFGS iteration 16 : ||r|| = 1.39, ||r||/||r_0|| = 0.9483
+LBFGS iteration 17 : ||r|| = 0.272891, ||r||/||r_0|| = 0.186175
+LBFGS iteration 18 : ||r|| = 0.165054, ||r||/||r_0|| = 0.112605
+LBFGS iteration 19 : ||r|| = 0.151718, ||r||/||r_0|| = 0.103506
+LBFGS iteration 20 : ||r|| = 0.331585, ||r||/||r_0|| = 0.226217
+LBFGS iteration 21 : ||r|| = 0.106143, ||r||/||r_0|| = 0.0724142
+LBFGS iteration 22 : ||r|| = 0.0594506, ||r||/||r_0|| = 0.040559
+LBFGS iteration 23 : ||r|| = 0.0596312, ||r||/||r_0|| = 0.0406822
+LBFGS iteration 24 : ||r|| = 0.171728, ||r||/||r_0|| = 0.117158
+LBFGS iteration 25 : ||r|| = 0.0533533, ||r||/||r_0|| = 0.0363992
+LBFGS iteration 26 : ||r|| = 0.0273829, ||r||/||r_0|| = 0.0186814
+LBFGS iteration 27 : ||r|| = 0.0191745, ||r||/||r_0|| = 0.0130814
+LBFGS iteration 28 : ||r|| = 0.0553769, ||r||/||r_0|| = 0.0377798
+LBFGS iteration 29 : ||r|| = 0.0141317, ||r||/||r_0|| = 0.00964106
+LBFGS iteration 30 : ||r|| = 0.00770544, ||r||/||r_0|| = 0.00525689
+LBFGS iteration 31 : ||r|| = 0.00709767, ||r||/||r_0|| = 0.00484225
+LBFGS iteration 32 : ||r|| = 0.00732886, ||r||/||r_0|| = 0.00499997
+LBFGS iteration 33 : ||r|| = 0.0153653, ||r||/||r_0|| = 0.0104827
+LBFGS iteration 34 : ||r|| = 0.00322618, ||r||/||r_0|| = 0.002201
+LBFGS iteration 35 : ||r|| = 0.00265732, ||r||/||r_0|| = 0.00181291
+LBFGS iteration 36 : ||r|| = 0.00296415, ||r||/||r_0|| = 0.00202224
+LBFGS iteration 37 : ||r|| = 0.00285425, ||r||/||r_0|| = 0.00194726
+LBFGS iteration 38 : ||r|| = 0.00619246, ||r||/||r_0|| = 0.00422468
+LBFGS iteration 39 : ||r|| = 0.000777538, ||r||/||r_0|| = 0.00053046
+LBFGS iteration 40 : ||r|| = 0.000623058, ||r||/||r_0|| = 0.000425069
+LBFGS iteration 41 : ||r|| = 0.00101854, ||r||/||r_0|| = 0.000694876
+LBFGS iteration 42 : ||r|| = 0.000787498, ||r||/||r_0|| = 0.000537255
+LBFGS iteration 43 : ||r|| = 0.000321394, ||r||/||r_0|| = 0.000219265
+LBFGS iteration 44 : ||r|| = 0.000233725, ||r||/||r_0|| = 0.000159455
+LBFGS iteration 45 : ||r|| = 0.000266519, ||r||/||r_0|| = 0.000181828
+LBFGS iteration 46 : ||r|| = 0.000373324, ||r||/||r_0|| = 0.000254693
+LBFGS iteration 47 : ||r|| = 0.000342685, ||r||/||r_0|| = 0.00023379
+LBFGS iteration 48 : ||r|| = 0.000147171, ||r||/||r_0|| = 0.000100404
+LBFGS iteration 49 : ||r|| = 0.000149241, ||r||/||r_0|| = 0.000101817
+LBFGS iteration 50 : ||r|| = 0.000200512, ||r||/||r_0|| = 0.000136796
+LBFGS iteration 51 : ||r|| = 0.000247277, ||r||/||r_0|| = 0.0001687
+LBFGS iteration 52 : ||r|| = 0.000138893, ||r||/||r_0|| = 9.4757e-05
+LBFGS iteration 53 : ||r|| = 0.000129112, ||r||/||r_0|| = 8.80844e-05
+LBFGS iteration 54 : ||r|| = 0.000175709, ||r||/||r_0|| = 0.000119874
+LBFGS iteration 55 : ||r|| = 7.87381e-05, ||r||/||r_0|| = 5.37175e-05
+LBFGS iteration 56 : ||r|| = 7.30614e-05, ||r||/||r_0|| = 4.98447e-05
+LBFGS iteration 57 : ||r|| = 9.55919e-05, ||r||/||r_0|| = 6.52157e-05
+LBFGS iteration 58 : ||r|| = 0.000134287, ||r||/||r_0|| = 9.16148e-05
+LBFGS iteration 59 : ||r|| = 6.66417e-05, ||r||/||r_0|| = 4.5465e-05
+LBFGS iteration 60 : ||r|| = 5.38494e-05, ||r||/||r_0|| = 3.67377e-05
+LBFGS iteration 61 : ||r|| = 5.80937e-05, ||r||/||r_0|| = 3.96333e-05
+LBFGS iteration 62 : ||r|| = 8.22887e-05, ||r||/||r_0|| = 5.61399e-05
+LBFGS iteration 63 : ||r|| = 4.59653e-05, ||r||/||r_0|| = 3.1359e-05
+LBFGS iteration 64 : ||r|| = 4.21774e-05, ||r||/||r_0|| = 2.87747e-05
+LBFGS iteration 65 : ||r|| = 4.36417e-05, ||r||/||r_0|| = 2.97737e-05
+LBFGS iteration 66 : ||r|| = 0.000102056, ||r||/||r_0|| = 6.96257e-05
+LBFGS iteration 67 : ||r|| = 2.55212e-05, ||r||/||r_0|| = 1.74114e-05
+LBFGS iteration 68 : ||r|| = 1.74447e-05, ||r||/||r_0|| = 1.19013e-05
+LBFGS iteration 69 : ||r|| = 1.55053e-05, ||r||/||r_0|| = 1.05782e-05
+LBFGS iteration 70 : ||r|| = 2.81845e-05, ||r||/||r_0|| = 1.92283e-05
+LBFGS iteration 71 : ||r|| = 8.05057e-06, ||r||/||r_0|| = 5.49234e-06
+LBFGS iteration 72 : ||r|| = 3.16352e-06, ||r||/||r_0|| = 2.15825e-06
+LBFGS iteration 73 : ||r|| = 2.31988e-06, ||r||/||r_0|| = 1.58269e-06
+LBFGS iteration 74 : ||r|| = 2.24328e-06, ||r||/||r_0|| = 1.53043e-06
+LBFGS iteration 75 : ||r|| = 6.49278e-06, ||r||/||r_0|| = 4.42957e-06
+LBFGS iteration 76 : ||r|| = 1.24208e-06, ||r||/||r_0|| = 8.47383e-07
+LBFGS/Newton+GMRES converged in 76 iterations with a residual norm of 1.24208e-06.
+solver took 3.23983s.
+|| q_h - q_ex || / || q_ex || = 0.000247126
+|| t_h - t_ex || / || t_ex || = 0.0002417

examples/regress_test/p1_o2_dg_hb_nld_newton.txt

@@ -0,0 +1,49 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --no-broken-RT
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00826646s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.055207s.
+Preconditioner took 4.3616e-05s.
+Newton iteration  0 : ||r|| = 1.46578
+Newton iteration  1 : ||r|| = 6.23817e-08, ||r||/||r_0|| = 4.25587e-08
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 6.23817e-08.
+solver took 0.338429s.
+|| q_h - q_ex || / || q_ex || = 0.000247131
+|| t_h - t_ex || / || t_ex || = 0.000241709

examples/regress_test/p1_o2_hb_nl.txt

@@ -0,0 +1,169 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0174704s.
+***********************************************************
+dim(V) = 1860
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3420
+***********************************************************
+Assembly took 0.0193046s.
+Preconditioner took 6.1853e-05s.
+LBFGS iteration 0 : ||r|| = 1.60422
+LBFGS iteration 1 : ||r|| = 4.04305, ||r||/||r_0|| = 2.52026
+LBFGS iteration 2 : ||r|| = 2.27103, ||r||/||r_0|| = 1.41566
+LBFGS iteration 3 : ||r|| = 2.86497, ||r||/||r_0|| = 1.7859
+LBFGS iteration 4 : ||r|| = 8.10595, ||r||/||r_0|| = 5.0529
+LBFGS iteration 5 : ||r|| = 8.73464, ||r||/||r_0|| = 5.4448
+LBFGS iteration 6 : ||r|| = 1.87803, ||r||/||r_0|| = 1.17069
+LBFGS iteration 7 : ||r|| = 1.07044, ||r||/||r_0|| = 0.667268
+LBFGS iteration 8 : ||r|| = 1.19802, ||r||/||r_0|| = 0.746794
+LBFGS iteration 9 : ||r|| = 2.05643, ||r||/||r_0|| = 1.28189
+LBFGS iteration 10 : ||r|| = 1.71473, ||r||/||r_0|| = 1.06889
+LBFGS iteration 11 : ||r|| = 1.80177, ||r||/||r_0|| = 1.12315
+LBFGS iteration 12 : ||r|| = 2.94979, ||r||/||r_0|| = 1.83878
+LBFGS iteration 13 : ||r|| = 0.788424, ||r||/||r_0|| = 0.49147
+LBFGS iteration 14 : ||r|| = 0.688495, ||r||/||r_0|| = 0.429178
+LBFGS iteration 15 : ||r|| = 1.15113, ||r||/||r_0|| = 0.717567
+LBFGS iteration 16 : ||r|| = 1.20461, ||r||/||r_0|| = 0.750902
+LBFGS iteration 17 : ||r|| = 4.95942, ||r||/||r_0|| = 3.09149
+LBFGS iteration 18 : ||r|| = 0.596949, ||r||/||r_0|| = 0.372113
+LBFGS iteration 19 : ||r|| = 0.467761, ||r||/||r_0|| = 0.291582
+LBFGS iteration 20 : ||r|| = 0.71786, ||r||/||r_0|| = 0.447483
+LBFGS iteration 21 : ||r|| = 0.836852, ||r||/||r_0|| = 0.521658
+LBFGS iteration 22 : ||r|| = 2.59644, ||r||/||r_0|| = 1.61851
+LBFGS iteration 23 : ||r|| = 0.388821, ||r||/||r_0|| = 0.242374
+LBFGS iteration 24 : ||r|| = 0.234827, ||r||/||r_0|| = 0.146381
+LBFGS iteration 25 : ||r|| = 0.263661, ||r||/||r_0|| = 0.164355
+LBFGS iteration 26 : ||r|| = 0.277796, ||r||/||r_0|| = 0.173166
+LBFGS iteration 27 : ||r|| = 0.975136, ||r||/||r_0|| = 0.607858
+LBFGS iteration 28 : ||r|| = 0.128984, ||r||/||r_0|| = 0.0804028
+LBFGS iteration 29 : ||r|| = 0.0994523, ||r||/||r_0|| = 0.0619943
+LBFGS iteration 30 : ||r|| = 0.102656, ||r||/||r_0|| = 0.0639912
+LBFGS iteration 31 : ||r|| = 0.430616, ||r||/||r_0|| = 0.268427
+LBFGS iteration 32 : ||r|| = 0.107659, ||r||/||r_0|| = 0.06711
+LBFGS iteration 33 : ||r|| = 0.0659709, ||r||/||r_0|| = 0.0411234
+LBFGS iteration 34 : ||r|| = 0.108932, ||r||/||r_0|| = 0.0679038
+LBFGS iteration 35 : ||r|| = 0.10333, ||r||/||r_0|| = 0.0644116
+LBFGS iteration 36 : ||r|| = 0.393613, ||r||/||r_0|| = 0.245362
+LBFGS iteration 37 : ||r|| = 0.044456, ||r||/||r_0|| = 0.027712
+LBFGS iteration 38 : ||r|| = 0.0293365, ||r||/||r_0|| = 0.0182871
+LBFGS iteration 39 : ||r|| = 0.0325774, ||r||/||r_0|| = 0.0203074
+LBFGS iteration 40 : ||r|| = 0.0383684, ||r||/||r_0|| = 0.0239172
+LBFGS iteration 41 : ||r|| = 0.0935856, ||r||/||r_0|| = 0.0583372
+LBFGS iteration 42 : ||r|| = 0.0181591, ||r||/||r_0|| = 0.0113196
+LBFGS iteration 43 : ||r|| = 0.0101241, ||r||/||r_0|| = 0.0063109
+LBFGS iteration 44 : ||r|| = 0.0103064, ||r||/||r_0|| = 0.00642455
+LBFGS iteration 45 : ||r|| = 0.0136856, ||r||/||r_0|| = 0.00853103
+LBFGS iteration 46 : ||r|| = 0.0224226, ||r||/||r_0|| = 0.0139773
+LBFGS iteration 47 : ||r|| = 0.0121399, ||r||/||r_0|| = 0.00756747
+LBFGS iteration 48 : ||r|| = 0.00565715, ||r||/||r_0|| = 0.00352643
+LBFGS iteration 49 : ||r|| = 0.00519774, ||r||/||r_0|| = 0.00324005
+LBFGS iteration 50 : ||r|| = 0.00683834, ||r||/||r_0|| = 0.00426273
+LBFGS iteration 51 : ||r|| = 0.0102297, ||r||/||r_0|| = 0.00637677
+LBFGS iteration 52 : ||r|| = 0.0178293, ||r||/||r_0|| = 0.011114
+LBFGS iteration 53 : ||r|| = 0.00410073, ||r||/||r_0|| = 0.00255622
+LBFGS iteration 54 : ||r|| = 0.00214889, ||r||/||r_0|| = 0.00133952
+LBFGS iteration 55 : ||r|| = 0.00179143, ||r||/||r_0|| = 0.0011167
+LBFGS iteration 56 : ||r|| = 0.00228298, ||r||/||r_0|| = 0.00142311
+LBFGS iteration 57 : ||r|| = 0.00331611, ||r||/||r_0|| = 0.00206712
+LBFGS iteration 58 : ||r|| = 0.00287553, ||r||/||r_0|| = 0.00179248
+LBFGS iteration 59 : ||r|| = 0.00174206, ||r||/||r_0|| = 0.00108593
+LBFGS iteration 60 : ||r|| = 0.00197402, ||r||/||r_0|| = 0.00123052
+LBFGS iteration 61 : ||r|| = 0.00271139, ||r||/||r_0|| = 0.00169016
+LBFGS iteration 62 : ||r|| = 0.0033751, ||r||/||r_0|| = 0.00210389
+LBFGS iteration 63 : ||r|| = 0.00675991, ||r||/||r_0|| = 0.00421384
+LBFGS iteration 64 : ||r|| = 0.00199077, ||r||/||r_0|| = 0.00124096
+LBFGS iteration 65 : ||r|| = 0.00103921, ||r||/||r_0|| = 0.000647797
+LBFGS iteration 66 : ||r|| = 0.00130432, ||r||/||r_0|| = 0.000813055
+LBFGS iteration 67 : ||r|| = 0.00173231, ||r||/||r_0|| = 0.00107985
+LBFGS iteration 68 : ||r|| = 0.00255953, ||r||/||r_0|| = 0.0015955
+LBFGS iteration 69 : ||r|| = 0.00178072, ||r||/||r_0|| = 0.00111003
+LBFGS iteration 70 : ||r|| = 0.000654644, ||r||/||r_0|| = 0.000408077
+LBFGS iteration 71 : ||r|| = 0.000543947, ||r||/||r_0|| = 0.000339073
+LBFGS iteration 72 : ||r|| = 0.000693809, ||r||/||r_0|| = 0.000432491
+LBFGS iteration 73 : ||r|| = 0.00123584, ||r||/||r_0|| = 0.000770371
+LBFGS iteration 74 : ||r|| = 0.000501059, ||r||/||r_0|| = 0.000312339
+LBFGS iteration 75 : ||r|| = 0.000265266, ||r||/||r_0|| = 0.000165356
+LBFGS iteration 76 : ||r|| = 0.000251954, ||r||/||r_0|| = 0.000157057
+LBFGS iteration 77 : ||r|| = 0.000333886, ||r||/||r_0|| = 0.00020813
+LBFGS iteration 78 : ||r|| = 0.000522524, ||r||/||r_0|| = 0.000325719
+LBFGS iteration 79 : ||r|| = 0.000369836, ||r||/||r_0|| = 0.00023054
+LBFGS iteration 80 : ||r|| = 0.000157428, ||r||/||r_0|| = 9.81341e-05
+LBFGS iteration 81 : ||r|| = 0.000134986, ||r||/||r_0|| = 8.41443e-05
+LBFGS iteration 82 : ||r|| = 0.000153649, ||r||/||r_0|| = 9.57781e-05
+LBFGS iteration 83 : ||r|| = 0.000245621, ||r||/||r_0|| = 0.00015311
+LBFGS iteration 84 : ||r|| = 0.000197426, ||r||/||r_0|| = 0.000123067
+LBFGS iteration 85 : ||r|| = 6.29115e-05, ||r||/||r_0|| = 3.92164e-05
+LBFGS iteration 86 : ||r|| = 5.17471e-05, ||r||/||r_0|| = 3.22569e-05
+LBFGS iteration 87 : ||r|| = 6.68762e-05, ||r||/||r_0|| = 4.16877e-05
+LBFGS iteration 88 : ||r|| = 7.26244e-05, ||r||/||r_0|| = 4.52709e-05
+LBFGS iteration 89 : ||r|| = 0.000227688, ||r||/||r_0|| = 0.000141931
+LBFGS iteration 90 : ||r|| = 3.31977e-05, ||r||/||r_0|| = 2.0694e-05
+LBFGS iteration 91 : ||r|| = 2.65641e-05, ||r||/||r_0|| = 1.65589e-05
+LBFGS iteration 92 : ||r|| = 3.49512e-05, ||r||/||r_0|| = 2.17871e-05
+LBFGS iteration 93 : ||r|| = 4.97308e-05, ||r||/||r_0|| = 3.10001e-05
+LBFGS iteration 94 : ||r|| = 3.34232e-05, ||r||/||r_0|| = 2.08346e-05
+LBFGS iteration 95 : ||r|| = 1.1803e-05, ||r||/||r_0|| = 7.35749e-06
+LBFGS iteration 96 : ||r|| = 1.02902e-05, ||r||/||r_0|| = 6.41446e-06
+LBFGS iteration 97 : ||r|| = 1.30043e-05, ||r||/||r_0|| = 8.10633e-06
+LBFGS iteration 98 : ||r|| = 2.26578e-05, ||r||/||r_0|| = 1.41239e-05
+LBFGS iteration 99 : ||r|| = 2.0364e-05, ||r||/||r_0|| = 1.2694e-05
+LBFGS iteration 100 : ||r|| = 1.01336e-05, ||r||/||r_0|| = 6.31686e-06
+LBFGS iteration 101 : ||r|| = 9.57449e-06, ||r||/||r_0|| = 5.96833e-06
+LBFGS iteration 102 : ||r|| = 1.17016e-05, ||r||/||r_0|| = 7.29425e-06
+LBFGS iteration 103 : ||r|| = 2.72813e-05, ||r||/||r_0|| = 1.7006e-05
+LBFGS iteration 104 : ||r|| = 9.72679e-06, ||r||/||r_0|| = 6.06327e-06
+LBFGS iteration 105 : ||r|| = 6.59627e-06, ||r||/||r_0|| = 4.11183e-06
+LBFGS iteration 106 : ||r|| = 7.66233e-06, ||r||/||r_0|| = 4.77637e-06
+LBFGS iteration 107 : ||r|| = 1.1227e-05, ||r||/||r_0|| = 6.99842e-06
+LBFGS iteration 108 : ||r|| = 7.81538e-06, ||r||/||r_0|| = 4.87177e-06
+LBFGS iteration 109 : ||r|| = 6.73626e-06, ||r||/||r_0|| = 4.1991e-06
+LBFGS iteration 110 : ||r|| = 5.02859e-06, ||r||/||r_0|| = 3.1346e-06
+LBFGS iteration 111 : ||r|| = 4.63857e-06, ||r||/||r_0|| = 2.89149e-06
+LBFGS iteration 112 : ||r|| = 7.50298e-06, ||r||/||r_0|| = 4.67704e-06
+LBFGS iteration 113 : ||r|| = 5.96133e-06, ||r||/||r_0|| = 3.71604e-06
+LBFGS iteration 114 : ||r|| = 3.93594e-06, ||r||/||r_0|| = 2.45349e-06
+LBFGS iteration 115 : ||r|| = 3.71031e-06, ||r||/||r_0|| = 2.31285e-06
+LBFGS iteration 116 : ||r|| = 4.97969e-06, ||r||/||r_0|| = 3.10413e-06
+LBFGS iteration 117 : ||r|| = 8.19517e-06, ||r||/||r_0|| = 5.10852e-06
+LBFGS iteration 118 : ||r|| = 2.17669e-06, ||r||/||r_0|| = 1.35685e-06
+LBFGS iteration 119 : ||r|| = 1.66053e-06, ||r||/||r_0|| = 1.0351e-06
+LBFGS iteration 120 : ||r|| = 1.84e-06, ||r||/||r_0|| = 1.14698e-06
+LBFGS iteration 121 : ||r|| = 3.54175e-06, ||r||/||r_0|| = 2.20777e-06
+LBFGS iteration 122 : ||r|| = 1.39257e-06, ||r||/||r_0|| = 8.6807e-07
+LBFGS/Newton+GMRES converged in 122 iterations with a residual norm of 1.39257e-06.
+solver took 21.8909s.
+|| q_h - q_ex || / || q_ex || = 6.12087e-06
+|| t_h - t_ex || / || t_ex || = 3.90288e-06

examples/regress_test/p1_o2_hb_nl_newton.txt

@@ -0,0 +1,47 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0137397s.
+***********************************************************
+dim(V) = 1860
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3420
+***********************************************************
+Assembly took 0.0117625s.
+Preconditioner took 3.3236e-05s.
+Newton iteration  0 : ||r|| = 1.60422
+Newton iteration  1 : ||r|| = 4.98725e-08, ||r||/||r_0|| = 3.10884e-08
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 4.98725e-08.
+solver took 0.601921s.
+|| q_h - q_ex || / || q_ex || = 6.10477e-06
+|| t_h - t_ex || / || t_ex || = 3.90155e-06

examples/regress_test/p1_o2_hb_nl_nld.txt

@@ -0,0 +1,170 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0109196s.
+***********************************************************
+dim(V) = 1860
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3420
+***********************************************************
+Assembly took 0.021188s.
+Preconditioner took 5.675e-05s.
+LBFGS iteration 0 : ||r|| = 1.60422
+LBFGS iteration 1 : ||r|| = 4.04305, ||r||/||r_0|| = 2.52026
+LBFGS iteration 2 : ||r|| = 2.27103, ||r||/||r_0|| = 1.41566
+LBFGS iteration 3 : ||r|| = 2.86497, ||r||/||r_0|| = 1.7859
+LBFGS iteration 4 : ||r|| = 8.10595, ||r||/||r_0|| = 5.0529
+LBFGS iteration 5 : ||r|| = 8.73464, ||r||/||r_0|| = 5.4448
+LBFGS iteration 6 : ||r|| = 1.87803, ||r||/||r_0|| = 1.17069
+LBFGS iteration 7 : ||r|| = 1.07044, ||r||/||r_0|| = 0.667268
+LBFGS iteration 8 : ||r|| = 1.19802, ||r||/||r_0|| = 0.746794
+LBFGS iteration 9 : ||r|| = 2.05643, ||r||/||r_0|| = 1.28189
+LBFGS iteration 10 : ||r|| = 1.71473, ||r||/||r_0|| = 1.06889
+LBFGS iteration 11 : ||r|| = 1.80177, ||r||/||r_0|| = 1.12315
+LBFGS iteration 12 : ||r|| = 2.94979, ||r||/||r_0|| = 1.83878
+LBFGS iteration 13 : ||r|| = 0.788424, ||r||/||r_0|| = 0.49147
+LBFGS iteration 14 : ||r|| = 0.688495, ||r||/||r_0|| = 0.429178
+LBFGS iteration 15 : ||r|| = 1.15113, ||r||/||r_0|| = 0.717567
+LBFGS iteration 16 : ||r|| = 1.20461, ||r||/||r_0|| = 0.750902
+LBFGS iteration 17 : ||r|| = 4.95942, ||r||/||r_0|| = 3.09149
+LBFGS iteration 18 : ||r|| = 0.596949, ||r||/||r_0|| = 0.372113
+LBFGS iteration 19 : ||r|| = 0.467761, ||r||/||r_0|| = 0.291582
+LBFGS iteration 20 : ||r|| = 0.71786, ||r||/||r_0|| = 0.447483
+LBFGS iteration 21 : ||r|| = 0.836852, ||r||/||r_0|| = 0.521658
+LBFGS iteration 22 : ||r|| = 2.59644, ||r||/||r_0|| = 1.61851
+LBFGS iteration 23 : ||r|| = 0.388821, ||r||/||r_0|| = 0.242374
+LBFGS iteration 24 : ||r|| = 0.234827, ||r||/||r_0|| = 0.146381
+LBFGS iteration 25 : ||r|| = 0.263661, ||r||/||r_0|| = 0.164355
+LBFGS iteration 26 : ||r|| = 0.277796, ||r||/||r_0|| = 0.173166
+LBFGS iteration 27 : ||r|| = 0.975136, ||r||/||r_0|| = 0.607858
+LBFGS iteration 28 : ||r|| = 0.128984, ||r||/||r_0|| = 0.0804028
+LBFGS iteration 29 : ||r|| = 0.0994523, ||r||/||r_0|| = 0.0619943
+LBFGS iteration 30 : ||r|| = 0.102656, ||r||/||r_0|| = 0.0639912
+LBFGS iteration 31 : ||r|| = 0.430616, ||r||/||r_0|| = 0.268427
+LBFGS iteration 32 : ||r|| = 0.107659, ||r||/||r_0|| = 0.06711
+LBFGS iteration 33 : ||r|| = 0.0659709, ||r||/||r_0|| = 0.0411234
+LBFGS iteration 34 : ||r|| = 0.108932, ||r||/||r_0|| = 0.0679038
+LBFGS iteration 35 : ||r|| = 0.10333, ||r||/||r_0|| = 0.0644116
+LBFGS iteration 36 : ||r|| = 0.393613, ||r||/||r_0|| = 0.245362
+LBFGS iteration 37 : ||r|| = 0.044456, ||r||/||r_0|| = 0.027712
+LBFGS iteration 38 : ||r|| = 0.0293365, ||r||/||r_0|| = 0.0182871
+LBFGS iteration 39 : ||r|| = 0.0325774, ||r||/||r_0|| = 0.0203074
+LBFGS iteration 40 : ||r|| = 0.0383684, ||r||/||r_0|| = 0.0239172
+LBFGS iteration 41 : ||r|| = 0.0935856, ||r||/||r_0|| = 0.0583372
+LBFGS iteration 42 : ||r|| = 0.0181591, ||r||/||r_0|| = 0.0113196
+LBFGS iteration 43 : ||r|| = 0.0101241, ||r||/||r_0|| = 0.0063109
+LBFGS iteration 44 : ||r|| = 0.0103064, ||r||/||r_0|| = 0.00642455
+LBFGS iteration 45 : ||r|| = 0.0136856, ||r||/||r_0|| = 0.00853103
+LBFGS iteration 46 : ||r|| = 0.0224226, ||r||/||r_0|| = 0.0139773
+LBFGS iteration 47 : ||r|| = 0.0121399, ||r||/||r_0|| = 0.00756747
+LBFGS iteration 48 : ||r|| = 0.00565715, ||r||/||r_0|| = 0.00352643
+LBFGS iteration 49 : ||r|| = 0.00519774, ||r||/||r_0|| = 0.00324005
+LBFGS iteration 50 : ||r|| = 0.00683834, ||r||/||r_0|| = 0.00426273
+LBFGS iteration 51 : ||r|| = 0.0102297, ||r||/||r_0|| = 0.00637677
+LBFGS iteration 52 : ||r|| = 0.0178293, ||r||/||r_0|| = 0.011114
+LBFGS iteration 53 : ||r|| = 0.00410073, ||r||/||r_0|| = 0.00255622
+LBFGS iteration 54 : ||r|| = 0.00214889, ||r||/||r_0|| = 0.00133952
+LBFGS iteration 55 : ||r|| = 0.00179143, ||r||/||r_0|| = 0.0011167
+LBFGS iteration 56 : ||r|| = 0.00228298, ||r||/||r_0|| = 0.00142311
+LBFGS iteration 57 : ||r|| = 0.00331611, ||r||/||r_0|| = 0.00206712
+LBFGS iteration 58 : ||r|| = 0.00287553, ||r||/||r_0|| = 0.00179248
+LBFGS iteration 59 : ||r|| = 0.00174206, ||r||/||r_0|| = 0.00108593
+LBFGS iteration 60 : ||r|| = 0.00197402, ||r||/||r_0|| = 0.00123052
+LBFGS iteration 61 : ||r|| = 0.00271139, ||r||/||r_0|| = 0.00169016
+LBFGS iteration 62 : ||r|| = 0.0033751, ||r||/||r_0|| = 0.00210389
+LBFGS iteration 63 : ||r|| = 0.00675992, ||r||/||r_0|| = 0.00421385
+LBFGS iteration 64 : ||r|| = 0.00199077, ||r||/||r_0|| = 0.00124096
+LBFGS iteration 65 : ||r|| = 0.00103921, ||r||/||r_0|| = 0.000647797
+LBFGS iteration 66 : ||r|| = 0.00130432, ||r||/||r_0|| = 0.000813055
+LBFGS iteration 67 : ||r|| = 0.00173231, ||r||/||r_0|| = 0.00107985
+LBFGS iteration 68 : ||r|| = 0.00255953, ||r||/||r_0|| = 0.0015955
+LBFGS iteration 69 : ||r|| = 0.00178073, ||r||/||r_0|| = 0.00111003
+LBFGS iteration 70 : ||r|| = 0.000654644, ||r||/||r_0|| = 0.000408077
+LBFGS iteration 71 : ||r|| = 0.000543947, ||r||/||r_0|| = 0.000339073
+LBFGS iteration 72 : ||r|| = 0.000693809, ||r||/||r_0|| = 0.000432491
+LBFGS iteration 73 : ||r|| = 0.00123584, ||r||/||r_0|| = 0.000770371
+LBFGS iteration 74 : ||r|| = 0.000501059, ||r||/||r_0|| = 0.000312339
+LBFGS iteration 75 : ||r|| = 0.000265266, ||r||/||r_0|| = 0.000165356
+LBFGS iteration 76 : ||r|| = 0.000251953, ||r||/||r_0|| = 0.000157057
+LBFGS iteration 77 : ||r|| = 0.000333886, ||r||/||r_0|| = 0.00020813
+LBFGS iteration 78 : ||r|| = 0.000522523, ||r||/||r_0|| = 0.000325719
+LBFGS iteration 79 : ||r|| = 0.000369834, ||r||/||r_0|| = 0.000230539
+LBFGS iteration 80 : ||r|| = 0.000157428, ||r||/||r_0|| = 9.81338e-05
+LBFGS iteration 81 : ||r|| = 0.000134985, ||r||/||r_0|| = 8.41439e-05
+LBFGS iteration 82 : ||r|| = 0.000153647, ||r||/||r_0|| = 9.5777e-05
+LBFGS iteration 83 : ||r|| = 0.000245494, ||r||/||r_0|| = 0.00015303
+LBFGS iteration 84 : ||r|| = 0.000197097, ||r||/||r_0|| = 0.000122862
+LBFGS iteration 85 : ||r|| = 6.28938e-05, ||r||/||r_0|| = 3.92053e-05
+LBFGS iteration 86 : ||r|| = 5.17492e-05, ||r||/||r_0|| = 3.22582e-05
+LBFGS iteration 87 : ||r|| = 6.68573e-05, ||r||/||r_0|| = 4.1676e-05
+LBFGS iteration 88 : ||r|| = 7.20488e-05, ||r||/||r_0|| = 4.49121e-05
+LBFGS iteration 89 : ||r|| = 0.000230595, ||r||/||r_0|| = 0.000143743
+LBFGS iteration 90 : ||r|| = 3.32498e-05, ||r||/||r_0|| = 2.07265e-05
+LBFGS iteration 91 : ||r|| = 2.65435e-05, ||r||/||r_0|| = 1.65461e-05
+LBFGS iteration 92 : ||r|| = 3.48386e-05, ||r||/||r_0|| = 2.17169e-05
+LBFGS iteration 93 : ||r|| = 4.93021e-05, ||r||/||r_0|| = 3.07328e-05
+LBFGS iteration 94 : ||r|| = 3.37321e-05, ||r||/||r_0|| = 2.10271e-05
+LBFGS iteration 95 : ||r|| = 1.17848e-05, ||r||/||r_0|| = 7.34615e-06
+LBFGS iteration 96 : ||r|| = 1.02097e-05, ||r||/||r_0|| = 6.3643e-06
+LBFGS iteration 97 : ||r|| = 1.29555e-05, ||r||/||r_0|| = 8.0759e-06
+LBFGS iteration 98 : ||r|| = 2.22505e-05, ||r||/||r_0|| = 1.387e-05
+LBFGS iteration 99 : ||r|| = 2.10878e-05, ||r||/||r_0|| = 1.31452e-05
+LBFGS iteration 100 : ||r|| = 1.02078e-05, ||r||/||r_0|| = 6.36309e-06
+LBFGS iteration 101 : ||r|| = 9.50017e-06, ||r||/||r_0|| = 5.922e-06
+LBFGS iteration 102 : ||r|| = 1.15863e-05, ||r||/||r_0|| = 7.22239e-06
+LBFGS iteration 103 : ||r|| = 2.69417e-05, ||r||/||r_0|| = 1.67943e-05
+LBFGS iteration 104 : ||r|| = 9.94455e-06, ||r||/||r_0|| = 6.19901e-06
+LBFGS iteration 105 : ||r|| = 6.55722e-06, ||r||/||r_0|| = 4.08749e-06
+LBFGS iteration 106 : ||r|| = 7.61877e-06, ||r||/||r_0|| = 4.74921e-06
+LBFGS iteration 107 : ||r|| = 1.09382e-05, ||r||/||r_0|| = 6.81844e-06
+LBFGS iteration 108 : ||r|| = 7.76942e-06, ||r||/||r_0|| = 4.84313e-06
+LBFGS iteration 109 : ||r|| = 7.29928e-06, ||r||/||r_0|| = 4.55006e-06
+LBFGS iteration 110 : ||r|| = 4.93978e-06, ||r||/||r_0|| = 3.07925e-06
+LBFGS iteration 111 : ||r|| = 4.5857e-06, ||r||/||r_0|| = 2.85853e-06
+LBFGS iteration 112 : ||r|| = 7.23401e-06, ||r||/||r_0|| = 4.50937e-06
+LBFGS iteration 113 : ||r|| = 6.2086e-06, ||r||/||r_0|| = 3.87018e-06
+LBFGS iteration 114 : ||r|| = 3.91586e-06, ||r||/||r_0|| = 2.44098e-06
+LBFGS iteration 115 : ||r|| = 3.8682e-06, ||r||/||r_0|| = 2.41127e-06
+LBFGS iteration 116 : ||r|| = 4.77772e-06, ||r||/||r_0|| = 2.97823e-06
+LBFGS iteration 117 : ||r|| = 1.05549e-05, ||r||/||r_0|| = 6.57945e-06
+LBFGS iteration 118 : ||r|| = 2.32515e-06, ||r||/||r_0|| = 1.4494e-06
+LBFGS iteration 119 : ||r|| = 1.65531e-06, ||r||/||r_0|| = 1.03185e-06
+LBFGS iteration 120 : ||r|| = 1.83133e-06, ||r||/||r_0|| = 1.14157e-06
+LBFGS iteration 121 : ||r|| = 2.81453e-06, ||r||/||r_0|| = 1.75445e-06
+LBFGS iteration 122 : ||r|| = 1.83419e-06, ||r||/||r_0|| = 1.14336e-06
+LBFGS iteration 123 : ||r|| = 8.4473e-07, ||r||/||r_0|| = 5.26568e-07
+LBFGS/Newton+GMRES converged in 123 iterations with a residual norm of 8.4473e-07.
+solver took 9.23797s.
+|| q_h - q_ex || / || q_ex || = 6.11146e-06
+|| t_h - t_ex || / || t_ex || = 3.90229e-06

examples/regress_test/p1_o2_hb_nl_nld_newton.txt

@@ -0,0 +1,47 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00863252s.
+***********************************************************
+dim(V) = 1860
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3420
+***********************************************************
+Assembly took 0.0111083s.
+Preconditioner took 1.9831e-05s.
+Newton iteration  0 : ||r|| = 1.60422
+Newton iteration  1 : ||r|| = 4.77667e-08, ||r||/||r_0|| = 2.97757e-08
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 4.77667e-08.
+solver took 0.454486s.
+|| q_h - q_ex || / || q_ex || = 6.10477e-06
+|| t_h - t_ex || / || t_ex || = 3.90155e-06

examples/regress_test/p1_o2_hb_nld_newton.txt

@@ -0,0 +1,47 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00990361s.
+***********************************************************
+dim(V) = 1860
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3420
+***********************************************************
+Assembly took 0.0162211s.
+Preconditioner took 2.4778e-05s.
+Newton iteration  0 : ||r|| = 1.60422
+Newton iteration  1 : ||r|| = 4.77667e-08, ||r||/||r_0|| = 2.97757e-08
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 4.77667e-08.
+solver took 0.461365s.
+|| q_h - q_ex || / || q_ex || = 6.10477e-06
+|| t_h - t_ex || / || t_ex || = 3.90155e-06

examples/regress_test/p1_o3.txt

@@ -0,0 +1,231 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-hybridization
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2112
+dim(W) = 1024
+dim(V+W) = 3136
+***********************************************************
+Assembly took 0.0122702s.
+Preconditioner took 0.00343498s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.828288
+   Pass :  1   Iteration :   1  ||B r|| = 0.828288
+   Pass :  1   Iteration :   2  ||B r|| = 0.780392
+   Pass :  1   Iteration :   3  ||B r|| = 0.775902
+   Pass :  1   Iteration :   4  ||B r|| = 0.718999
+   Pass :  1   Iteration :   5  ||B r|| = 0.712741
+   Pass :  1   Iteration :   6  ||B r|| = 0.709216
+   Pass :  1   Iteration :   7  ||B r|| = 0.699357
+   Pass :  1   Iteration :   8  ||B r|| = 0.685558
+   Pass :  1   Iteration :   9  ||B r|| = 0.624758
+   Pass :  1   Iteration :  10  ||B r|| = 0.61651
+   Pass :  1   Iteration :  11  ||B r|| = 0.491672
+   Pass :  1   Iteration :  12  ||B r|| = 0.490509
+   Pass :  1   Iteration :  13  ||B r|| = 0.43273
+   Pass :  1   Iteration :  14  ||B r|| = 0.432532
+   Pass :  1   Iteration :  15  ||B r|| = 0.391607
+   Pass :  1   Iteration :  16  ||B r|| = 0.387505
+   Pass :  1   Iteration :  17  ||B r|| = 0.369287
+   Pass :  1   Iteration :  18  ||B r|| = 0.349727
+   Pass :  1   Iteration :  19  ||B r|| = 0.344534
+   Pass :  1   Iteration :  20  ||B r|| = 0.308102
+   Pass :  1   Iteration :  21  ||B r|| = 0.307918
+   Pass :  1   Iteration :  22  ||B r|| = 0.275424
+   Pass :  1   Iteration :  23  ||B r|| = 0.275336
+   Pass :  1   Iteration :  24  ||B r|| = 0.241166
+   Pass :  1   Iteration :  25  ||B r|| = 0.236098
+   Pass :  1   Iteration :  26  ||B r|| = 0.220482
+   Pass :  1   Iteration :  27  ||B r|| = 0.209195
+   Pass :  1   Iteration :  28  ||B r|| = 0.203284
+   Pass :  1   Iteration :  29  ||B r|| = 0.184134
+   Pass :  1   Iteration :  30  ||B r|| = 0.183885
+   Pass :  1   Iteration :  31  ||B r|| = 0.158572
+   Pass :  1   Iteration :  32  ||B r|| = 0.15785
+   Pass :  1   Iteration :  33  ||B r|| = 0.128252
+   Pass :  1   Iteration :  34  ||B r|| = 0.121277
+   Pass :  1   Iteration :  35  ||B r|| = 0.105019
+   Pass :  1   Iteration :  36  ||B r|| = 0.0877653
+   Pass :  1   Iteration :  37  ||B r|| = 0.0857034
+   Pass :  1   Iteration :  38  ||B r|| = 0.0695776
+   Pass :  1   Iteration :  39  ||B r|| = 0.0693421
+   Pass :  1   Iteration :  40  ||B r|| = 0.060764
+   Pass :  1   Iteration :  41  ||B r|| = 0.0583294
+   Pass :  1   Iteration :  42  ||B r|| = 0.0513009
+   Pass :  1   Iteration :  43  ||B r|| = 0.046381
+   Pass :  1   Iteration :  44  ||B r|| = 0.0446401
+   Pass :  1   Iteration :  45  ||B r|| = 0.0351366
+   Pass :  1   Iteration :  46  ||B r|| = 0.0350703
+   Pass :  1   Iteration :  47  ||B r|| = 0.0285254
+   Pass :  1   Iteration :  48  ||B r|| = 0.0275435
+   Pass :  1   Iteration :  49  ||B r|| = 0.0233101
+   Pass :  1   Iteration :  50  ||B r|| = 0.0205522
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 0.0201743
+   Pass :  2   Iteration :  52  ||B r|| = 0.0178036
+   Pass :  2   Iteration :  53  ||B r|| = 0.0177657
+   Pass :  2   Iteration :  54  ||B r|| = 0.0155379
+   Pass :  2   Iteration :  55  ||B r|| = 0.0145024
+   Pass :  2   Iteration :  56  ||B r|| = 0.0129692
+   Pass :  2   Iteration :  57  ||B r|| = 0.0111895
+   Pass :  2   Iteration :  58  ||B r|| = 0.0106264
+   Pass :  2   Iteration :  59  ||B r|| = 0.00883739
+   Pass :  2   Iteration :  60  ||B r|| = 0.00881869
+   Pass :  2   Iteration :  61  ||B r|| = 0.00734547
+   Pass :  2   Iteration :  62  ||B r|| = 0.00727023
+   Pass :  2   Iteration :  63  ||B r|| = 0.00664677
+   Pass :  2   Iteration :  64  ||B r|| = 0.00606592
+   Pass :  2   Iteration :  65  ||B r|| = 0.00584805
+   Pass :  2   Iteration :  66  ||B r|| = 0.00471596
+   Pass :  2   Iteration :  67  ||B r|| = 0.00467814
+   Pass :  2   Iteration :  68  ||B r|| = 0.00343373
+   Pass :  2   Iteration :  69  ||B r|| = 0.0034201
+   Pass :  2   Iteration :  70  ||B r|| = 0.00280534
+   Pass :  2   Iteration :  71  ||B r|| = 0.00270379
+   Pass :  2   Iteration :  72  ||B r|| = 0.0025783
+   Pass :  2   Iteration :  73  ||B r|| = 0.0022472
+   Pass :  2   Iteration :  74  ||B r|| = 0.00221863
+   Pass :  2   Iteration :  75  ||B r|| = 0.00186269
+   Pass :  2   Iteration :  76  ||B r|| = 0.00186179
+   Pass :  2   Iteration :  77  ||B r|| = 0.00160985
+   Pass :  2   Iteration :  78  ||B r|| = 0.00160018
+   Pass :  2   Iteration :  79  ||B r|| = 0.00148445
+   Pass :  2   Iteration :  80  ||B r|| = 0.00141886
+   Pass :  2   Iteration :  81  ||B r|| = 0.00139003
+   Pass :  2   Iteration :  82  ||B r|| = 0.00125305
+   Pass :  2   Iteration :  83  ||B r|| = 0.00124651
+   Pass :  2   Iteration :  84  ||B r|| = 0.00111105
+   Pass :  2   Iteration :  85  ||B r|| = 0.00110481
+   Pass :  2   Iteration :  86  ||B r|| = 0.001019
+   Pass :  2   Iteration :  87  ||B r|| = 0.000986979
+   Pass :  2   Iteration :  88  ||B r|| = 0.000943191
+   Pass :  2   Iteration :  89  ||B r|| = 0.000887917
+   Pass :  2   Iteration :  90  ||B r|| = 0.000878207
+   Pass :  2   Iteration :  91  ||B r|| = 0.000792828
+   Pass :  2   Iteration :  92  ||B r|| = 0.000792314
+   Pass :  2   Iteration :  93  ||B r|| = 0.00067918
+   Pass :  2   Iteration :  94  ||B r|| = 0.000661497
+   Pass :  2   Iteration :  95  ||B r|| = 0.000607798
+   Pass :  2   Iteration :  96  ||B r|| = 0.000585659
+   Pass :  2   Iteration :  97  ||B r|| = 0.000575458
+   Pass :  2   Iteration :  98  ||B r|| = 0.000536371
+   Pass :  2   Iteration :  99  ||B r|| = 0.000533329
+   Pass :  2   Iteration : 100  ||B r|| = 0.000476474
+Restarting...
+   Pass :  3   Iteration : 101  ||B r|| = 0.000476389
+   Pass :  3   Iteration : 102  ||B r|| = 0.000450568
+   Pass :  3   Iteration : 103  ||B r|| = 0.00044946
+   Pass :  3   Iteration : 104  ||B r|| = 0.000448032
+   Pass :  3   Iteration : 105  ||B r|| = 0.000436727
+   Pass :  3   Iteration : 106  ||B r|| = 0.000433054
+   Pass :  3   Iteration : 107  ||B r|| = 0.000384572
+   Pass :  3   Iteration : 108  ||B r|| = 0.000384151
+   Pass :  3   Iteration : 109  ||B r|| = 0.000326889
+   Pass :  3   Iteration : 110  ||B r|| = 0.000320214
+   Pass :  3   Iteration : 111  ||B r|| = 0.000295531
+   Pass :  3   Iteration : 112  ||B r|| = 0.00028017
+   Pass :  3   Iteration : 113  ||B r|| = 0.000271805
+   Pass :  3   Iteration : 114  ||B r|| = 0.000253182
+   Pass :  3   Iteration : 115  ||B r|| = 0.000251705
+   Pass :  3   Iteration : 116  ||B r|| = 0.000224202
+   Pass :  3   Iteration : 117  ||B r|| = 0.00022401
+   Pass :  3   Iteration : 118  ||B r|| = 0.000201373
+   Pass :  3   Iteration : 119  ||B r|| = 0.000195487
+   Pass :  3   Iteration : 120  ||B r|| = 0.000178312
+   Pass :  3   Iteration : 121  ||B r|| = 0.000163707
+   Pass :  3   Iteration : 122  ||B r|| = 0.000159212
+   Pass :  3   Iteration : 123  ||B r|| = 0.000143717
+   Pass :  3   Iteration : 124  ||B r|| = 0.000142938
+   Pass :  3   Iteration : 125  ||B r|| = 0.000129618
+   Pass :  3   Iteration : 126  ||B r|| = 0.000128535
+   Pass :  3   Iteration : 127  ||B r|| = 0.000120081
+   Pass :  3   Iteration : 128  ||B r|| = 0.000114142
+   Pass :  3   Iteration : 129  ||B r|| = 0.000109227
+   Pass :  3   Iteration : 130  ||B r|| = 9.74187e-05
+   Pass :  3   Iteration : 131  ||B r|| = 9.41802e-05
+   Pass :  3   Iteration : 132  ||B r|| = 7.97569e-05
+   Pass :  3   Iteration : 133  ||B r|| = 7.97329e-05
+   Pass :  3   Iteration : 134  ||B r|| = 6.96569e-05
+   Pass :  3   Iteration : 135  ||B r|| = 6.80129e-05
+   Pass :  3   Iteration : 136  ||B r|| = 6.39905e-05
+   Pass :  3   Iteration : 137  ||B r|| = 5.48303e-05
+   Pass :  3   Iteration : 138  ||B r|| = 5.33803e-05
+   Pass :  3   Iteration : 139  ||B r|| = 4.51005e-05
+   Pass :  3   Iteration : 140  ||B r|| = 4.47538e-05
+   Pass :  3   Iteration : 141  ||B r|| = 3.79739e-05
+   Pass :  3   Iteration : 142  ||B r|| = 3.79237e-05
+   Pass :  3   Iteration : 143  ||B r|| = 3.34755e-05
+   Pass :  3   Iteration : 144  ||B r|| = 3.19968e-05
+   Pass :  3   Iteration : 145  ||B r|| = 3.00248e-05
+   Pass :  3   Iteration : 146  ||B r|| = 2.43567e-05
+   Pass :  3   Iteration : 147  ||B r|| = 2.40027e-05
+   Pass :  3   Iteration : 148  ||B r|| = 1.75885e-05
+   Pass :  3   Iteration : 149  ||B r|| = 1.74341e-05
+   Pass :  3   Iteration : 150  ||B r|| = 1.38964e-05
+Restarting...
+   Pass :  4   Iteration : 151  ||B r|| = 1.33084e-05
+   Pass :  4   Iteration : 152  ||B r|| = 1.25291e-05
+   Pass :  4   Iteration : 153  ||B r|| = 1.15613e-05
+   Pass :  4   Iteration : 154  ||B r|| = 1.15039e-05
+   Pass :  4   Iteration : 155  ||B r|| = 8.97445e-06
+   Pass :  4   Iteration : 156  ||B r|| = 8.93619e-06
+   Pass :  4   Iteration : 157  ||B r|| = 7.17725e-06
+   Pass :  4   Iteration : 158  ||B r|| = 7.03949e-06
+   Pass :  4   Iteration : 159  ||B r|| = 6.28998e-06
+   Pass :  4   Iteration : 160  ||B r|| = 5.80418e-06
+   Pass :  4   Iteration : 161  ||B r|| = 5.6565e-06
+   Pass :  4   Iteration : 162  ||B r|| = 4.98291e-06
+   Pass :  4   Iteration : 163  ||B r|| = 4.97198e-06
+   Pass :  4   Iteration : 164  ||B r|| = 4.1327e-06
+   Pass :  4   Iteration : 165  ||B r|| = 4.04729e-06
+   Pass :  4   Iteration : 166  ||B r|| = 3.41458e-06
+   Pass :  4   Iteration : 167  ||B r|| = 3.2682e-06
+   Pass :  4   Iteration : 168  ||B r|| = 3.07084e-06
+   Pass :  4   Iteration : 169  ||B r|| = 2.6426e-06
+   Pass :  4   Iteration : 170  ||B r|| = 2.63354e-06
+   Pass :  4   Iteration : 171  ||B r|| = 2.17891e-06
+   Pass :  4   Iteration : 172  ||B r|| = 2.15133e-06
+   Pass :  4   Iteration : 173  ||B r|| = 1.91418e-06
+   Pass :  4   Iteration : 174  ||B r|| = 1.87277e-06
+   Pass :  4   Iteration : 175  ||B r|| = 1.75707e-06
+   Pass :  4   Iteration : 176  ||B r|| = 1.66039e-06
+   Pass :  4   Iteration : 177  ||B r|| = 1.62259e-06
+   Pass :  4   Iteration : 178  ||B r|| = 1.51352e-06
+   Pass :  4   Iteration : 179  ||B r|| = 1.51341e-06
+   Pass :  4   Iteration : 180  ||B r|| = 1.35973e-06
+   Pass :  4   Iteration : 181  ||B r|| = 1.34071e-06
+   Pass :  4   Iteration : 182  ||B r|| = 1.2227e-06
+   Pass :  4   Iteration : 183  ||B r|| = 1.16459e-06
+   Pass :  4   Iteration : 184  ||B r|| = 1.10473e-06
+   Pass :  4   Iteration : 185  ||B r|| = 9.95649e-07
+   Pass :  4   Iteration : 186  ||B r|| = 9.93491e-07
+   Pass :  4   Iteration : 187  ||B r|| = 9.20855e-07
+   Pass :  4   Iteration : 188  ||B r|| = 9.17534e-07
+   Pass :  4   Iteration : 189  ||B r|| = 8.48816e-07
+   Pass :  4   Iteration : 190  ||B r|| = 8.13729e-07
+GMRES+GS converged in 190 iterations with a residual norm of 8.13729e-07.
+GMRES solver took 0.110362s.
+|| q_h - q_ex || / || q_ex || = 1.02359e-06
+|| t_h - t_ex || / || t_ex || = 1.03461e-06

examples/regress_test/p1_o3_dg.txt

@@ -0,0 +1,420 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-hybridization
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2048
+dim(W) = 1024
+dim(V+W) = 3072
+***********************************************************
+Assembly took 0.0167388s.
+Preconditioner took 0.00560065s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.900577
+   Pass :  1   Iteration :   1  ||B r|| = 0.900577
+   Pass :  1   Iteration :   2  ||B r|| = 0.900434
+   Pass :  1   Iteration :   3  ||B r|| = 0.900408
+   Pass :  1   Iteration :   4  ||B r|| = 0.900243
+   Pass :  1   Iteration :   5  ||B r|| = 0.899912
+   Pass :  1   Iteration :   6  ||B r|| = 0.899901
+   Pass :  1   Iteration :   7  ||B r|| = 0.898453
+   Pass :  1   Iteration :   8  ||B r|| = 0.898147
+   Pass :  1   Iteration :   9  ||B r|| = 0.892867
+   Pass :  1   Iteration :  10  ||B r|| = 0.89046
+   Pass :  1   Iteration :  11  ||B r|| = 0.890149
+   Pass :  1   Iteration :  12  ||B r|| = 0.887881
+   Pass :  1   Iteration :  13  ||B r|| = 0.886497
+   Pass :  1   Iteration :  14  ||B r|| = 0.881958
+   Pass :  1   Iteration :  15  ||B r|| = 0.873768
+   Pass :  1   Iteration :  16  ||B r|| = 0.866676
+   Pass :  1   Iteration :  17  ||B r|| = 0.862158
+   Pass :  1   Iteration :  18  ||B r|| = 0.862121
+   Pass :  1   Iteration :  19  ||B r|| = 0.861983
+   Pass :  1   Iteration :  20  ||B r|| = 0.852531
+   Pass :  1   Iteration :  21  ||B r|| = 0.851407
+   Pass :  1   Iteration :  22  ||B r|| = 0.81114
+   Pass :  1   Iteration :  23  ||B r|| = 0.811092
+   Pass :  1   Iteration :  24  ||B r|| = 0.794531
+   Pass :  1   Iteration :  25  ||B r|| = 0.794531
+   Pass :  1   Iteration :  26  ||B r|| = 0.788509
+   Pass :  1   Iteration :  27  ||B r|| = 0.783442
+   Pass :  1   Iteration :  28  ||B r|| = 0.75365
+   Pass :  1   Iteration :  29  ||B r|| = 0.736124
+   Pass :  1   Iteration :  30  ||B r|| = 0.718001
+   Pass :  1   Iteration :  31  ||B r|| = 0.70199
+   Pass :  1   Iteration :  32  ||B r|| = 0.701983
+   Pass :  1   Iteration :  33  ||B r|| = 0.691506
+   Pass :  1   Iteration :  34  ||B r|| = 0.687431
+   Pass :  1   Iteration :  35  ||B r|| = 0.620939
+   Pass :  1   Iteration :  36  ||B r|| = 0.620787
+   Pass :  1   Iteration :  37  ||B r|| = 0.579878
+   Pass :  1   Iteration :  38  ||B r|| = 0.577254
+   Pass :  1   Iteration :  39  ||B r|| = 0.577153
+   Pass :  1   Iteration :  40  ||B r|| = 0.573348
+   Pass :  1   Iteration :  41  ||B r|| = 0.540128
+   Pass :  1   Iteration :  42  ||B r|| = 0.500686
+   Pass :  1   Iteration :  43  ||B r|| = 0.474183
+   Pass :  1   Iteration :  44  ||B r|| = 0.447715
+   Pass :  1   Iteration :  45  ||B r|| = 0.441645
+   Pass :  1   Iteration :  46  ||B r|| = 0.43763
+   Pass :  1   Iteration :  47  ||B r|| = 0.437304
+   Pass :  1   Iteration :  48  ||B r|| = 0.388192
+   Pass :  1   Iteration :  49  ||B r|| = 0.386414
+   Pass :  1   Iteration :  50  ||B r|| = 0.346785
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 0.346783
+   Pass :  2   Iteration :  52  ||B r|| = 0.346753
+   Pass :  2   Iteration :  53  ||B r|| = 0.346725
+   Pass :  2   Iteration :  54  ||B r|| = 0.346369
+   Pass :  2   Iteration :  55  ||B r|| = 0.345779
+   Pass :  2   Iteration :  56  ||B r|| = 0.340784
+   Pass :  2   Iteration :  57  ||B r|| = 0.338059
+   Pass :  2   Iteration :  58  ||B r|| = 0.330718
+   Pass :  2   Iteration :  59  ||B r|| = 0.32847
+   Pass :  2   Iteration :  60  ||B r|| = 0.326365
+   Pass :  2   Iteration :  61  ||B r|| = 0.32017
+   Pass :  2   Iteration :  62  ||B r|| = 0.319864
+   Pass :  2   Iteration :  63  ||B r|| = 0.290191
+   Pass :  2   Iteration :  64  ||B r|| = 0.29019
+   Pass :  2   Iteration :  65  ||B r|| = 0.275545
+   Pass :  2   Iteration :  66  ||B r|| = 0.274977
+   Pass :  2   Iteration :  67  ||B r|| = 0.274975
+   Pass :  2   Iteration :  68  ||B r|| = 0.250095
+   Pass :  2   Iteration :  69  ||B r|| = 0.245757
+   Pass :  2   Iteration :  70  ||B r|| = 0.226498
+   Pass :  2   Iteration :  71  ||B r|| = 0.21832
+   Pass :  2   Iteration :  72  ||B r|| = 0.209813
+   Pass :  2   Iteration :  73  ||B r|| = 0.197498
+   Pass :  2   Iteration :  74  ||B r|| = 0.194375
+   Pass :  2   Iteration :  75  ||B r|| = 0.185865
+   Pass :  2   Iteration :  76  ||B r|| = 0.160081
+   Pass :  2   Iteration :  77  ||B r|| = 0.155704
+   Pass :  2   Iteration :  78  ||B r|| = 0.140027
+   Pass :  2   Iteration :  79  ||B r|| = 0.138448
+   Pass :  2   Iteration :  80  ||B r|| = 0.138139
+   Pass :  2   Iteration :  81  ||B r|| = 0.125615
+   Pass :  2   Iteration :  82  ||B r|| = 0.12453
+   Pass :  2   Iteration :  83  ||B r|| = 0.109713
+   Pass :  2   Iteration :  84  ||B r|| = 0.108677
+   Pass :  2   Iteration :  85  ||B r|| = 0.105206
+   Pass :  2   Iteration :  86  ||B r|| = 0.10045
+   Pass :  2   Iteration :  87  ||B r|| = 0.0995337
+   Pass :  2   Iteration :  88  ||B r|| = 0.0927337
+   Pass :  2   Iteration :  89  ||B r|| = 0.0865765
+   Pass :  2   Iteration :  90  ||B r|| = 0.0836921
+   Pass :  2   Iteration :  91  ||B r|| = 0.0777179
+   Pass :  2   Iteration :  92  ||B r|| = 0.0777125
+   Pass :  2   Iteration :  93  ||B r|| = 0.075328
+   Pass :  2   Iteration :  94  ||B r|| = 0.0698781
+   Pass :  2   Iteration :  95  ||B r|| = 0.0695923
+   Pass :  2   Iteration :  96  ||B r|| = 0.0582517
+   Pass :  2   Iteration :  97  ||B r|| = 0.0578877
+   Pass :  2   Iteration :  98  ||B r|| = 0.0509695
+   Pass :  2   Iteration :  99  ||B r|| = 0.0492122
+   Pass :  2   Iteration : 100  ||B r|| = 0.049119
+Restarting...
+   Pass :  3   Iteration : 101  ||B r|| = 0.0491174
+   Pass :  3   Iteration : 102  ||B r|| = 0.048935
+   Pass :  3   Iteration : 103  ||B r|| = 0.0487952
+   Pass :  3   Iteration : 104  ||B r|| = 0.048271
+   Pass :  3   Iteration : 105  ||B r|| = 0.0456151
+   Pass :  3   Iteration : 106  ||B r|| = 0.0420326
+   Pass :  3   Iteration : 107  ||B r|| = 0.0405407
+   Pass :  3   Iteration : 108  ||B r|| = 0.0376982
+   Pass :  3   Iteration : 109  ||B r|| = 0.0374234
+   Pass :  3   Iteration : 110  ||B r|| = 0.0359602
+   Pass :  3   Iteration : 111  ||B r|| = 0.0336756
+   Pass :  3   Iteration : 112  ||B r|| = 0.0331036
+   Pass :  3   Iteration : 113  ||B r|| = 0.0304233
+   Pass :  3   Iteration : 114  ||B r|| = 0.0303832
+   Pass :  3   Iteration : 115  ||B r|| = 0.0290383
+   Pass :  3   Iteration : 116  ||B r|| = 0.0270094
+   Pass :  3   Iteration : 117  ||B r|| = 0.0269671
+   Pass :  3   Iteration : 118  ||B r|| = 0.0234557
+   Pass :  3   Iteration : 119  ||B r|| = 0.0233749
+   Pass :  3   Iteration : 120  ||B r|| = 0.0222709
+   Pass :  3   Iteration : 121  ||B r|| = 0.0210607
+   Pass :  3   Iteration : 122  ||B r|| = 0.0210189
+   Pass :  3   Iteration : 123  ||B r|| = 0.019523
+   Pass :  3   Iteration : 124  ||B r|| = 0.0190986
+   Pass :  3   Iteration : 125  ||B r|| = 0.0182602
+   Pass :  3   Iteration : 126  ||B r|| = 0.0165908
+   Pass :  3   Iteration : 127  ||B r|| = 0.0165826
+   Pass :  3   Iteration : 128  ||B r|| = 0.0155958
+   Pass :  3   Iteration : 129  ||B r|| = 0.0149154
+   Pass :  3   Iteration : 130  ||B r|| = 0.0148837
+   Pass :  3   Iteration : 131  ||B r|| = 0.0133188
+   Pass :  3   Iteration : 132  ||B r|| = 0.0133041
+   Pass :  3   Iteration : 133  ||B r|| = 0.0126119
+   Pass :  3   Iteration : 134  ||B r|| = 0.012336
+   Pass :  3   Iteration : 135  ||B r|| = 0.0123217
+   Pass :  3   Iteration : 136  ||B r|| = 0.0111051
+   Pass :  3   Iteration : 137  ||B r|| = 0.0110814
+   Pass :  3   Iteration : 138  ||B r|| = 0.0105874
+   Pass :  3   Iteration : 139  ||B r|| = 0.0104149
+   Pass :  3   Iteration : 140  ||B r|| = 0.0104149
+   Pass :  3   Iteration : 141  ||B r|| = 0.00988104
+   Pass :  3   Iteration : 142  ||B r|| = 0.00946548
+   Pass :  3   Iteration : 143  ||B r|| = 0.00898965
+   Pass :  3   Iteration : 144  ||B r|| = 0.00849411
+   Pass :  3   Iteration : 145  ||B r|| = 0.00847611
+   Pass :  3   Iteration : 146  ||B r|| = 0.00791422
+   Pass :  3   Iteration : 147  ||B r|| = 0.00760638
+   Pass :  3   Iteration : 148  ||B r|| = 0.00739417
+   Pass :  3   Iteration : 149  ||B r|| = 0.00658704
+   Pass :  3   Iteration : 150  ||B r|| = 0.00657621
+Restarting...
+   Pass :  4   Iteration : 151  ||B r|| = 0.00657611
+   Pass :  4   Iteration : 152  ||B r|| = 0.00631889
+   Pass :  4   Iteration : 153  ||B r|| = 0.00630107
+   Pass :  4   Iteration : 154  ||B r|| = 0.00628496
+   Pass :  4   Iteration : 155  ||B r|| = 0.00581361
+   Pass :  4   Iteration : 156  ||B r|| = 0.00572566
+   Pass :  4   Iteration : 157  ||B r|| = 0.00558237
+   Pass :  4   Iteration : 158  ||B r|| = 0.00520369
+   Pass :  4   Iteration : 159  ||B r|| = 0.0052025
+   Pass :  4   Iteration : 160  ||B r|| = 0.00487642
+   Pass :  4   Iteration : 161  ||B r|| = 0.00479177
+   Pass :  4   Iteration : 162  ||B r|| = 0.00468477
+   Pass :  4   Iteration : 163  ||B r|| = 0.00440739
+   Pass :  4   Iteration : 164  ||B r|| = 0.00440725
+   Pass :  4   Iteration : 165  ||B r|| = 0.00415237
+   Pass :  4   Iteration : 166  ||B r|| = 0.00404373
+   Pass :  4   Iteration : 167  ||B r|| = 0.00399217
+   Pass :  4   Iteration : 168  ||B r|| = 0.00361744
+   Pass :  4   Iteration : 169  ||B r|| = 0.00361199
+   Pass :  4   Iteration : 170  ||B r|| = 0.00342198
+   Pass :  4   Iteration : 171  ||B r|| = 0.00332275
+   Pass :  4   Iteration : 172  ||B r|| = 0.00328849
+   Pass :  4   Iteration : 173  ||B r|| = 0.00301807
+   Pass :  4   Iteration : 174  ||B r|| = 0.00297077
+   Pass :  4   Iteration : 175  ||B r|| = 0.00278725
+   Pass :  4   Iteration : 176  ||B r|| = 0.00265647
+   Pass :  4   Iteration : 177  ||B r|| = 0.00265138
+   Pass :  4   Iteration : 178  ||B r|| = 0.00249713
+   Pass :  4   Iteration : 179  ||B r|| = 0.0024458
+   Pass :  4   Iteration : 180  ||B r|| = 0.00226749
+   Pass :  4   Iteration : 181  ||B r|| = 0.00211128
+   Pass :  4   Iteration : 182  ||B r|| = 0.00209348
+   Pass :  4   Iteration : 183  ||B r|| = 0.00199424
+   Pass :  4   Iteration : 184  ||B r|| = 0.00190927
+   Pass :  4   Iteration : 185  ||B r|| = 0.00186211
+   Pass :  4   Iteration : 186  ||B r|| = 0.00157145
+   Pass :  4   Iteration : 187  ||B r|| = 0.00157142
+   Pass :  4   Iteration : 188  ||B r|| = 0.00141191
+   Pass :  4   Iteration : 189  ||B r|| = 0.00136095
+   Pass :  4   Iteration : 190  ||B r|| = 0.00133934
+   Pass :  4   Iteration : 191  ||B r|| = 0.00123125
+   Pass :  4   Iteration : 192  ||B r|| = 0.00122694
+   Pass :  4   Iteration : 193  ||B r|| = 0.00112965
+   Pass :  4   Iteration : 194  ||B r|| = 0.00106884
+   Pass :  4   Iteration : 195  ||B r|| = 0.00106156
+   Pass :  4   Iteration : 196  ||B r|| = 0.000979129
+   Pass :  4   Iteration : 197  ||B r|| = 0.000974447
+   Pass :  4   Iteration : 198  ||B r|| = 0.000913577
+   Pass :  4   Iteration : 199  ||B r|| = 0.000824117
+   Pass :  4   Iteration : 200  ||B r|| = 0.000819664
+Restarting...
+   Pass :  5   Iteration : 201  ||B r|| = 0.000819566
+   Pass :  5   Iteration : 202  ||B r|| = 0.000802101
+   Pass :  5   Iteration : 203  ||B r|| = 0.000793705
+   Pass :  5   Iteration : 204  ||B r|| = 0.000779788
+   Pass :  5   Iteration : 205  ||B r|| = 0.000730173
+   Pass :  5   Iteration : 206  ||B r|| = 0.000710072
+   Pass :  5   Iteration : 207  ||B r|| = 0.000686091
+   Pass :  5   Iteration : 208  ||B r|| = 0.000635314
+   Pass :  5   Iteration : 209  ||B r|| = 0.000635226
+   Pass :  5   Iteration : 210  ||B r|| = 0.000604069
+   Pass :  5   Iteration : 211  ||B r|| = 0.000565668
+   Pass :  5   Iteration : 212  ||B r|| = 0.000557792
+   Pass :  5   Iteration : 213  ||B r|| = 0.000515749
+   Pass :  5   Iteration : 214  ||B r|| = 0.000513034
+   Pass :  5   Iteration : 215  ||B r|| = 0.000481894
+   Pass :  5   Iteration : 216  ||B r|| = 0.000451544
+   Pass :  5   Iteration : 217  ||B r|| = 0.00044852
+   Pass :  5   Iteration : 218  ||B r|| = 0.000393422
+   Pass :  5   Iteration : 219  ||B r|| = 0.000381413
+   Pass :  5   Iteration : 220  ||B r|| = 0.000361236
+   Pass :  5   Iteration : 221  ||B r|| = 0.000336538
+   Pass :  5   Iteration : 222  ||B r|| = 0.000336118
+   Pass :  5   Iteration : 223  ||B r|| = 0.000320216
+   Pass :  5   Iteration : 224  ||B r|| = 0.000311681
+   Pass :  5   Iteration : 225  ||B r|| = 0.000300208
+   Pass :  5   Iteration : 226  ||B r|| = 0.000280096
+   Pass :  5   Iteration : 227  ||B r|| = 0.000280017
+   Pass :  5   Iteration : 228  ||B r|| = 0.000265884
+   Pass :  5   Iteration : 229  ||B r|| = 0.000254531
+   Pass :  5   Iteration : 230  ||B r|| = 0.000253443
+   Pass :  5   Iteration : 231  ||B r|| = 0.000232182
+   Pass :  5   Iteration : 232  ||B r|| = 0.000231948
+   Pass :  5   Iteration : 233  ||B r|| = 0.000219717
+   Pass :  5   Iteration : 234  ||B r|| = 0.000210106
+   Pass :  5   Iteration : 235  ||B r|| = 0.000208378
+   Pass :  5   Iteration : 236  ||B r|| = 0.000192791
+   Pass :  5   Iteration : 237  ||B r|| = 0.000191389
+   Pass :  5   Iteration : 238  ||B r|| = 0.000181136
+   Pass :  5   Iteration : 239  ||B r|| = 0.000173082
+   Pass :  5   Iteration : 240  ||B r|| = 0.000172178
+   Pass :  5   Iteration : 241  ||B r|| = 0.000163582
+   Pass :  5   Iteration : 242  ||B r|| = 0.000160314
+   Pass :  5   Iteration : 243  ||B r|| = 0.000154194
+   Pass :  5   Iteration : 244  ||B r|| = 0.000142641
+   Pass :  5   Iteration : 245  ||B r|| = 0.000142245
+   Pass :  5   Iteration : 246  ||B r|| = 0.000135685
+   Pass :  5   Iteration : 247  ||B r|| = 0.000134161
+   Pass :  5   Iteration : 248  ||B r|| = 0.00013191
+   Pass :  5   Iteration : 249  ||B r|| = 0.00011789
+   Pass :  5   Iteration : 250  ||B r|| = 0.000117448
+Restarting...
+   Pass :  6   Iteration : 251  ||B r|| = 0.000117443
+   Pass :  6   Iteration : 252  ||B r|| = 0.000111241
+   Pass :  6   Iteration : 253  ||B r|| = 0.000111092
+   Pass :  6   Iteration : 254  ||B r|| = 0.000111075
+   Pass :  6   Iteration : 255  ||B r|| = 0.000101403
+   Pass :  6   Iteration : 256  ||B r|| = 0.000100984
+   Pass :  6   Iteration : 257  ||B r|| = 9.60892e-05
+   Pass :  6   Iteration : 258  ||B r|| = 9.16341e-05
+   Pass :  6   Iteration : 259  ||B r|| = 9.1184e-05
+   Pass :  6   Iteration : 260  ||B r|| = 8.57519e-05
+   Pass :  6   Iteration : 261  ||B r|| = 8.49038e-05
+   Pass :  6   Iteration : 262  ||B r|| = 8.25868e-05
+   Pass :  6   Iteration : 263  ||B r|| = 7.84909e-05
+   Pass :  6   Iteration : 264  ||B r|| = 7.84882e-05
+   Pass :  6   Iteration : 265  ||B r|| = 7.17122e-05
+   Pass :  6   Iteration : 266  ||B r|| = 7.06387e-05
+   Pass :  6   Iteration : 267  ||B r|| = 6.88435e-05
+   Pass :  6   Iteration : 268  ||B r|| = 6.51125e-05
+   Pass :  6   Iteration : 269  ||B r|| = 6.51119e-05
+   Pass :  6   Iteration : 270  ||B r|| = 6.11726e-05
+   Pass :  6   Iteration : 271  ||B r|| = 5.95685e-05
+   Pass :  6   Iteration : 272  ||B r|| = 5.69221e-05
+   Pass :  6   Iteration : 273  ||B r|| = 5.31348e-05
+   Pass :  6   Iteration : 274  ||B r|| = 5.29896e-05
+   Pass :  6   Iteration : 275  ||B r|| = 5.06603e-05
+   Pass :  6   Iteration : 276  ||B r|| = 4.77003e-05
+   Pass :  6   Iteration : 277  ||B r|| = 4.69104e-05
+   Pass :  6   Iteration : 278  ||B r|| = 4.35213e-05
+   Pass :  6   Iteration : 279  ||B r|| = 4.34584e-05
+   Pass :  6   Iteration : 280  ||B r|| = 4.13801e-05
+   Pass :  6   Iteration : 281  ||B r|| = 3.80137e-05
+   Pass :  6   Iteration : 282  ||B r|| = 3.73519e-05
+   Pass :  6   Iteration : 283  ||B r|| = 3.40659e-05
+   Pass :  6   Iteration : 284  ||B r|| = 3.35469e-05
+   Pass :  6   Iteration : 285  ||B r|| = 3.24228e-05
+   Pass :  6   Iteration : 286  ||B r|| = 2.82691e-05
+   Pass :  6   Iteration : 287  ||B r|| = 2.82415e-05
+   Pass :  6   Iteration : 288  ||B r|| = 2.4949e-05
+   Pass :  6   Iteration : 289  ||B r|| = 2.42639e-05
+   Pass :  6   Iteration : 290  ||B r|| = 2.35408e-05
+   Pass :  6   Iteration : 291  ||B r|| = 2.19407e-05
+   Pass :  6   Iteration : 292  ||B r|| = 2.19132e-05
+   Pass :  6   Iteration : 293  ||B r|| = 2.03845e-05
+   Pass :  6   Iteration : 294  ||B r|| = 1.92894e-05
+   Pass :  6   Iteration : 295  ||B r|| = 1.89518e-05
+   Pass :  6   Iteration : 296  ||B r|| = 1.72028e-05
+   Pass :  6   Iteration : 297  ||B r|| = 1.71928e-05
+   Pass :  6   Iteration : 298  ||B r|| = 1.63643e-05
+   Pass :  6   Iteration : 299  ||B r|| = 1.56163e-05
+   Pass :  6   Iteration : 300  ||B r|| = 1.54755e-05
+Restarting...
+   Pass :  7   Iteration : 301  ||B r|| = 1.54724e-05
+   Pass :  7   Iteration : 302  ||B r|| = 1.53376e-05
+   Pass :  7   Iteration : 303  ||B r|| = 1.50205e-05
+   Pass :  7   Iteration : 304  ||B r|| = 1.47195e-05
+   Pass :  7   Iteration : 305  ||B r|| = 1.34414e-05
+   Pass :  7   Iteration : 306  ||B r|| = 1.30372e-05
+   Pass :  7   Iteration : 307  ||B r|| = 1.26163e-05
+   Pass :  7   Iteration : 308  ||B r|| = 1.17954e-05
+   Pass :  7   Iteration : 309  ||B r|| = 1.17113e-05
+   Pass :  7   Iteration : 310  ||B r|| = 1.12938e-05
+   Pass :  7   Iteration : 311  ||B r|| = 1.04865e-05
+   Pass :  7   Iteration : 312  ||B r|| = 1.03571e-05
+   Pass :  7   Iteration : 313  ||B r|| = 9.56454e-06
+   Pass :  7   Iteration : 314  ||B r|| = 9.44709e-06
+   Pass :  7   Iteration : 315  ||B r|| = 9.02016e-06
+   Pass :  7   Iteration : 316  ||B r|| = 8.27621e-06
+   Pass :  7   Iteration : 317  ||B r|| = 8.26159e-06
+   Pass :  7   Iteration : 318  ||B r|| = 7.18002e-06
+   Pass :  7   Iteration : 319  ||B r|| = 6.95003e-06
+   Pass :  7   Iteration : 320  ||B r|| = 6.73497e-06
+   Pass :  7   Iteration : 321  ||B r|| = 6.25227e-06
+   Pass :  7   Iteration : 322  ||B r|| = 6.24358e-06
+   Pass :  7   Iteration : 323  ||B r|| = 5.90685e-06
+   Pass :  7   Iteration : 324  ||B r|| = 5.69217e-06
+   Pass :  7   Iteration : 325  ||B r|| = 5.59816e-06
+   Pass :  7   Iteration : 326  ||B r|| = 5.19767e-06
+   Pass :  7   Iteration : 327  ||B r|| = 5.18732e-06
+   Pass :  7   Iteration : 328  ||B r|| = 4.978e-06
+   Pass :  7   Iteration : 329  ||B r|| = 4.61108e-06
+   Pass :  7   Iteration : 330  ||B r|| = 4.60926e-06
+   Pass :  7   Iteration : 331  ||B r|| = 4.23343e-06
+   Pass :  7   Iteration : 332  ||B r|| = 4.23029e-06
+   Pass :  7   Iteration : 333  ||B r|| = 4.01039e-06
+   Pass :  7   Iteration : 334  ||B r|| = 3.86812e-06
+   Pass :  7   Iteration : 335  ||B r|| = 3.86282e-06
+   Pass :  7   Iteration : 336  ||B r|| = 3.60676e-06
+   Pass :  7   Iteration : 337  ||B r|| = 3.53527e-06
+   Pass :  7   Iteration : 338  ||B r|| = 3.33113e-06
+   Pass :  7   Iteration : 339  ||B r|| = 3.15944e-06
+   Pass :  7   Iteration : 340  ||B r|| = 3.14716e-06
+   Pass :  7   Iteration : 341  ||B r|| = 2.97802e-06
+   Pass :  7   Iteration : 342  ||B r|| = 2.95139e-06
+   Pass :  7   Iteration : 343  ||B r|| = 2.86922e-06
+   Pass :  7   Iteration : 344  ||B r|| = 2.65035e-06
+   Pass :  7   Iteration : 345  ||B r|| = 2.64952e-06
+   Pass :  7   Iteration : 346  ||B r|| = 2.48989e-06
+   Pass :  7   Iteration : 347  ||B r|| = 2.42609e-06
+   Pass :  7   Iteration : 348  ||B r|| = 2.35361e-06
+   Pass :  7   Iteration : 349  ||B r|| = 2.0977e-06
+   Pass :  7   Iteration : 350  ||B r|| = 2.0743e-06
+Restarting...
+   Pass :  8   Iteration : 351  ||B r|| = 2.074e-06
+   Pass :  8   Iteration : 352  ||B r|| = 1.9458e-06
+   Pass :  8   Iteration : 353  ||B r|| = 1.91268e-06
+   Pass :  8   Iteration : 354  ||B r|| = 1.9109e-06
+   Pass :  8   Iteration : 355  ||B r|| = 1.71169e-06
+   Pass :  8   Iteration : 356  ||B r|| = 1.70656e-06
+   Pass :  8   Iteration : 357  ||B r|| = 1.61858e-06
+   Pass :  8   Iteration : 358  ||B r|| = 1.53201e-06
+   Pass :  8   Iteration : 359  ||B r|| = 1.52511e-06
+   Pass :  8   Iteration : 360  ||B r|| = 1.4294e-06
+   Pass :  8   Iteration : 361  ||B r|| = 1.40067e-06
+   Pass :  8   Iteration : 362  ||B r|| = 1.35966e-06
+   Pass :  8   Iteration : 363  ||B r|| = 1.29997e-06
+   Pass :  8   Iteration : 364  ||B r|| = 1.29896e-06
+   Pass :  8   Iteration : 365  ||B r|| = 1.192e-06
+   Pass :  8   Iteration : 366  ||B r|| = 1.17842e-06
+   Pass :  8   Iteration : 367  ||B r|| = 1.14545e-06
+   Pass :  8   Iteration : 368  ||B r|| = 1.08481e-06
+   Pass :  8   Iteration : 369  ||B r|| = 1.08408e-06
+   Pass :  8   Iteration : 370  ||B r|| = 1.01158e-06
+   Pass :  8   Iteration : 371  ||B r|| = 9.87365e-07
+   Pass :  8   Iteration : 372  ||B r|| = 9.53571e-07
+   Pass :  8   Iteration : 373  ||B r|| = 9.02865e-07
+   Pass :  8   Iteration : 374  ||B r|| = 9.02529e-07
+   Pass :  8   Iteration : 375  ||B r|| = 8.35677e-07
+GMRES+GS converged in 375 iterations with a residual norm of 8.35677e-07.
+GMRES solver took 0.203855s.
+|| q_h - q_ex || / || q_ex || = 5.07159e-05
+|| t_h - t_ex || / || t_ex || = 2.61662e-05

examples/regress_test/p1_o3_dg_hb.txt

@@ -0,0 +1,60 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --hybridization
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2048
+dim(W) = 1024
+dim(V+W) = 3072
+***********************************************************
+Assembly took 0.0120309s.
+Preconditioner took 9.286e-06s.
+   Pass :  1   Iteration :   0  ||B r|| = 1.96731
+   Pass :  1   Iteration :   1  ||B r|| = 1.24082
+   Pass :  1   Iteration :   2  ||B r|| = 0.785152
+   Pass :  1   Iteration :   3  ||B r|| = 0.612962
+   Pass :  1   Iteration :   4  ||B r|| = 0.444865
+   Pass :  1   Iteration :   5  ||B r|| = 0.308536
+   Pass :  1   Iteration :   6  ||B r|| = 0.181062
+   Pass :  1   Iteration :   7  ||B r|| = 0.0872824
+   Pass :  1   Iteration :   8  ||B r|| = 0.048816
+   Pass :  1   Iteration :   9  ||B r|| = 0.0234022
+   Pass :  1   Iteration :  10  ||B r|| = 0.0119249
+   Pass :  1   Iteration :  11  ||B r|| = 0.00419618
+   Pass :  1   Iteration :  12  ||B r|| = 0.00219869
+   Pass :  1   Iteration :  13  ||B r|| = 0.00115642
+   Pass :  1   Iteration :  14  ||B r|| = 0.000637756
+   Pass :  1   Iteration :  15  ||B r|| = 0.000297414
+   Pass :  1   Iteration :  16  ||B r|| = 0.000196751
+   Pass :  1   Iteration :  17  ||B r|| = 0.000123272
+   Pass :  1   Iteration :  18  ||B r|| = 6.14247e-05
+   Pass :  1   Iteration :  19  ||B r|| = 2.32696e-05
+   Pass :  1   Iteration :  20  ||B r|| = 1.13978e-05
+   Pass :  1   Iteration :  21  ||B r|| = 4.39964e-06
+   Pass :  1   Iteration :  22  ||B r|| = 1.71455e-06
+GMRES+GS converged in 22 iterations with a residual norm of 1.71455e-06.
+GMRES solver took 0.00161297s.
+|| q_h - q_ex || / || q_ex || = 1.03793e-05
+|| t_h - t_ex || / || t_ex || = 1.12283e-05

examples/regress_test/p1_o3_dg_nl.txt

@@ -0,0 +1,424 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --hdg_scheme 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2048
+dim(W) = 1024
+dim(V+W) = 3072
+***********************************************************
+Assembly took 0.113936s.
+Preconditioner took 0.0180309s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.900577
+   Pass :  1   Iteration :   1  ||B r|| = 0.900577
+   Pass :  1   Iteration :   2  ||B r|| = 0.900434
+   Pass :  1   Iteration :   3  ||B r|| = 0.900408
+   Pass :  1   Iteration :   4  ||B r|| = 0.900243
+   Pass :  1   Iteration :   5  ||B r|| = 0.899912
+   Pass :  1   Iteration :   6  ||B r|| = 0.899901
+   Pass :  1   Iteration :   7  ||B r|| = 0.898453
+   Pass :  1   Iteration :   8  ||B r|| = 0.898147
+   Pass :  1   Iteration :   9  ||B r|| = 0.892867
+   Pass :  1   Iteration :  10  ||B r|| = 0.89046
+   Pass :  1   Iteration :  11  ||B r|| = 0.890149
+   Pass :  1   Iteration :  12  ||B r|| = 0.887881
+   Pass :  1   Iteration :  13  ||B r|| = 0.886497
+   Pass :  1   Iteration :  14  ||B r|| = 0.881958
+   Pass :  1   Iteration :  15  ||B r|| = 0.873768
+   Pass :  1   Iteration :  16  ||B r|| = 0.866676
+   Pass :  1   Iteration :  17  ||B r|| = 0.862158
+   Pass :  1   Iteration :  18  ||B r|| = 0.862121
+   Pass :  1   Iteration :  19  ||B r|| = 0.861983
+   Pass :  1   Iteration :  20  ||B r|| = 0.852531
+   Pass :  1   Iteration :  21  ||B r|| = 0.851407
+   Pass :  1   Iteration :  22  ||B r|| = 0.81114
+   Pass :  1   Iteration :  23  ||B r|| = 0.811092
+   Pass :  1   Iteration :  24  ||B r|| = 0.794531
+   Pass :  1   Iteration :  25  ||B r|| = 0.794531
+   Pass :  1   Iteration :  26  ||B r|| = 0.788509
+   Pass :  1   Iteration :  27  ||B r|| = 0.783442
+   Pass :  1   Iteration :  28  ||B r|| = 0.75365
+   Pass :  1   Iteration :  29  ||B r|| = 0.736124
+   Pass :  1   Iteration :  30  ||B r|| = 0.718001
+   Pass :  1   Iteration :  31  ||B r|| = 0.70199
+   Pass :  1   Iteration :  32  ||B r|| = 0.701983
+   Pass :  1   Iteration :  33  ||B r|| = 0.691506
+   Pass :  1   Iteration :  34  ||B r|| = 0.687431
+   Pass :  1   Iteration :  35  ||B r|| = 0.620939
+   Pass :  1   Iteration :  36  ||B r|| = 0.620787
+   Pass :  1   Iteration :  37  ||B r|| = 0.579878
+   Pass :  1   Iteration :  38  ||B r|| = 0.577254
+   Pass :  1   Iteration :  39  ||B r|| = 0.577153
+   Pass :  1   Iteration :  40  ||B r|| = 0.573348
+   Pass :  1   Iteration :  41  ||B r|| = 0.540128
+   Pass :  1   Iteration :  42  ||B r|| = 0.500686
+   Pass :  1   Iteration :  43  ||B r|| = 0.474183
+   Pass :  1   Iteration :  44  ||B r|| = 0.447715
+   Pass :  1   Iteration :  45  ||B r|| = 0.441645
+   Pass :  1   Iteration :  46  ||B r|| = 0.43763
+   Pass :  1   Iteration :  47  ||B r|| = 0.437304
+   Pass :  1   Iteration :  48  ||B r|| = 0.388192
+   Pass :  1   Iteration :  49  ||B r|| = 0.386414
+   Pass :  1   Iteration :  50  ||B r|| = 0.346785
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 0.346783
+   Pass :  2   Iteration :  52  ||B r|| = 0.346753
+   Pass :  2   Iteration :  53  ||B r|| = 0.346725
+   Pass :  2   Iteration :  54  ||B r|| = 0.346369
+   Pass :  2   Iteration :  55  ||B r|| = 0.345779
+   Pass :  2   Iteration :  56  ||B r|| = 0.340784
+   Pass :  2   Iteration :  57  ||B r|| = 0.338059
+   Pass :  2   Iteration :  58  ||B r|| = 0.330718
+   Pass :  2   Iteration :  59  ||B r|| = 0.32847
+   Pass :  2   Iteration :  60  ||B r|| = 0.326365
+   Pass :  2   Iteration :  61  ||B r|| = 0.32017
+   Pass :  2   Iteration :  62  ||B r|| = 0.319864
+   Pass :  2   Iteration :  63  ||B r|| = 0.290191
+   Pass :  2   Iteration :  64  ||B r|| = 0.29019
+   Pass :  2   Iteration :  65  ||B r|| = 0.275545
+   Pass :  2   Iteration :  66  ||B r|| = 0.274977
+   Pass :  2   Iteration :  67  ||B r|| = 0.274975
+   Pass :  2   Iteration :  68  ||B r|| = 0.250095
+   Pass :  2   Iteration :  69  ||B r|| = 0.245757
+   Pass :  2   Iteration :  70  ||B r|| = 0.226498
+   Pass :  2   Iteration :  71  ||B r|| = 0.21832
+   Pass :  2   Iteration :  72  ||B r|| = 0.209813
+   Pass :  2   Iteration :  73  ||B r|| = 0.197498
+   Pass :  2   Iteration :  74  ||B r|| = 0.194375
+   Pass :  2   Iteration :  75  ||B r|| = 0.185865
+   Pass :  2   Iteration :  76  ||B r|| = 0.160081
+   Pass :  2   Iteration :  77  ||B r|| = 0.155704
+   Pass :  2   Iteration :  78  ||B r|| = 0.140027
+   Pass :  2   Iteration :  79  ||B r|| = 0.138448
+   Pass :  2   Iteration :  80  ||B r|| = 0.138139
+   Pass :  2   Iteration :  81  ||B r|| = 0.125615
+   Pass :  2   Iteration :  82  ||B r|| = 0.12453
+   Pass :  2   Iteration :  83  ||B r|| = 0.109713
+   Pass :  2   Iteration :  84  ||B r|| = 0.108677
+   Pass :  2   Iteration :  85  ||B r|| = 0.105206
+   Pass :  2   Iteration :  86  ||B r|| = 0.10045
+   Pass :  2   Iteration :  87  ||B r|| = 0.0995337
+   Pass :  2   Iteration :  88  ||B r|| = 0.0927337
+   Pass :  2   Iteration :  89  ||B r|| = 0.0865765
+   Pass :  2   Iteration :  90  ||B r|| = 0.0836921
+   Pass :  2   Iteration :  91  ||B r|| = 0.0777179
+   Pass :  2   Iteration :  92  ||B r|| = 0.0777125
+   Pass :  2   Iteration :  93  ||B r|| = 0.075328
+   Pass :  2   Iteration :  94  ||B r|| = 0.0698781
+   Pass :  2   Iteration :  95  ||B r|| = 0.0695923
+   Pass :  2   Iteration :  96  ||B r|| = 0.0582517
+   Pass :  2   Iteration :  97  ||B r|| = 0.0578877
+   Pass :  2   Iteration :  98  ||B r|| = 0.0509695
+   Pass :  2   Iteration :  99  ||B r|| = 0.0492122
+   Pass :  2   Iteration : 100  ||B r|| = 0.049119
+Restarting...
+   Pass :  3   Iteration : 101  ||B r|| = 0.0491174
+   Pass :  3   Iteration : 102  ||B r|| = 0.048935
+   Pass :  3   Iteration : 103  ||B r|| = 0.0487952
+   Pass :  3   Iteration : 104  ||B r|| = 0.048271
+   Pass :  3   Iteration : 105  ||B r|| = 0.0456151
+   Pass :  3   Iteration : 106  ||B r|| = 0.0420326
+   Pass :  3   Iteration : 107  ||B r|| = 0.0405407
+   Pass :  3   Iteration : 108  ||B r|| = 0.0376982
+   Pass :  3   Iteration : 109  ||B r|| = 0.0374234
+   Pass :  3   Iteration : 110  ||B r|| = 0.0359602
+   Pass :  3   Iteration : 111  ||B r|| = 0.0336756
+   Pass :  3   Iteration : 112  ||B r|| = 0.0331036
+   Pass :  3   Iteration : 113  ||B r|| = 0.0304233
+   Pass :  3   Iteration : 114  ||B r|| = 0.0303832
+   Pass :  3   Iteration : 115  ||B r|| = 0.0290383
+   Pass :  3   Iteration : 116  ||B r|| = 0.0270094
+   Pass :  3   Iteration : 117  ||B r|| = 0.0269671
+   Pass :  3   Iteration : 118  ||B r|| = 0.0234557
+   Pass :  3   Iteration : 119  ||B r|| = 0.0233749
+   Pass :  3   Iteration : 120  ||B r|| = 0.0222709
+   Pass :  3   Iteration : 121  ||B r|| = 0.0210607
+   Pass :  3   Iteration : 122  ||B r|| = 0.0210189
+   Pass :  3   Iteration : 123  ||B r|| = 0.019523
+   Pass :  3   Iteration : 124  ||B r|| = 0.0190986
+   Pass :  3   Iteration : 125  ||B r|| = 0.0182602
+   Pass :  3   Iteration : 126  ||B r|| = 0.0165908
+   Pass :  3   Iteration : 127  ||B r|| = 0.0165826
+   Pass :  3   Iteration : 128  ||B r|| = 0.0155958
+   Pass :  3   Iteration : 129  ||B r|| = 0.0149154
+   Pass :  3   Iteration : 130  ||B r|| = 0.0148837
+   Pass :  3   Iteration : 131  ||B r|| = 0.0133188
+   Pass :  3   Iteration : 132  ||B r|| = 0.0133041
+   Pass :  3   Iteration : 133  ||B r|| = 0.0126119
+   Pass :  3   Iteration : 134  ||B r|| = 0.012336
+   Pass :  3   Iteration : 135  ||B r|| = 0.0123217
+   Pass :  3   Iteration : 136  ||B r|| = 0.0111051
+   Pass :  3   Iteration : 137  ||B r|| = 0.0110814
+   Pass :  3   Iteration : 138  ||B r|| = 0.0105874
+   Pass :  3   Iteration : 139  ||B r|| = 0.0104149
+   Pass :  3   Iteration : 140  ||B r|| = 0.0104149
+   Pass :  3   Iteration : 141  ||B r|| = 0.00988104
+   Pass :  3   Iteration : 142  ||B r|| = 0.00946548
+   Pass :  3   Iteration : 143  ||B r|| = 0.00898965
+   Pass :  3   Iteration : 144  ||B r|| = 0.00849411
+   Pass :  3   Iteration : 145  ||B r|| = 0.00847611
+   Pass :  3   Iteration : 146  ||B r|| = 0.00791422
+   Pass :  3   Iteration : 147  ||B r|| = 0.00760638
+   Pass :  3   Iteration : 148  ||B r|| = 0.00739417
+   Pass :  3   Iteration : 149  ||B r|| = 0.00658704
+   Pass :  3   Iteration : 150  ||B r|| = 0.00657621
+Restarting...
+   Pass :  4   Iteration : 151  ||B r|| = 0.00657611
+   Pass :  4   Iteration : 152  ||B r|| = 0.00631889
+   Pass :  4   Iteration : 153  ||B r|| = 0.00630107
+   Pass :  4   Iteration : 154  ||B r|| = 0.00628496
+   Pass :  4   Iteration : 155  ||B r|| = 0.00581361
+   Pass :  4   Iteration : 156  ||B r|| = 0.00572566
+   Pass :  4   Iteration : 157  ||B r|| = 0.00558237
+   Pass :  4   Iteration : 158  ||B r|| = 0.00520369
+   Pass :  4   Iteration : 159  ||B r|| = 0.0052025
+   Pass :  4   Iteration : 160  ||B r|| = 0.00487642
+   Pass :  4   Iteration : 161  ||B r|| = 0.00479177
+   Pass :  4   Iteration : 162  ||B r|| = 0.00468477
+   Pass :  4   Iteration : 163  ||B r|| = 0.00440739
+   Pass :  4   Iteration : 164  ||B r|| = 0.00440725
+   Pass :  4   Iteration : 165  ||B r|| = 0.00415237
+   Pass :  4   Iteration : 166  ||B r|| = 0.00404373
+   Pass :  4   Iteration : 167  ||B r|| = 0.00399217
+   Pass :  4   Iteration : 168  ||B r|| = 0.00361744
+   Pass :  4   Iteration : 169  ||B r|| = 0.00361199
+   Pass :  4   Iteration : 170  ||B r|| = 0.00342198
+   Pass :  4   Iteration : 171  ||B r|| = 0.00332275
+   Pass :  4   Iteration : 172  ||B r|| = 0.00328849
+   Pass :  4   Iteration : 173  ||B r|| = 0.00301807
+   Pass :  4   Iteration : 174  ||B r|| = 0.00297077
+   Pass :  4   Iteration : 175  ||B r|| = 0.00278725
+   Pass :  4   Iteration : 176  ||B r|| = 0.00265647
+   Pass :  4   Iteration : 177  ||B r|| = 0.00265138
+   Pass :  4   Iteration : 178  ||B r|| = 0.00249713
+   Pass :  4   Iteration : 179  ||B r|| = 0.0024458
+   Pass :  4   Iteration : 180  ||B r|| = 0.00226749
+   Pass :  4   Iteration : 181  ||B r|| = 0.00211128
+   Pass :  4   Iteration : 182  ||B r|| = 0.00209348
+   Pass :  4   Iteration : 183  ||B r|| = 0.00199424
+   Pass :  4   Iteration : 184  ||B r|| = 0.00190927
+   Pass :  4   Iteration : 185  ||B r|| = 0.00186211
+   Pass :  4   Iteration : 186  ||B r|| = 0.00157145
+   Pass :  4   Iteration : 187  ||B r|| = 0.00157142
+   Pass :  4   Iteration : 188  ||B r|| = 0.00141191
+   Pass :  4   Iteration : 189  ||B r|| = 0.00136095
+   Pass :  4   Iteration : 190  ||B r|| = 0.00133934
+   Pass :  4   Iteration : 191  ||B r|| = 0.00123125
+   Pass :  4   Iteration : 192  ||B r|| = 0.00122694
+   Pass :  4   Iteration : 193  ||B r|| = 0.00112965
+   Pass :  4   Iteration : 194  ||B r|| = 0.00106884
+   Pass :  4   Iteration : 195  ||B r|| = 0.00106156
+   Pass :  4   Iteration : 196  ||B r|| = 0.000979129
+   Pass :  4   Iteration : 197  ||B r|| = 0.000974447
+   Pass :  4   Iteration : 198  ||B r|| = 0.000913577
+   Pass :  4   Iteration : 199  ||B r|| = 0.000824117
+   Pass :  4   Iteration : 200  ||B r|| = 0.000819664
+Restarting...
+   Pass :  5   Iteration : 201  ||B r|| = 0.000819566
+   Pass :  5   Iteration : 202  ||B r|| = 0.000802101
+   Pass :  5   Iteration : 203  ||B r|| = 0.000793705
+   Pass :  5   Iteration : 204  ||B r|| = 0.000779788
+   Pass :  5   Iteration : 205  ||B r|| = 0.000730173
+   Pass :  5   Iteration : 206  ||B r|| = 0.000710072
+   Pass :  5   Iteration : 207  ||B r|| = 0.000686091
+   Pass :  5   Iteration : 208  ||B r|| = 0.000635314
+   Pass :  5   Iteration : 209  ||B r|| = 0.000635226
+   Pass :  5   Iteration : 210  ||B r|| = 0.000604069
+   Pass :  5   Iteration : 211  ||B r|| = 0.000565668
+   Pass :  5   Iteration : 212  ||B r|| = 0.000557792
+   Pass :  5   Iteration : 213  ||B r|| = 0.000515749
+   Pass :  5   Iteration : 214  ||B r|| = 0.000513034
+   Pass :  5   Iteration : 215  ||B r|| = 0.000481894
+   Pass :  5   Iteration : 216  ||B r|| = 0.000451544
+   Pass :  5   Iteration : 217  ||B r|| = 0.00044852
+   Pass :  5   Iteration : 218  ||B r|| = 0.000393422
+   Pass :  5   Iteration : 219  ||B r|| = 0.000381413
+   Pass :  5   Iteration : 220  ||B r|| = 0.000361236
+   Pass :  5   Iteration : 221  ||B r|| = 0.000336538
+   Pass :  5   Iteration : 222  ||B r|| = 0.000336118
+   Pass :  5   Iteration : 223  ||B r|| = 0.000320216
+   Pass :  5   Iteration : 224  ||B r|| = 0.000311681
+   Pass :  5   Iteration : 225  ||B r|| = 0.000300208
+   Pass :  5   Iteration : 226  ||B r|| = 0.000280096
+   Pass :  5   Iteration : 227  ||B r|| = 0.000280017
+   Pass :  5   Iteration : 228  ||B r|| = 0.000265884
+   Pass :  5   Iteration : 229  ||B r|| = 0.000254531
+   Pass :  5   Iteration : 230  ||B r|| = 0.000253443
+   Pass :  5   Iteration : 231  ||B r|| = 0.000232182
+   Pass :  5   Iteration : 232  ||B r|| = 0.000231948
+   Pass :  5   Iteration : 233  ||B r|| = 0.000219717
+   Pass :  5   Iteration : 234  ||B r|| = 0.000210106
+   Pass :  5   Iteration : 235  ||B r|| = 0.000208378
+   Pass :  5   Iteration : 236  ||B r|| = 0.000192791
+   Pass :  5   Iteration : 237  ||B r|| = 0.000191389
+   Pass :  5   Iteration : 238  ||B r|| = 0.000181136
+   Pass :  5   Iteration : 239  ||B r|| = 0.000173082
+   Pass :  5   Iteration : 240  ||B r|| = 0.000172178
+   Pass :  5   Iteration : 241  ||B r|| = 0.000163582
+   Pass :  5   Iteration : 242  ||B r|| = 0.000160314
+   Pass :  5   Iteration : 243  ||B r|| = 0.000154194
+   Pass :  5   Iteration : 244  ||B r|| = 0.000142641
+   Pass :  5   Iteration : 245  ||B r|| = 0.000142245
+   Pass :  5   Iteration : 246  ||B r|| = 0.000135685
+   Pass :  5   Iteration : 247  ||B r|| = 0.000134161
+   Pass :  5   Iteration : 248  ||B r|| = 0.00013191
+   Pass :  5   Iteration : 249  ||B r|| = 0.00011789
+   Pass :  5   Iteration : 250  ||B r|| = 0.000117448
+Restarting...
+   Pass :  6   Iteration : 251  ||B r|| = 0.000117443
+   Pass :  6   Iteration : 252  ||B r|| = 0.000111241
+   Pass :  6   Iteration : 253  ||B r|| = 0.000111092
+   Pass :  6   Iteration : 254  ||B r|| = 0.000111075
+   Pass :  6   Iteration : 255  ||B r|| = 0.000101403
+   Pass :  6   Iteration : 256  ||B r|| = 0.000100984
+   Pass :  6   Iteration : 257  ||B r|| = 9.60892e-05
+   Pass :  6   Iteration : 258  ||B r|| = 9.16341e-05
+   Pass :  6   Iteration : 259  ||B r|| = 9.1184e-05
+   Pass :  6   Iteration : 260  ||B r|| = 8.57519e-05
+   Pass :  6   Iteration : 261  ||B r|| = 8.49038e-05
+   Pass :  6   Iteration : 262  ||B r|| = 8.25868e-05
+   Pass :  6   Iteration : 263  ||B r|| = 7.84909e-05
+   Pass :  6   Iteration : 264  ||B r|| = 7.84882e-05
+   Pass :  6   Iteration : 265  ||B r|| = 7.17122e-05
+   Pass :  6   Iteration : 266  ||B r|| = 7.06387e-05
+   Pass :  6   Iteration : 267  ||B r|| = 6.88435e-05
+   Pass :  6   Iteration : 268  ||B r|| = 6.51125e-05
+   Pass :  6   Iteration : 269  ||B r|| = 6.51119e-05
+   Pass :  6   Iteration : 270  ||B r|| = 6.11726e-05
+   Pass :  6   Iteration : 271  ||B r|| = 5.95685e-05
+   Pass :  6   Iteration : 272  ||B r|| = 5.69221e-05
+   Pass :  6   Iteration : 273  ||B r|| = 5.31348e-05
+   Pass :  6   Iteration : 274  ||B r|| = 5.29896e-05
+   Pass :  6   Iteration : 275  ||B r|| = 5.06603e-05
+   Pass :  6   Iteration : 276  ||B r|| = 4.77003e-05
+   Pass :  6   Iteration : 277  ||B r|| = 4.69104e-05
+   Pass :  6   Iteration : 278  ||B r|| = 4.35213e-05
+   Pass :  6   Iteration : 279  ||B r|| = 4.34584e-05
+   Pass :  6   Iteration : 280  ||B r|| = 4.13801e-05
+   Pass :  6   Iteration : 281  ||B r|| = 3.80137e-05
+   Pass :  6   Iteration : 282  ||B r|| = 3.73519e-05
+   Pass :  6   Iteration : 283  ||B r|| = 3.40659e-05
+   Pass :  6   Iteration : 284  ||B r|| = 3.35469e-05
+   Pass :  6   Iteration : 285  ||B r|| = 3.24228e-05
+   Pass :  6   Iteration : 286  ||B r|| = 2.82691e-05
+   Pass :  6   Iteration : 287  ||B r|| = 2.82415e-05
+   Pass :  6   Iteration : 288  ||B r|| = 2.4949e-05
+   Pass :  6   Iteration : 289  ||B r|| = 2.42639e-05
+   Pass :  6   Iteration : 290  ||B r|| = 2.35408e-05
+   Pass :  6   Iteration : 291  ||B r|| = 2.19407e-05
+   Pass :  6   Iteration : 292  ||B r|| = 2.19132e-05
+   Pass :  6   Iteration : 293  ||B r|| = 2.03845e-05
+   Pass :  6   Iteration : 294  ||B r|| = 1.92894e-05
+   Pass :  6   Iteration : 295  ||B r|| = 1.89518e-05
+   Pass :  6   Iteration : 296  ||B r|| = 1.72028e-05
+   Pass :  6   Iteration : 297  ||B r|| = 1.71928e-05
+   Pass :  6   Iteration : 298  ||B r|| = 1.63643e-05
+   Pass :  6   Iteration : 299  ||B r|| = 1.56163e-05
+   Pass :  6   Iteration : 300  ||B r|| = 1.54755e-05
+Restarting...
+   Pass :  7   Iteration : 301  ||B r|| = 1.54724e-05
+   Pass :  7   Iteration : 302  ||B r|| = 1.53376e-05
+   Pass :  7   Iteration : 303  ||B r|| = 1.50205e-05
+   Pass :  7   Iteration : 304  ||B r|| = 1.47195e-05
+   Pass :  7   Iteration : 305  ||B r|| = 1.34414e-05
+   Pass :  7   Iteration : 306  ||B r|| = 1.30372e-05
+   Pass :  7   Iteration : 307  ||B r|| = 1.26163e-05
+   Pass :  7   Iteration : 308  ||B r|| = 1.17954e-05
+   Pass :  7   Iteration : 309  ||B r|| = 1.17113e-05
+   Pass :  7   Iteration : 310  ||B r|| = 1.12938e-05
+   Pass :  7   Iteration : 311  ||B r|| = 1.04865e-05
+   Pass :  7   Iteration : 312  ||B r|| = 1.03571e-05
+   Pass :  7   Iteration : 313  ||B r|| = 9.56454e-06
+   Pass :  7   Iteration : 314  ||B r|| = 9.44709e-06
+   Pass :  7   Iteration : 315  ||B r|| = 9.02016e-06
+   Pass :  7   Iteration : 316  ||B r|| = 8.27621e-06
+   Pass :  7   Iteration : 317  ||B r|| = 8.26159e-06
+   Pass :  7   Iteration : 318  ||B r|| = 7.18002e-06
+   Pass :  7   Iteration : 319  ||B r|| = 6.95003e-06
+   Pass :  7   Iteration : 320  ||B r|| = 6.73497e-06
+   Pass :  7   Iteration : 321  ||B r|| = 6.25227e-06
+   Pass :  7   Iteration : 322  ||B r|| = 6.24358e-06
+   Pass :  7   Iteration : 323  ||B r|| = 5.90685e-06
+   Pass :  7   Iteration : 324  ||B r|| = 5.69217e-06
+   Pass :  7   Iteration : 325  ||B r|| = 5.59816e-06
+   Pass :  7   Iteration : 326  ||B r|| = 5.19767e-06
+   Pass :  7   Iteration : 327  ||B r|| = 5.18732e-06
+   Pass :  7   Iteration : 328  ||B r|| = 4.978e-06
+   Pass :  7   Iteration : 329  ||B r|| = 4.61108e-06
+   Pass :  7   Iteration : 330  ||B r|| = 4.60926e-06
+   Pass :  7   Iteration : 331  ||B r|| = 4.23343e-06
+   Pass :  7   Iteration : 332  ||B r|| = 4.23029e-06
+   Pass :  7   Iteration : 333  ||B r|| = 4.01039e-06
+   Pass :  7   Iteration : 334  ||B r|| = 3.86812e-06
+   Pass :  7   Iteration : 335  ||B r|| = 3.86282e-06
+   Pass :  7   Iteration : 336  ||B r|| = 3.60676e-06
+   Pass :  7   Iteration : 337  ||B r|| = 3.53527e-06
+   Pass :  7   Iteration : 338  ||B r|| = 3.33113e-06
+   Pass :  7   Iteration : 339  ||B r|| = 3.15944e-06
+   Pass :  7   Iteration : 340  ||B r|| = 3.14716e-06
+   Pass :  7   Iteration : 341  ||B r|| = 2.97802e-06
+   Pass :  7   Iteration : 342  ||B r|| = 2.95139e-06
+   Pass :  7   Iteration : 343  ||B r|| = 2.86922e-06
+   Pass :  7   Iteration : 344  ||B r|| = 2.65035e-06
+   Pass :  7   Iteration : 345  ||B r|| = 2.64952e-06
+   Pass :  7   Iteration : 346  ||B r|| = 2.48989e-06
+   Pass :  7   Iteration : 347  ||B r|| = 2.42609e-06
+   Pass :  7   Iteration : 348  ||B r|| = 2.35361e-06
+   Pass :  7   Iteration : 349  ||B r|| = 2.0977e-06
+   Pass :  7   Iteration : 350  ||B r|| = 2.0743e-06
+Restarting...
+   Pass :  8   Iteration : 351  ||B r|| = 2.074e-06
+   Pass :  8   Iteration : 352  ||B r|| = 1.9458e-06
+   Pass :  8   Iteration : 353  ||B r|| = 1.91268e-06
+   Pass :  8   Iteration : 354  ||B r|| = 1.9109e-06
+   Pass :  8   Iteration : 355  ||B r|| = 1.71169e-06
+   Pass :  8   Iteration : 356  ||B r|| = 1.70656e-06
+   Pass :  8   Iteration : 357  ||B r|| = 1.61858e-06
+   Pass :  8   Iteration : 358  ||B r|| = 1.53201e-06
+   Pass :  8   Iteration : 359  ||B r|| = 1.52511e-06
+   Pass :  8   Iteration : 360  ||B r|| = 1.4294e-06
+   Pass :  8   Iteration : 361  ||B r|| = 1.40067e-06
+   Pass :  8   Iteration : 362  ||B r|| = 1.35966e-06
+   Pass :  8   Iteration : 363  ||B r|| = 1.29997e-06
+   Pass :  8   Iteration : 364  ||B r|| = 1.29896e-06
+   Pass :  8   Iteration : 365  ||B r|| = 1.192e-06
+   Pass :  8   Iteration : 366  ||B r|| = 1.17842e-06
+   Pass :  8   Iteration : 367  ||B r|| = 1.14545e-06
+   Pass :  8   Iteration : 368  ||B r|| = 1.08481e-06
+   Pass :  8   Iteration : 369  ||B r|| = 1.08408e-06
+   Pass :  8   Iteration : 370  ||B r|| = 1.01158e-06
+   Pass :  8   Iteration : 371  ||B r|| = 9.87365e-07
+   Pass :  8   Iteration : 372  ||B r|| = 9.53571e-07
+   Pass :  8   Iteration : 373  ||B r|| = 9.02865e-07
+   Pass :  8   Iteration : 374  ||B r|| = 9.02529e-07
+   Pass :  8   Iteration : 375  ||B r|| = 8.35677e-07
+GMRES+GS converged in 375 iterations with a residual norm of 8.35677e-07.
+solver took 3.20645s.
+|| q_h - q_ex || / || q_ex || = 5.07159e-05
+|| t_h - t_ex || / || t_ex || = 2.61662e-05

examples/regress_test/p1_o3_dg_nl_umfpack.txt

@@ -0,0 +1,56 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --hdg_scheme 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2048
+dim(W) = 1024
+dim(V+W) = 3072
+***********************************************************
+Assembly took 0.109221s.
+Preconditioner took 0.0286016s.
+   Pass :  1   Iteration :   0  ||B r|| = 34.0948
+   Pass :  1   Iteration :   1  ||B r|| = 34.0948
+   Pass :  1   Iteration :   2  ||B r|| = 0.0882945
+   Pass :  1   Iteration :   3  ||B r|| = 0.0197291
+   Pass :  1   Iteration :   4  ||B r|| = 0.0182002
+   Pass :  1   Iteration :   5  ||B r|| = 0.00466911
+   Pass :  1   Iteration :   6  ||B r|| = 0.00191841
+   Pass :  1   Iteration :   7  ||B r|| = 0.00153367
+   Pass :  1   Iteration :   8  ||B r|| = 0.00108376
+   Pass :  1   Iteration :   9  ||B r|| = 0.00106531
+   Pass :  1   Iteration :  10  ||B r|| = 0.000264455
+   Pass :  1   Iteration :  11  ||B r|| = 9.66463e-05
+   Pass :  1   Iteration :  12  ||B r|| = 9.54134e-05
+   Pass :  1   Iteration :  13  ||B r|| = 4.64374e-05
+   Pass :  1   Iteration :  14  ||B r|| = 2.53717e-05
+GMRES+UMFPack converged in 14 iterations with a residual norm of 2.53717e-05.
+solver took 0.128301s.
+|| q_h - q_ex || / || q_ex || = 5.06633e-05
+|| t_h - t_ex || / || t_ex || = 2.61371e-05

examples/regress_test/p1_o3_dg_nld.txt

@@ -0,0 +1,425 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2048
+dim(W) = 1024
+dim(V+W) = 3072
+***********************************************************
+Assembly took 0.125661s.
+Preconditioner took 0.06072s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.900577
+   Pass :  1   Iteration :   1  ||B r|| = 0.900577
+   Pass :  1   Iteration :   2  ||B r|| = 0.900434
+   Pass :  1   Iteration :   3  ||B r|| = 0.900408
+   Pass :  1   Iteration :   4  ||B r|| = 0.900243
+   Pass :  1   Iteration :   5  ||B r|| = 0.899912
+   Pass :  1   Iteration :   6  ||B r|| = 0.899901
+   Pass :  1   Iteration :   7  ||B r|| = 0.898453
+   Pass :  1   Iteration :   8  ||B r|| = 0.898147
+   Pass :  1   Iteration :   9  ||B r|| = 0.892867
+   Pass :  1   Iteration :  10  ||B r|| = 0.89046
+   Pass :  1   Iteration :  11  ||B r|| = 0.890149
+   Pass :  1   Iteration :  12  ||B r|| = 0.887881
+   Pass :  1   Iteration :  13  ||B r|| = 0.886497
+   Pass :  1   Iteration :  14  ||B r|| = 0.881958
+   Pass :  1   Iteration :  15  ||B r|| = 0.873768
+   Pass :  1   Iteration :  16  ||B r|| = 0.866676
+   Pass :  1   Iteration :  17  ||B r|| = 0.862158
+   Pass :  1   Iteration :  18  ||B r|| = 0.862121
+   Pass :  1   Iteration :  19  ||B r|| = 0.861983
+   Pass :  1   Iteration :  20  ||B r|| = 0.852531
+   Pass :  1   Iteration :  21  ||B r|| = 0.851407
+   Pass :  1   Iteration :  22  ||B r|| = 0.81114
+   Pass :  1   Iteration :  23  ||B r|| = 0.811092
+   Pass :  1   Iteration :  24  ||B r|| = 0.794531
+   Pass :  1   Iteration :  25  ||B r|| = 0.794531
+   Pass :  1   Iteration :  26  ||B r|| = 0.788509
+   Pass :  1   Iteration :  27  ||B r|| = 0.783442
+   Pass :  1   Iteration :  28  ||B r|| = 0.75365
+   Pass :  1   Iteration :  29  ||B r|| = 0.736124
+   Pass :  1   Iteration :  30  ||B r|| = 0.718001
+   Pass :  1   Iteration :  31  ||B r|| = 0.70199
+   Pass :  1   Iteration :  32  ||B r|| = 0.701983
+   Pass :  1   Iteration :  33  ||B r|| = 0.691506
+   Pass :  1   Iteration :  34  ||B r|| = 0.687431
+   Pass :  1   Iteration :  35  ||B r|| = 0.620939
+   Pass :  1   Iteration :  36  ||B r|| = 0.620787
+   Pass :  1   Iteration :  37  ||B r|| = 0.579878
+   Pass :  1   Iteration :  38  ||B r|| = 0.577254
+   Pass :  1   Iteration :  39  ||B r|| = 0.577153
+   Pass :  1   Iteration :  40  ||B r|| = 0.573348
+   Pass :  1   Iteration :  41  ||B r|| = 0.540128
+   Pass :  1   Iteration :  42  ||B r|| = 0.500686
+   Pass :  1   Iteration :  43  ||B r|| = 0.474183
+   Pass :  1   Iteration :  44  ||B r|| = 0.447715
+   Pass :  1   Iteration :  45  ||B r|| = 0.441645
+   Pass :  1   Iteration :  46  ||B r|| = 0.43763
+   Pass :  1   Iteration :  47  ||B r|| = 0.437304
+   Pass :  1   Iteration :  48  ||B r|| = 0.388192
+   Pass :  1   Iteration :  49  ||B r|| = 0.386414
+   Pass :  1   Iteration :  50  ||B r|| = 0.346785
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 0.346783
+   Pass :  2   Iteration :  52  ||B r|| = 0.346753
+   Pass :  2   Iteration :  53  ||B r|| = 0.346725
+   Pass :  2   Iteration :  54  ||B r|| = 0.346369
+   Pass :  2   Iteration :  55  ||B r|| = 0.345779
+   Pass :  2   Iteration :  56  ||B r|| = 0.340784
+   Pass :  2   Iteration :  57  ||B r|| = 0.338059
+   Pass :  2   Iteration :  58  ||B r|| = 0.330718
+   Pass :  2   Iteration :  59  ||B r|| = 0.32847
+   Pass :  2   Iteration :  60  ||B r|| = 0.326365
+   Pass :  2   Iteration :  61  ||B r|| = 0.32017
+   Pass :  2   Iteration :  62  ||B r|| = 0.319864
+   Pass :  2   Iteration :  63  ||B r|| = 0.290191
+   Pass :  2   Iteration :  64  ||B r|| = 0.29019
+   Pass :  2   Iteration :  65  ||B r|| = 0.275545
+   Pass :  2   Iteration :  66  ||B r|| = 0.274977
+   Pass :  2   Iteration :  67  ||B r|| = 0.274975
+   Pass :  2   Iteration :  68  ||B r|| = 0.250095
+   Pass :  2   Iteration :  69  ||B r|| = 0.245757
+   Pass :  2   Iteration :  70  ||B r|| = 0.226498
+   Pass :  2   Iteration :  71  ||B r|| = 0.21832
+   Pass :  2   Iteration :  72  ||B r|| = 0.209813
+   Pass :  2   Iteration :  73  ||B r|| = 0.197498
+   Pass :  2   Iteration :  74  ||B r|| = 0.194375
+   Pass :  2   Iteration :  75  ||B r|| = 0.185865
+   Pass :  2   Iteration :  76  ||B r|| = 0.160081
+   Pass :  2   Iteration :  77  ||B r|| = 0.155704
+   Pass :  2   Iteration :  78  ||B r|| = 0.140027
+   Pass :  2   Iteration :  79  ||B r|| = 0.138448
+   Pass :  2   Iteration :  80  ||B r|| = 0.138139
+   Pass :  2   Iteration :  81  ||B r|| = 0.125615
+   Pass :  2   Iteration :  82  ||B r|| = 0.12453
+   Pass :  2   Iteration :  83  ||B r|| = 0.109713
+   Pass :  2   Iteration :  84  ||B r|| = 0.108677
+   Pass :  2   Iteration :  85  ||B r|| = 0.105206
+   Pass :  2   Iteration :  86  ||B r|| = 0.10045
+   Pass :  2   Iteration :  87  ||B r|| = 0.0995337
+   Pass :  2   Iteration :  88  ||B r|| = 0.0927337
+   Pass :  2   Iteration :  89  ||B r|| = 0.0865765
+   Pass :  2   Iteration :  90  ||B r|| = 0.0836921
+   Pass :  2   Iteration :  91  ||B r|| = 0.0777179
+   Pass :  2   Iteration :  92  ||B r|| = 0.0777125
+   Pass :  2   Iteration :  93  ||B r|| = 0.075328
+   Pass :  2   Iteration :  94  ||B r|| = 0.0698781
+   Pass :  2   Iteration :  95  ||B r|| = 0.0695923
+   Pass :  2   Iteration :  96  ||B r|| = 0.0582517
+   Pass :  2   Iteration :  97  ||B r|| = 0.0578877
+   Pass :  2   Iteration :  98  ||B r|| = 0.0509695
+   Pass :  2   Iteration :  99  ||B r|| = 0.0492122
+   Pass :  2   Iteration : 100  ||B r|| = 0.049119
+Restarting...
+   Pass :  3   Iteration : 101  ||B r|| = 0.0491174
+   Pass :  3   Iteration : 102  ||B r|| = 0.048935
+   Pass :  3   Iteration : 103  ||B r|| = 0.0487952
+   Pass :  3   Iteration : 104  ||B r|| = 0.048271
+   Pass :  3   Iteration : 105  ||B r|| = 0.0456151
+   Pass :  3   Iteration : 106  ||B r|| = 0.0420326
+   Pass :  3   Iteration : 107  ||B r|| = 0.0405407
+   Pass :  3   Iteration : 108  ||B r|| = 0.0376982
+   Pass :  3   Iteration : 109  ||B r|| = 0.0374234
+   Pass :  3   Iteration : 110  ||B r|| = 0.0359602
+   Pass :  3   Iteration : 111  ||B r|| = 0.0336756
+   Pass :  3   Iteration : 112  ||B r|| = 0.0331036
+   Pass :  3   Iteration : 113  ||B r|| = 0.0304233
+   Pass :  3   Iteration : 114  ||B r|| = 0.0303832
+   Pass :  3   Iteration : 115  ||B r|| = 0.0290383
+   Pass :  3   Iteration : 116  ||B r|| = 0.0270094
+   Pass :  3   Iteration : 117  ||B r|| = 0.0269671
+   Pass :  3   Iteration : 118  ||B r|| = 0.0234557
+   Pass :  3   Iteration : 119  ||B r|| = 0.0233749
+   Pass :  3   Iteration : 120  ||B r|| = 0.0222709
+   Pass :  3   Iteration : 121  ||B r|| = 0.0210607
+   Pass :  3   Iteration : 122  ||B r|| = 0.0210189
+   Pass :  3   Iteration : 123  ||B r|| = 0.019523
+   Pass :  3   Iteration : 124  ||B r|| = 0.0190986
+   Pass :  3   Iteration : 125  ||B r|| = 0.0182602
+   Pass :  3   Iteration : 126  ||B r|| = 0.0165908
+   Pass :  3   Iteration : 127  ||B r|| = 0.0165826
+   Pass :  3   Iteration : 128  ||B r|| = 0.0155958
+   Pass :  3   Iteration : 129  ||B r|| = 0.0149154
+   Pass :  3   Iteration : 130  ||B r|| = 0.0148837
+   Pass :  3   Iteration : 131  ||B r|| = 0.0133188
+   Pass :  3   Iteration : 132  ||B r|| = 0.0133041
+   Pass :  3   Iteration : 133  ||B r|| = 0.0126119
+   Pass :  3   Iteration : 134  ||B r|| = 0.012336
+   Pass :  3   Iteration : 135  ||B r|| = 0.0123217
+   Pass :  3   Iteration : 136  ||B r|| = 0.0111051
+   Pass :  3   Iteration : 137  ||B r|| = 0.0110814
+   Pass :  3   Iteration : 138  ||B r|| = 0.0105874
+   Pass :  3   Iteration : 139  ||B r|| = 0.0104149
+   Pass :  3   Iteration : 140  ||B r|| = 0.0104149
+   Pass :  3   Iteration : 141  ||B r|| = 0.00988104
+   Pass :  3   Iteration : 142  ||B r|| = 0.00946548
+   Pass :  3   Iteration : 143  ||B r|| = 0.00898965
+   Pass :  3   Iteration : 144  ||B r|| = 0.00849411
+   Pass :  3   Iteration : 145  ||B r|| = 0.00847611
+   Pass :  3   Iteration : 146  ||B r|| = 0.00791422
+   Pass :  3   Iteration : 147  ||B r|| = 0.00760638
+   Pass :  3   Iteration : 148  ||B r|| = 0.00739417
+   Pass :  3   Iteration : 149  ||B r|| = 0.00658704
+   Pass :  3   Iteration : 150  ||B r|| = 0.00657621
+Restarting...
+   Pass :  4   Iteration : 151  ||B r|| = 0.00657611
+   Pass :  4   Iteration : 152  ||B r|| = 0.00631889
+   Pass :  4   Iteration : 153  ||B r|| = 0.00630107
+   Pass :  4   Iteration : 154  ||B r|| = 0.00628496
+   Pass :  4   Iteration : 155  ||B r|| = 0.00581361
+   Pass :  4   Iteration : 156  ||B r|| = 0.00572566
+   Pass :  4   Iteration : 157  ||B r|| = 0.00558237
+   Pass :  4   Iteration : 158  ||B r|| = 0.00520369
+   Pass :  4   Iteration : 159  ||B r|| = 0.0052025
+   Pass :  4   Iteration : 160  ||B r|| = 0.00487642
+   Pass :  4   Iteration : 161  ||B r|| = 0.00479177
+   Pass :  4   Iteration : 162  ||B r|| = 0.00468477
+   Pass :  4   Iteration : 163  ||B r|| = 0.00440739
+   Pass :  4   Iteration : 164  ||B r|| = 0.00440725
+   Pass :  4   Iteration : 165  ||B r|| = 0.00415237
+   Pass :  4   Iteration : 166  ||B r|| = 0.00404373
+   Pass :  4   Iteration : 167  ||B r|| = 0.00399217
+   Pass :  4   Iteration : 168  ||B r|| = 0.00361744
+   Pass :  4   Iteration : 169  ||B r|| = 0.00361199
+   Pass :  4   Iteration : 170  ||B r|| = 0.00342198
+   Pass :  4   Iteration : 171  ||B r|| = 0.00332275
+   Pass :  4   Iteration : 172  ||B r|| = 0.00328849
+   Pass :  4   Iteration : 173  ||B r|| = 0.00301807
+   Pass :  4   Iteration : 174  ||B r|| = 0.00297077
+   Pass :  4   Iteration : 175  ||B r|| = 0.00278725
+   Pass :  4   Iteration : 176  ||B r|| = 0.00265647
+   Pass :  4   Iteration : 177  ||B r|| = 0.00265138
+   Pass :  4   Iteration : 178  ||B r|| = 0.00249713
+   Pass :  4   Iteration : 179  ||B r|| = 0.0024458
+   Pass :  4   Iteration : 180  ||B r|| = 0.00226749
+   Pass :  4   Iteration : 181  ||B r|| = 0.00211128
+   Pass :  4   Iteration : 182  ||B r|| = 0.00209348
+   Pass :  4   Iteration : 183  ||B r|| = 0.00199424
+   Pass :  4   Iteration : 184  ||B r|| = 0.00190927
+   Pass :  4   Iteration : 185  ||B r|| = 0.00186211
+   Pass :  4   Iteration : 186  ||B r|| = 0.00157145
+   Pass :  4   Iteration : 187  ||B r|| = 0.00157142
+   Pass :  4   Iteration : 188  ||B r|| = 0.00141191
+   Pass :  4   Iteration : 189  ||B r|| = 0.00136095
+   Pass :  4   Iteration : 190  ||B r|| = 0.00133934
+   Pass :  4   Iteration : 191  ||B r|| = 0.00123125
+   Pass :  4   Iteration : 192  ||B r|| = 0.00122694
+   Pass :  4   Iteration : 193  ||B r|| = 0.00112965
+   Pass :  4   Iteration : 194  ||B r|| = 0.00106884
+   Pass :  4   Iteration : 195  ||B r|| = 0.00106156
+   Pass :  4   Iteration : 196  ||B r|| = 0.000979129
+   Pass :  4   Iteration : 197  ||B r|| = 0.000974447
+   Pass :  4   Iteration : 198  ||B r|| = 0.000913577
+   Pass :  4   Iteration : 199  ||B r|| = 0.000824117
+   Pass :  4   Iteration : 200  ||B r|| = 0.000819664
+Restarting...
+   Pass :  5   Iteration : 201  ||B r|| = 0.000819566
+   Pass :  5   Iteration : 202  ||B r|| = 0.000802101
+   Pass :  5   Iteration : 203  ||B r|| = 0.000793705
+   Pass :  5   Iteration : 204  ||B r|| = 0.000779788
+   Pass :  5   Iteration : 205  ||B r|| = 0.000730173
+   Pass :  5   Iteration : 206  ||B r|| = 0.000710072
+   Pass :  5   Iteration : 207  ||B r|| = 0.000686091
+   Pass :  5   Iteration : 208  ||B r|| = 0.000635314
+   Pass :  5   Iteration : 209  ||B r|| = 0.000635226
+   Pass :  5   Iteration : 210  ||B r|| = 0.000604069
+   Pass :  5   Iteration : 211  ||B r|| = 0.000565668
+   Pass :  5   Iteration : 212  ||B r|| = 0.000557792
+   Pass :  5   Iteration : 213  ||B r|| = 0.000515749
+   Pass :  5   Iteration : 214  ||B r|| = 0.000513034
+   Pass :  5   Iteration : 215  ||B r|| = 0.000481894
+   Pass :  5   Iteration : 216  ||B r|| = 0.000451544
+   Pass :  5   Iteration : 217  ||B r|| = 0.00044852
+   Pass :  5   Iteration : 218  ||B r|| = 0.000393422
+   Pass :  5   Iteration : 219  ||B r|| = 0.000381413
+   Pass :  5   Iteration : 220  ||B r|| = 0.000361236
+   Pass :  5   Iteration : 221  ||B r|| = 0.000336538
+   Pass :  5   Iteration : 222  ||B r|| = 0.000336118
+   Pass :  5   Iteration : 223  ||B r|| = 0.000320216
+   Pass :  5   Iteration : 224  ||B r|| = 0.000311681
+   Pass :  5   Iteration : 225  ||B r|| = 0.000300208
+   Pass :  5   Iteration : 226  ||B r|| = 0.000280096
+   Pass :  5   Iteration : 227  ||B r|| = 0.000280017
+   Pass :  5   Iteration : 228  ||B r|| = 0.000265884
+   Pass :  5   Iteration : 229  ||B r|| = 0.000254531
+   Pass :  5   Iteration : 230  ||B r|| = 0.000253443
+   Pass :  5   Iteration : 231  ||B r|| = 0.000232182
+   Pass :  5   Iteration : 232  ||B r|| = 0.000231948
+   Pass :  5   Iteration : 233  ||B r|| = 0.000219717
+   Pass :  5   Iteration : 234  ||B r|| = 0.000210106
+   Pass :  5   Iteration : 235  ||B r|| = 0.000208378
+   Pass :  5   Iteration : 236  ||B r|| = 0.000192791
+   Pass :  5   Iteration : 237  ||B r|| = 0.000191389
+   Pass :  5   Iteration : 238  ||B r|| = 0.000181136
+   Pass :  5   Iteration : 239  ||B r|| = 0.000173082
+   Pass :  5   Iteration : 240  ||B r|| = 0.000172178
+   Pass :  5   Iteration : 241  ||B r|| = 0.000163582
+   Pass :  5   Iteration : 242  ||B r|| = 0.000160314
+   Pass :  5   Iteration : 243  ||B r|| = 0.000154194
+   Pass :  5   Iteration : 244  ||B r|| = 0.000142641
+   Pass :  5   Iteration : 245  ||B r|| = 0.000142245
+   Pass :  5   Iteration : 246  ||B r|| = 0.000135685
+   Pass :  5   Iteration : 247  ||B r|| = 0.000134161
+   Pass :  5   Iteration : 248  ||B r|| = 0.00013191
+   Pass :  5   Iteration : 249  ||B r|| = 0.00011789
+   Pass :  5   Iteration : 250  ||B r|| = 0.000117448
+Restarting...
+   Pass :  6   Iteration : 251  ||B r|| = 0.000117443
+   Pass :  6   Iteration : 252  ||B r|| = 0.000111241
+   Pass :  6   Iteration : 253  ||B r|| = 0.000111092
+   Pass :  6   Iteration : 254  ||B r|| = 0.000111075
+   Pass :  6   Iteration : 255  ||B r|| = 0.000101403
+   Pass :  6   Iteration : 256  ||B r|| = 0.000100984
+   Pass :  6   Iteration : 257  ||B r|| = 9.60892e-05
+   Pass :  6   Iteration : 258  ||B r|| = 9.16341e-05
+   Pass :  6   Iteration : 259  ||B r|| = 9.1184e-05
+   Pass :  6   Iteration : 260  ||B r|| = 8.57519e-05
+   Pass :  6   Iteration : 261  ||B r|| = 8.49038e-05
+   Pass :  6   Iteration : 262  ||B r|| = 8.25868e-05
+   Pass :  6   Iteration : 263  ||B r|| = 7.84909e-05
+   Pass :  6   Iteration : 264  ||B r|| = 7.84882e-05
+   Pass :  6   Iteration : 265  ||B r|| = 7.17122e-05
+   Pass :  6   Iteration : 266  ||B r|| = 7.06387e-05
+   Pass :  6   Iteration : 267  ||B r|| = 6.88435e-05
+   Pass :  6   Iteration : 268  ||B r|| = 6.51125e-05
+   Pass :  6   Iteration : 269  ||B r|| = 6.51119e-05
+   Pass :  6   Iteration : 270  ||B r|| = 6.11726e-05
+   Pass :  6   Iteration : 271  ||B r|| = 5.95685e-05
+   Pass :  6   Iteration : 272  ||B r|| = 5.69221e-05
+   Pass :  6   Iteration : 273  ||B r|| = 5.31348e-05
+   Pass :  6   Iteration : 274  ||B r|| = 5.29896e-05
+   Pass :  6   Iteration : 275  ||B r|| = 5.06603e-05
+   Pass :  6   Iteration : 276  ||B r|| = 4.77003e-05
+   Pass :  6   Iteration : 277  ||B r|| = 4.69104e-05
+   Pass :  6   Iteration : 278  ||B r|| = 4.35213e-05
+   Pass :  6   Iteration : 279  ||B r|| = 4.34584e-05
+   Pass :  6   Iteration : 280  ||B r|| = 4.13801e-05
+   Pass :  6   Iteration : 281  ||B r|| = 3.80137e-05
+   Pass :  6   Iteration : 282  ||B r|| = 3.73519e-05
+   Pass :  6   Iteration : 283  ||B r|| = 3.40659e-05
+   Pass :  6   Iteration : 284  ||B r|| = 3.35469e-05
+   Pass :  6   Iteration : 285  ||B r|| = 3.24228e-05
+   Pass :  6   Iteration : 286  ||B r|| = 2.82691e-05
+   Pass :  6   Iteration : 287  ||B r|| = 2.82415e-05
+   Pass :  6   Iteration : 288  ||B r|| = 2.4949e-05
+   Pass :  6   Iteration : 289  ||B r|| = 2.42639e-05
+   Pass :  6   Iteration : 290  ||B r|| = 2.35408e-05
+   Pass :  6   Iteration : 291  ||B r|| = 2.19407e-05
+   Pass :  6   Iteration : 292  ||B r|| = 2.19132e-05
+   Pass :  6   Iteration : 293  ||B r|| = 2.03845e-05
+   Pass :  6   Iteration : 294  ||B r|| = 1.92894e-05
+   Pass :  6   Iteration : 295  ||B r|| = 1.89518e-05
+   Pass :  6   Iteration : 296  ||B r|| = 1.72028e-05
+   Pass :  6   Iteration : 297  ||B r|| = 1.71928e-05
+   Pass :  6   Iteration : 298  ||B r|| = 1.63643e-05
+   Pass :  6   Iteration : 299  ||B r|| = 1.56163e-05
+   Pass :  6   Iteration : 300  ||B r|| = 1.54755e-05
+Restarting...
+   Pass :  7   Iteration : 301  ||B r|| = 1.54724e-05
+   Pass :  7   Iteration : 302  ||B r|| = 1.53376e-05
+   Pass :  7   Iteration : 303  ||B r|| = 1.50205e-05
+   Pass :  7   Iteration : 304  ||B r|| = 1.47195e-05
+   Pass :  7   Iteration : 305  ||B r|| = 1.34414e-05
+   Pass :  7   Iteration : 306  ||B r|| = 1.30372e-05
+   Pass :  7   Iteration : 307  ||B r|| = 1.26163e-05
+   Pass :  7   Iteration : 308  ||B r|| = 1.17954e-05
+   Pass :  7   Iteration : 309  ||B r|| = 1.17113e-05
+   Pass :  7   Iteration : 310  ||B r|| = 1.12938e-05
+   Pass :  7   Iteration : 311  ||B r|| = 1.04865e-05
+   Pass :  7   Iteration : 312  ||B r|| = 1.03571e-05
+   Pass :  7   Iteration : 313  ||B r|| = 9.56454e-06
+   Pass :  7   Iteration : 314  ||B r|| = 9.44709e-06
+   Pass :  7   Iteration : 315  ||B r|| = 9.02016e-06
+   Pass :  7   Iteration : 316  ||B r|| = 8.27621e-06
+   Pass :  7   Iteration : 317  ||B r|| = 8.26159e-06
+   Pass :  7   Iteration : 318  ||B r|| = 7.18002e-06
+   Pass :  7   Iteration : 319  ||B r|| = 6.95003e-06
+   Pass :  7   Iteration : 320  ||B r|| = 6.73497e-06
+   Pass :  7   Iteration : 321  ||B r|| = 6.25227e-06
+   Pass :  7   Iteration : 322  ||B r|| = 6.24358e-06
+   Pass :  7   Iteration : 323  ||B r|| = 5.90685e-06
+   Pass :  7   Iteration : 324  ||B r|| = 5.69217e-06
+   Pass :  7   Iteration : 325  ||B r|| = 5.59816e-06
+   Pass :  7   Iteration : 326  ||B r|| = 5.19767e-06
+   Pass :  7   Iteration : 327  ||B r|| = 5.18732e-06
+   Pass :  7   Iteration : 328  ||B r|| = 4.978e-06
+   Pass :  7   Iteration : 329  ||B r|| = 4.61108e-06
+   Pass :  7   Iteration : 330  ||B r|| = 4.60926e-06
+   Pass :  7   Iteration : 331  ||B r|| = 4.23343e-06
+   Pass :  7   Iteration : 332  ||B r|| = 4.23029e-06
+   Pass :  7   Iteration : 333  ||B r|| = 4.01039e-06
+   Pass :  7   Iteration : 334  ||B r|| = 3.86812e-06
+   Pass :  7   Iteration : 335  ||B r|| = 3.86282e-06
+   Pass :  7   Iteration : 336  ||B r|| = 3.60676e-06
+   Pass :  7   Iteration : 337  ||B r|| = 3.53527e-06
+   Pass :  7   Iteration : 338  ||B r|| = 3.33113e-06
+   Pass :  7   Iteration : 339  ||B r|| = 3.15944e-06
+   Pass :  7   Iteration : 340  ||B r|| = 3.14716e-06
+   Pass :  7   Iteration : 341  ||B r|| = 2.97802e-06
+   Pass :  7   Iteration : 342  ||B r|| = 2.95139e-06
+   Pass :  7   Iteration : 343  ||B r|| = 2.86922e-06
+   Pass :  7   Iteration : 344  ||B r|| = 2.65035e-06
+   Pass :  7   Iteration : 345  ||B r|| = 2.64952e-06
+   Pass :  7   Iteration : 346  ||B r|| = 2.48989e-06
+   Pass :  7   Iteration : 347  ||B r|| = 2.42609e-06
+   Pass :  7   Iteration : 348  ||B r|| = 2.35361e-06
+   Pass :  7   Iteration : 349  ||B r|| = 2.0977e-06
+   Pass :  7   Iteration : 350  ||B r|| = 2.0743e-06
+Restarting...
+   Pass :  8   Iteration : 351  ||B r|| = 2.074e-06
+   Pass :  8   Iteration : 352  ||B r|| = 1.9458e-06
+   Pass :  8   Iteration : 353  ||B r|| = 1.91268e-06
+   Pass :  8   Iteration : 354  ||B r|| = 1.9109e-06
+   Pass :  8   Iteration : 355  ||B r|| = 1.71169e-06
+   Pass :  8   Iteration : 356  ||B r|| = 1.70656e-06
+   Pass :  8   Iteration : 357  ||B r|| = 1.61858e-06
+   Pass :  8   Iteration : 358  ||B r|| = 1.53201e-06
+   Pass :  8   Iteration : 359  ||B r|| = 1.52511e-06
+   Pass :  8   Iteration : 360  ||B r|| = 1.4294e-06
+   Pass :  8   Iteration : 361  ||B r|| = 1.40067e-06
+   Pass :  8   Iteration : 362  ||B r|| = 1.35966e-06
+   Pass :  8   Iteration : 363  ||B r|| = 1.29997e-06
+   Pass :  8   Iteration : 364  ||B r|| = 1.29896e-06
+   Pass :  8   Iteration : 365  ||B r|| = 1.192e-06
+   Pass :  8   Iteration : 366  ||B r|| = 1.17842e-06
+   Pass :  8   Iteration : 367  ||B r|| = 1.14545e-06
+   Pass :  8   Iteration : 368  ||B r|| = 1.08481e-06
+   Pass :  8   Iteration : 369  ||B r|| = 1.08408e-06
+   Pass :  8   Iteration : 370  ||B r|| = 1.01158e-06
+   Pass :  8   Iteration : 371  ||B r|| = 9.87365e-07
+   Pass :  8   Iteration : 372  ||B r|| = 9.53571e-07
+   Pass :  8   Iteration : 373  ||B r|| = 9.02865e-07
+   Pass :  8   Iteration : 374  ||B r|| = 9.02529e-07
+   Pass :  8   Iteration : 375  ||B r|| = 8.35677e-07
+GMRES+GS converged in 375 iterations with a residual norm of 8.35677e-07.
+solver took 2.17952s.
+|| q_h - q_ex || / || q_ex || = 5.07159e-05
+|| t_h - t_ex || / || t_ex || = 2.61662e-05

examples/regress_test/p1_o3_dg_nld_umfpack.txt

@@ -0,0 +1,57 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2048
+dim(W) = 1024
+dim(V+W) = 3072
+***********************************************************
+Assembly took 0.141771s.
+Preconditioner took 0.0573248s.
+   Pass :  1   Iteration :   0  ||B r|| = 34.0948
+   Pass :  1   Iteration :   1  ||B r|| = 34.0948
+   Pass :  1   Iteration :   2  ||B r|| = 0.0882945
+   Pass :  1   Iteration :   3  ||B r|| = 0.0197291
+   Pass :  1   Iteration :   4  ||B r|| = 0.0182002
+   Pass :  1   Iteration :   5  ||B r|| = 0.00466911
+   Pass :  1   Iteration :   6  ||B r|| = 0.00191841
+   Pass :  1   Iteration :   7  ||B r|| = 0.00153367
+   Pass :  1   Iteration :   8  ||B r|| = 0.00108376
+   Pass :  1   Iteration :   9  ||B r|| = 0.00106531
+   Pass :  1   Iteration :  10  ||B r|| = 0.000264455
+   Pass :  1   Iteration :  11  ||B r|| = 9.66463e-05
+   Pass :  1   Iteration :  12  ||B r|| = 9.54134e-05
+   Pass :  1   Iteration :  13  ||B r|| = 4.64374e-05
+   Pass :  1   Iteration :  14  ||B r|| = 2.53717e-05
+GMRES+UMFPack converged in 14 iterations with a residual norm of 2.53717e-05.
+solver took 0.0894688s.
+|| q_h - q_ex || / || q_ex || = 5.06633e-05
+|| t_h - t_ex || / || t_ex || = 2.61371e-05

examples/regress_test/p1_o3_dg_rd.txt

@@ -0,0 +1,80 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --reduction
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Reduction init took 0.000134119s.
+***********************************************************
+dim(W) = 1024
+***********************************************************
+Assembly took 0.136547s.
+Preconditioner took 1.374e-05s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.940451
+   Pass :  1   Iteration :   1  ||B r|| = 0.842832
+   Pass :  1   Iteration :   2  ||B r|| = 0.725223
+   Pass :  1   Iteration :   3  ||B r|| = 0.522084
+   Pass :  1   Iteration :   4  ||B r|| = 0.445295
+   Pass :  1   Iteration :   5  ||B r|| = 0.355162
+   Pass :  1   Iteration :   6  ||B r|| = 0.297819
+   Pass :  1   Iteration :   7  ||B r|| = 0.238349
+   Pass :  1   Iteration :   8  ||B r|| = 0.192402
+   Pass :  1   Iteration :   9  ||B r|| = 0.143872
+   Pass :  1   Iteration :  10  ||B r|| = 0.0949139
+   Pass :  1   Iteration :  11  ||B r|| = 0.0606282
+   Pass :  1   Iteration :  12  ||B r|| = 0.0414828
+   Pass :  1   Iteration :  13  ||B r|| = 0.0284458
+   Pass :  1   Iteration :  14  ||B r|| = 0.0188111
+   Pass :  1   Iteration :  15  ||B r|| = 0.0114118
+   Pass :  1   Iteration :  16  ||B r|| = 0.00590335
+   Pass :  1   Iteration :  17  ||B r|| = 0.00348072
+   Pass :  1   Iteration :  18  ||B r|| = 0.00219975
+   Pass :  1   Iteration :  19  ||B r|| = 0.00152431
+   Pass :  1   Iteration :  20  ||B r|| = 0.00105872
+   Pass :  1   Iteration :  21  ||B r|| = 0.000589053
+   Pass :  1   Iteration :  22  ||B r|| = 0.000294206
+   Pass :  1   Iteration :  23  ||B r|| = 0.00017458
+   Pass :  1   Iteration :  24  ||B r|| = 0.000108035
+   Pass :  1   Iteration :  25  ||B r|| = 7.75177e-05
+   Pass :  1   Iteration :  26  ||B r|| = 5.53841e-05
+   Pass :  1   Iteration :  27  ||B r|| = 4.10593e-05
+   Pass :  1   Iteration :  28  ||B r|| = 2.95403e-05
+   Pass :  1   Iteration :  29  ||B r|| = 2.27173e-05
+   Pass :  1   Iteration :  30  ||B r|| = 1.53028e-05
+   Pass :  1   Iteration :  31  ||B r|| = 9.45566e-06
+   Pass :  1   Iteration :  32  ||B r|| = 5.05412e-06
+   Pass :  1   Iteration :  33  ||B r|| = 2.90871e-06
+   Pass :  1   Iteration :  34  ||B r|| = 1.67544e-06
+   Pass :  1   Iteration :  35  ||B r|| = 9.57804e-07
+   Pass :  1   Iteration :  36  ||B r|| = 5.39153e-07
+GMRES+GS converged in 36 iterations with a residual norm of 5.39153e-07.
+solver took 0.0189671s.
+|| q_h - q_ex || / || q_ex || = 5.07039e-05
+|| t_h - t_ex || / || t_ex || = 2.61565e-05

examples/regress_test/p1_o3_dg_rd_umfpack.txt

@@ -0,0 +1,45 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --reduction
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Reduction init took 0.00110061s.
+***********************************************************
+dim(W) = 1024
+***********************************************************
+Assembly took 0.134487s.
+Preconditioner took 0.00721732s.
+   Pass :  1   Iteration :   0  ||B r|| = 46.4068
+   Pass :  1   Iteration :   1  ||B r|| = 6.79805e-14
+GMRES+UMFPack converged in 1 iterations with a residual norm of 6.79805e-14.
+solver took 0.00359861s.
+|| q_h - q_ex || / || q_ex || = 5.07127e-05
+|| t_h - t_ex || / || t_ex || = 2.6156e-05

examples/regress_test/p1_o3_dg_umfpack.txt

@@ -0,0 +1,52 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-hybridization
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2048
+dim(W) = 1024
+dim(V+W) = 3072
+***********************************************************
+Assembly took 0.140492s.
+Preconditioner took 0.0152542s.
+   Pass :  1   Iteration :   0  ||B r|| = 34.0948
+   Pass :  1   Iteration :   1  ||B r|| = 34.0948
+   Pass :  1   Iteration :   2  ||B r|| = 0.0882945
+   Pass :  1   Iteration :   3  ||B r|| = 0.0197291
+   Pass :  1   Iteration :   4  ||B r|| = 0.0182002
+   Pass :  1   Iteration :   5  ||B r|| = 0.00466911
+   Pass :  1   Iteration :   6  ||B r|| = 0.00191841
+   Pass :  1   Iteration :   7  ||B r|| = 0.00153367
+   Pass :  1   Iteration :   8  ||B r|| = 0.00108376
+   Pass :  1   Iteration :   9  ||B r|| = 0.00106531
+   Pass :  1   Iteration :  10  ||B r|| = 0.000264455
+   Pass :  1   Iteration :  11  ||B r|| = 9.66463e-05
+   Pass :  1   Iteration :  12  ||B r|| = 9.54134e-05
+   Pass :  1   Iteration :  13  ||B r|| = 4.64374e-05
+   Pass :  1   Iteration :  14  ||B r|| = 2.53717e-05
+GMRES+UMFPack converged in 14 iterations with a residual norm of 2.53717e-05.
+GMRES solver took 0.0206901s.
+|| q_h - q_ex || / || q_ex || = 5.06633e-05
+|| t_h - t_ex || / || t_ex || = 2.61371e-05

examples/regress_test/p1_o3_hb.txt

@@ -0,0 +1,63 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --hybridization
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2112
+dim(W) = 1024
+dim(V+W) = 3136
+***********************************************************
+Assembly took 0.0342793s.
+Preconditioner took 1.2454e-05s.
+   Pass :  1   Iteration :   0  ||B r|| = 1.36532
+   Pass :  1   Iteration :   1  ||B r|| = 0.999065
+   Pass :  1   Iteration :   2  ||B r|| = 0.687902
+   Pass :  1   Iteration :   3  ||B r|| = 0.493004
+   Pass :  1   Iteration :   4  ||B r|| = 0.376497
+   Pass :  1   Iteration :   5  ||B r|| = 0.282937
+   Pass :  1   Iteration :   6  ||B r|| = 0.178236
+   Pass :  1   Iteration :   7  ||B r|| = 0.108367
+   Pass :  1   Iteration :   8  ||B r|| = 0.0611648
+   Pass :  1   Iteration :   9  ||B r|| = 0.0306066
+   Pass :  1   Iteration :  10  ||B r|| = 0.0182875
+   Pass :  1   Iteration :  11  ||B r|| = 0.00795556
+   Pass :  1   Iteration :  12  ||B r|| = 0.00414347
+   Pass :  1   Iteration :  13  ||B r|| = 0.00181918
+   Pass :  1   Iteration :  14  ||B r|| = 0.00121887
+   Pass :  1   Iteration :  15  ||B r|| = 0.000633013
+   Pass :  1   Iteration :  16  ||B r|| = 0.000336192
+   Pass :  1   Iteration :  17  ||B r|| = 0.000190052
+   Pass :  1   Iteration :  18  ||B r|| = 0.000142776
+   Pass :  1   Iteration :  19  ||B r|| = 8.08217e-05
+   Pass :  1   Iteration :  20  ||B r|| = 4.04241e-05
+   Pass :  1   Iteration :  21  ||B r|| = 1.64814e-05
+   Pass :  1   Iteration :  22  ||B r|| = 9.59614e-06
+   Pass :  1   Iteration :  23  ||B r|| = 2.9853e-06
+   Pass :  1   Iteration :  24  ||B r|| = 1.56186e-06
+   Pass :  1   Iteration :  25  ||B r|| = 4.80159e-07
+GMRES+GS converged in 25 iterations with a residual norm of 4.80159e-07.
+GMRES solver took 0.00317834s.
+|| q_h - q_ex || / || q_ex || = 3.55334e-07
+|| t_h - t_ex || / || t_ex || = 1.76357e-07

examples/regress_test/p1_o3_nl_nld.txt

@@ -0,0 +1,236 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2112
+dim(W) = 1024
+dim(V+W) = 3136
+***********************************************************
+Assembly took 0.0541371s.
+Preconditioner took 0.129626s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.828288
+   Pass :  1   Iteration :   1  ||B r|| = 0.828288
+   Pass :  1   Iteration :   2  ||B r|| = 0.780392
+   Pass :  1   Iteration :   3  ||B r|| = 0.775902
+   Pass :  1   Iteration :   4  ||B r|| = 0.718999
+   Pass :  1   Iteration :   5  ||B r|| = 0.712741
+   Pass :  1   Iteration :   6  ||B r|| = 0.709216
+   Pass :  1   Iteration :   7  ||B r|| = 0.699357
+   Pass :  1   Iteration :   8  ||B r|| = 0.685558
+   Pass :  1   Iteration :   9  ||B r|| = 0.624758
+   Pass :  1   Iteration :  10  ||B r|| = 0.61651
+   Pass :  1   Iteration :  11  ||B r|| = 0.491672
+   Pass :  1   Iteration :  12  ||B r|| = 0.490509
+   Pass :  1   Iteration :  13  ||B r|| = 0.43273
+   Pass :  1   Iteration :  14  ||B r|| = 0.432532
+   Pass :  1   Iteration :  15  ||B r|| = 0.391607
+   Pass :  1   Iteration :  16  ||B r|| = 0.387505
+   Pass :  1   Iteration :  17  ||B r|| = 0.369287
+   Pass :  1   Iteration :  18  ||B r|| = 0.349727
+   Pass :  1   Iteration :  19  ||B r|| = 0.344534
+   Pass :  1   Iteration :  20  ||B r|| = 0.308102
+   Pass :  1   Iteration :  21  ||B r|| = 0.307918
+   Pass :  1   Iteration :  22  ||B r|| = 0.275424
+   Pass :  1   Iteration :  23  ||B r|| = 0.275336
+   Pass :  1   Iteration :  24  ||B r|| = 0.241166
+   Pass :  1   Iteration :  25  ||B r|| = 0.236098
+   Pass :  1   Iteration :  26  ||B r|| = 0.220482
+   Pass :  1   Iteration :  27  ||B r|| = 0.209195
+   Pass :  1   Iteration :  28  ||B r|| = 0.203284
+   Pass :  1   Iteration :  29  ||B r|| = 0.184134
+   Pass :  1   Iteration :  30  ||B r|| = 0.183885
+   Pass :  1   Iteration :  31  ||B r|| = 0.158572
+   Pass :  1   Iteration :  32  ||B r|| = 0.15785
+   Pass :  1   Iteration :  33  ||B r|| = 0.128252
+   Pass :  1   Iteration :  34  ||B r|| = 0.121277
+   Pass :  1   Iteration :  35  ||B r|| = 0.105019
+   Pass :  1   Iteration :  36  ||B r|| = 0.0877653
+   Pass :  1   Iteration :  37  ||B r|| = 0.0857034
+   Pass :  1   Iteration :  38  ||B r|| = 0.0695776
+   Pass :  1   Iteration :  39  ||B r|| = 0.0693421
+   Pass :  1   Iteration :  40  ||B r|| = 0.060764
+   Pass :  1   Iteration :  41  ||B r|| = 0.0583294
+   Pass :  1   Iteration :  42  ||B r|| = 0.0513009
+   Pass :  1   Iteration :  43  ||B r|| = 0.046381
+   Pass :  1   Iteration :  44  ||B r|| = 0.0446401
+   Pass :  1   Iteration :  45  ||B r|| = 0.0351366
+   Pass :  1   Iteration :  46  ||B r|| = 0.0350703
+   Pass :  1   Iteration :  47  ||B r|| = 0.0285254
+   Pass :  1   Iteration :  48  ||B r|| = 0.0275435
+   Pass :  1   Iteration :  49  ||B r|| = 0.0233101
+   Pass :  1   Iteration :  50  ||B r|| = 0.0205522
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 0.0201743
+   Pass :  2   Iteration :  52  ||B r|| = 0.0178036
+   Pass :  2   Iteration :  53  ||B r|| = 0.0177657
+   Pass :  2   Iteration :  54  ||B r|| = 0.0155379
+   Pass :  2   Iteration :  55  ||B r|| = 0.0145024
+   Pass :  2   Iteration :  56  ||B r|| = 0.0129692
+   Pass :  2   Iteration :  57  ||B r|| = 0.0111895
+   Pass :  2   Iteration :  58  ||B r|| = 0.0106264
+   Pass :  2   Iteration :  59  ||B r|| = 0.00883739
+   Pass :  2   Iteration :  60  ||B r|| = 0.00881869
+   Pass :  2   Iteration :  61  ||B r|| = 0.00734547
+   Pass :  2   Iteration :  62  ||B r|| = 0.00727023
+   Pass :  2   Iteration :  63  ||B r|| = 0.00664677
+   Pass :  2   Iteration :  64  ||B r|| = 0.00606592
+   Pass :  2   Iteration :  65  ||B r|| = 0.00584805
+   Pass :  2   Iteration :  66  ||B r|| = 0.00471596
+   Pass :  2   Iteration :  67  ||B r|| = 0.00467814
+   Pass :  2   Iteration :  68  ||B r|| = 0.00343373
+   Pass :  2   Iteration :  69  ||B r|| = 0.0034201
+   Pass :  2   Iteration :  70  ||B r|| = 0.00280534
+   Pass :  2   Iteration :  71  ||B r|| = 0.00270379
+   Pass :  2   Iteration :  72  ||B r|| = 0.0025783
+   Pass :  2   Iteration :  73  ||B r|| = 0.0022472
+   Pass :  2   Iteration :  74  ||B r|| = 0.00221863
+   Pass :  2   Iteration :  75  ||B r|| = 0.00186269
+   Pass :  2   Iteration :  76  ||B r|| = 0.00186179
+   Pass :  2   Iteration :  77  ||B r|| = 0.00160985
+   Pass :  2   Iteration :  78  ||B r|| = 0.00160018
+   Pass :  2   Iteration :  79  ||B r|| = 0.00148445
+   Pass :  2   Iteration :  80  ||B r|| = 0.00141886
+   Pass :  2   Iteration :  81  ||B r|| = 0.00139003
+   Pass :  2   Iteration :  82  ||B r|| = 0.00125305
+   Pass :  2   Iteration :  83  ||B r|| = 0.00124651
+   Pass :  2   Iteration :  84  ||B r|| = 0.00111105
+   Pass :  2   Iteration :  85  ||B r|| = 0.00110481
+   Pass :  2   Iteration :  86  ||B r|| = 0.001019
+   Pass :  2   Iteration :  87  ||B r|| = 0.000986979
+   Pass :  2   Iteration :  88  ||B r|| = 0.000943191
+   Pass :  2   Iteration :  89  ||B r|| = 0.000887917
+   Pass :  2   Iteration :  90  ||B r|| = 0.000878207
+   Pass :  2   Iteration :  91  ||B r|| = 0.000792828
+   Pass :  2   Iteration :  92  ||B r|| = 0.000792314
+   Pass :  2   Iteration :  93  ||B r|| = 0.00067918
+   Pass :  2   Iteration :  94  ||B r|| = 0.000661497
+   Pass :  2   Iteration :  95  ||B r|| = 0.000607798
+   Pass :  2   Iteration :  96  ||B r|| = 0.000585659
+   Pass :  2   Iteration :  97  ||B r|| = 0.000575458
+   Pass :  2   Iteration :  98  ||B r|| = 0.000536371
+   Pass :  2   Iteration :  99  ||B r|| = 0.000533329
+   Pass :  2   Iteration : 100  ||B r|| = 0.000476474
+Restarting...
+   Pass :  3   Iteration : 101  ||B r|| = 0.000476389
+   Pass :  3   Iteration : 102  ||B r|| = 0.000450568
+   Pass :  3   Iteration : 103  ||B r|| = 0.00044946
+   Pass :  3   Iteration : 104  ||B r|| = 0.000448032
+   Pass :  3   Iteration : 105  ||B r|| = 0.000436727
+   Pass :  3   Iteration : 106  ||B r|| = 0.000433054
+   Pass :  3   Iteration : 107  ||B r|| = 0.000384572
+   Pass :  3   Iteration : 108  ||B r|| = 0.000384151
+   Pass :  3   Iteration : 109  ||B r|| = 0.000326889
+   Pass :  3   Iteration : 110  ||B r|| = 0.000320214
+   Pass :  3   Iteration : 111  ||B r|| = 0.000295531
+   Pass :  3   Iteration : 112  ||B r|| = 0.00028017
+   Pass :  3   Iteration : 113  ||B r|| = 0.000271805
+   Pass :  3   Iteration : 114  ||B r|| = 0.000253182
+   Pass :  3   Iteration : 115  ||B r|| = 0.000251705
+   Pass :  3   Iteration : 116  ||B r|| = 0.000224202
+   Pass :  3   Iteration : 117  ||B r|| = 0.00022401
+   Pass :  3   Iteration : 118  ||B r|| = 0.000201373
+   Pass :  3   Iteration : 119  ||B r|| = 0.000195487
+   Pass :  3   Iteration : 120  ||B r|| = 0.000178312
+   Pass :  3   Iteration : 121  ||B r|| = 0.000163707
+   Pass :  3   Iteration : 122  ||B r|| = 0.000159212
+   Pass :  3   Iteration : 123  ||B r|| = 0.000143717
+   Pass :  3   Iteration : 124  ||B r|| = 0.000142938
+   Pass :  3   Iteration : 125  ||B r|| = 0.000129618
+   Pass :  3   Iteration : 126  ||B r|| = 0.000128535
+   Pass :  3   Iteration : 127  ||B r|| = 0.000120081
+   Pass :  3   Iteration : 128  ||B r|| = 0.000114142
+   Pass :  3   Iteration : 129  ||B r|| = 0.000109227
+   Pass :  3   Iteration : 130  ||B r|| = 9.74187e-05
+   Pass :  3   Iteration : 131  ||B r|| = 9.41802e-05
+   Pass :  3   Iteration : 132  ||B r|| = 7.97569e-05
+   Pass :  3   Iteration : 133  ||B r|| = 7.97329e-05
+   Pass :  3   Iteration : 134  ||B r|| = 6.96569e-05
+   Pass :  3   Iteration : 135  ||B r|| = 6.80129e-05
+   Pass :  3   Iteration : 136  ||B r|| = 6.39905e-05
+   Pass :  3   Iteration : 137  ||B r|| = 5.48303e-05
+   Pass :  3   Iteration : 138  ||B r|| = 5.33803e-05
+   Pass :  3   Iteration : 139  ||B r|| = 4.51005e-05
+   Pass :  3   Iteration : 140  ||B r|| = 4.47538e-05
+   Pass :  3   Iteration : 141  ||B r|| = 3.79739e-05
+   Pass :  3   Iteration : 142  ||B r|| = 3.79237e-05
+   Pass :  3   Iteration : 143  ||B r|| = 3.34755e-05
+   Pass :  3   Iteration : 144  ||B r|| = 3.19968e-05
+   Pass :  3   Iteration : 145  ||B r|| = 3.00248e-05
+   Pass :  3   Iteration : 146  ||B r|| = 2.43567e-05
+   Pass :  3   Iteration : 147  ||B r|| = 2.40027e-05
+   Pass :  3   Iteration : 148  ||B r|| = 1.75885e-05
+   Pass :  3   Iteration : 149  ||B r|| = 1.74341e-05
+   Pass :  3   Iteration : 150  ||B r|| = 1.38964e-05
+Restarting...
+   Pass :  4   Iteration : 151  ||B r|| = 1.33084e-05
+   Pass :  4   Iteration : 152  ||B r|| = 1.25291e-05
+   Pass :  4   Iteration : 153  ||B r|| = 1.15613e-05
+   Pass :  4   Iteration : 154  ||B r|| = 1.15039e-05
+   Pass :  4   Iteration : 155  ||B r|| = 8.97445e-06
+   Pass :  4   Iteration : 156  ||B r|| = 8.93619e-06
+   Pass :  4   Iteration : 157  ||B r|| = 7.17725e-06
+   Pass :  4   Iteration : 158  ||B r|| = 7.03949e-06
+   Pass :  4   Iteration : 159  ||B r|| = 6.28998e-06
+   Pass :  4   Iteration : 160  ||B r|| = 5.80418e-06
+   Pass :  4   Iteration : 161  ||B r|| = 5.6565e-06
+   Pass :  4   Iteration : 162  ||B r|| = 4.98291e-06
+   Pass :  4   Iteration : 163  ||B r|| = 4.97198e-06
+   Pass :  4   Iteration : 164  ||B r|| = 4.1327e-06
+   Pass :  4   Iteration : 165  ||B r|| = 4.04729e-06
+   Pass :  4   Iteration : 166  ||B r|| = 3.41458e-06
+   Pass :  4   Iteration : 167  ||B r|| = 3.2682e-06
+   Pass :  4   Iteration : 168  ||B r|| = 3.07084e-06
+   Pass :  4   Iteration : 169  ||B r|| = 2.6426e-06
+   Pass :  4   Iteration : 170  ||B r|| = 2.63354e-06
+   Pass :  4   Iteration : 171  ||B r|| = 2.17891e-06
+   Pass :  4   Iteration : 172  ||B r|| = 2.15133e-06
+   Pass :  4   Iteration : 173  ||B r|| = 1.91418e-06
+   Pass :  4   Iteration : 174  ||B r|| = 1.87277e-06
+   Pass :  4   Iteration : 175  ||B r|| = 1.75707e-06
+   Pass :  4   Iteration : 176  ||B r|| = 1.66039e-06
+   Pass :  4   Iteration : 177  ||B r|| = 1.62259e-06
+   Pass :  4   Iteration : 178  ||B r|| = 1.51352e-06
+   Pass :  4   Iteration : 179  ||B r|| = 1.51341e-06
+   Pass :  4   Iteration : 180  ||B r|| = 1.35973e-06
+   Pass :  4   Iteration : 181  ||B r|| = 1.34071e-06
+   Pass :  4   Iteration : 182  ||B r|| = 1.2227e-06
+   Pass :  4   Iteration : 183  ||B r|| = 1.16459e-06
+   Pass :  4   Iteration : 184  ||B r|| = 1.10473e-06
+   Pass :  4   Iteration : 185  ||B r|| = 9.95649e-07
+   Pass :  4   Iteration : 186  ||B r|| = 9.93491e-07
+   Pass :  4   Iteration : 187  ||B r|| = 9.20855e-07
+   Pass :  4   Iteration : 188  ||B r|| = 9.17534e-07
+   Pass :  4   Iteration : 189  ||B r|| = 8.48816e-07
+   Pass :  4   Iteration : 190  ||B r|| = 8.13729e-07
+GMRES+GS converged in 190 iterations with a residual norm of 8.13729e-07.
+solver took 1.79382s.
+|| q_h - q_ex || / || q_ex || = 1.02359e-06
+|| t_h - t_ex || / || t_ex || = 1.03461e-06

examples/regress_test/p1_o3_nl_nld_umfpack.txt

@@ -0,0 +1,47 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2112
+dim(W) = 1024
+dim(V+W) = 3136
+***********************************************************
+Assembly took 0.0474844s.
+Preconditioner took 0.140224s.
+   Pass :  1   Iteration :   0  ||B r|| = 41.2501
+   Pass :  1   Iteration :   1  ||B r|| = 41.2501
+   Pass :  1   Iteration :   2  ||B r|| = 0.000174926
+   Pass :  1   Iteration :   3  ||B r|| = 4.73276e-05
+   Pass :  1   Iteration :   4  ||B r|| = 5.87823e-06
+GMRES+UMFPack converged in 4 iterations with a residual norm of 5.87823e-06.
+solver took 0.0465522s.
+|| q_h - q_ex || / || q_ex || = 3.02391e-07
+|| t_h - t_ex || / || t_ex || = 1.63476e-07

examples/regress_test/p1_o3_umfpack.txt

@@ -0,0 +1,42 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-hybridization
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2112
+dim(W) = 1024
+dim(V+W) = 3136
+***********************************************************
+Assembly took 0.185992s.
+Preconditioner took 0.0221916s.
+   Pass :  1   Iteration :   0  ||B r|| = 41.2501
+   Pass :  1   Iteration :   1  ||B r|| = 41.2501
+   Pass :  1   Iteration :   2  ||B r|| = 0.000174926
+   Pass :  1   Iteration :   3  ||B r|| = 4.73276e-05
+   Pass :  1   Iteration :   4  ||B r|| = 5.87823e-06
+GMRES+UMFPack converged in 4 iterations with a residual norm of 5.87823e-06.
+GMRES solver took 0.0108975s.
+|| q_h - q_ex || / || q_ex || = 3.02391e-07
+|| t_h - t_ex || / || t_ex || = 1.63476e-07

examples/regress_test/p2_o2_dg_hb_nl.txt

@@ -0,0 +1,126 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 0
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00686143s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.0120627s.
+Preconditioner took 7.2073e-05s.
+LBFGS iteration 0 : ||r|| = 0.0487525
+LBFGS iteration 1 : ||r|| = 0.0692476, ||r||/||r_0|| = 1.42039
+LBFGS iteration 2 : ||r|| = 0.0822451, ||r||/||r_0|| = 1.68699
+LBFGS iteration 3 : ||r|| = 0.118638, ||r||/||r_0|| = 2.43348
+LBFGS iteration 4 : ||r|| = 0.10805, ||r||/||r_0|| = 2.2163
+LBFGS iteration 5 : ||r|| = 0.123018, ||r||/||r_0|| = 2.52331
+LBFGS iteration 6 : ||r|| = 0.0331166, ||r||/||r_0|| = 0.67928
+LBFGS iteration 7 : ||r|| = 0.028239, ||r||/||r_0|| = 0.579233
+LBFGS iteration 8 : ||r|| = 0.0339501, ||r||/||r_0|| = 0.696376
+LBFGS iteration 9 : ||r|| = 0.0632489, ||r||/||r_0|| = 1.29735
+LBFGS iteration 10 : ||r|| = 0.0197064, ||r||/||r_0|| = 0.404214
+LBFGS iteration 11 : ||r|| = 0.0115797, ||r||/||r_0|| = 0.23752
+LBFGS iteration 12 : ||r|| = 0.0132388, ||r||/||r_0|| = 0.271551
+LBFGS iteration 13 : ||r|| = 0.0185307, ||r||/||r_0|| = 0.380097
+LBFGS iteration 14 : ||r|| = 0.0080584, ||r||/||r_0|| = 0.165292
+LBFGS iteration 15 : ||r|| = 0.0039921, ||r||/||r_0|| = 0.0818851
+LBFGS iteration 16 : ||r|| = 0.00336111, ||r||/||r_0|| = 0.0689424
+LBFGS iteration 17 : ||r|| = 0.00385752, ||r||/||r_0|| = 0.0791246
+LBFGS iteration 18 : ||r|| = 0.00192135, ||r||/||r_0|| = 0.0394103
+LBFGS iteration 19 : ||r|| = 0.000721511, ||r||/||r_0|| = 0.0147995
+LBFGS iteration 20 : ||r|| = 0.000602175, ||r||/||r_0|| = 0.0123517
+LBFGS iteration 21 : ||r|| = 0.000652919, ||r||/||r_0|| = 0.0133925
+LBFGS iteration 22 : ||r|| = 0.00115966, ||r||/||r_0|| = 0.0237866
+LBFGS iteration 23 : ||r|| = 0.000458624, ||r||/||r_0|| = 0.00940719
+LBFGS iteration 24 : ||r|| = 0.000389708, ||r||/||r_0|| = 0.0079936
+LBFGS iteration 25 : ||r|| = 0.000556569, ||r||/||r_0|| = 0.0114162
+LBFGS iteration 26 : ||r|| = 0.000629825, ||r||/||r_0|| = 0.0129188
+LBFGS iteration 27 : ||r|| = 0.00235984, ||r||/||r_0|| = 0.0484044
+LBFGS iteration 28 : ||r|| = 0.000319451, ||r||/||r_0|| = 0.00655251
+LBFGS iteration 29 : ||r|| = 0.000182618, ||r||/||r_0|| = 0.00374581
+LBFGS iteration 30 : ||r|| = 0.000134455, ||r||/||r_0|| = 0.00275791
+LBFGS iteration 31 : ||r|| = 0.000165894, ||r||/||r_0|| = 0.00340278
+LBFGS iteration 32 : ||r|| = 0.000266006, ||r||/||r_0|| = 0.00545626
+LBFGS iteration 33 : ||r|| = 0.000247654, ||r||/||r_0|| = 0.00507981
+LBFGS iteration 34 : ||r|| = 8.2696e-05, ||r||/||r_0|| = 0.00169624
+LBFGS iteration 35 : ||r|| = 6.20613e-05, ||r||/||r_0|| = 0.00127299
+LBFGS iteration 36 : ||r|| = 7.09828e-05, ||r||/||r_0|| = 0.00145598
+LBFGS iteration 37 : ||r|| = 0.000188153, ||r||/||r_0|| = 0.00385936
+LBFGS iteration 38 : ||r|| = 7.43305e-05, ||r||/||r_0|| = 0.00152465
+LBFGS iteration 39 : ||r|| = 5.84411e-05, ||r||/||r_0|| = 0.00119873
+LBFGS iteration 40 : ||r|| = 6.66851e-05, ||r||/||r_0|| = 0.00136783
+LBFGS iteration 41 : ||r|| = 8.73801e-05, ||r||/||r_0|| = 0.00179232
+LBFGS iteration 42 : ||r|| = 5.69932e-05, ||r||/||r_0|| = 0.00116903
+LBFGS iteration 43 : ||r|| = 1.66973e-05, ||r||/||r_0|| = 0.000342492
+LBFGS iteration 44 : ||r|| = 1.28376e-05, ||r||/||r_0|| = 0.000263322
+LBFGS iteration 45 : ||r|| = 1.44508e-05, ||r||/||r_0|| = 0.000296411
+LBFGS iteration 46 : ||r|| = 2.93946e-05, ||r||/||r_0|| = 0.000602936
+LBFGS iteration 47 : ||r|| = 6.07783e-06, ||r||/||r_0|| = 0.000124667
+LBFGS iteration 48 : ||r|| = 4.09353e-06, ||r||/||r_0|| = 8.39656e-05
+LBFGS iteration 49 : ||r|| = 4.37315e-06, ||r||/||r_0|| = 8.9701e-05
+LBFGS iteration 50 : ||r|| = 5.92802e-06, ||r||/||r_0|| = 0.000121594
+LBFGS iteration 51 : ||r|| = 6.92108e-06, ||r||/||r_0|| = 0.000141964
+LBFGS iteration 52 : ||r|| = 2.81197e-06, ||r||/||r_0|| = 5.76786e-05
+LBFGS iteration 53 : ||r|| = 2.16963e-06, ||r||/||r_0|| = 4.4503e-05
+LBFGS iteration 54 : ||r|| = 2.09303e-06, ||r||/||r_0|| = 4.29317e-05
+LBFGS iteration 55 : ||r|| = 3.14986e-06, ||r||/||r_0|| = 6.46092e-05
+LBFGS iteration 56 : ||r|| = 1.71347e-06, ||r||/||r_0|| = 3.51464e-05
+LBFGS iteration 57 : ||r|| = 1.61416e-06, ||r||/||r_0|| = 3.31093e-05
+LBFGS iteration 58 : ||r|| = 1.84854e-06, ||r||/||r_0|| = 3.79169e-05
+LBFGS iteration 59 : ||r|| = 4.36115e-06, ||r||/||r_0|| = 8.9455e-05
+LBFGS iteration 60 : ||r|| = 8.47721e-07, ||r||/||r_0|| = 1.73883e-05
+LBFGS iteration 61 : ||r|| = 4.73673e-07, ||r||/||r_0|| = 9.71588e-06
+LBFGS iteration 62 : ||r|| = 5.08728e-07, ||r||/||r_0|| = 1.04349e-05
+LBFGS iteration 63 : ||r|| = 5.89533e-07, ||r||/||r_0|| = 1.20924e-05
+LBFGS iteration 64 : ||r|| = 9.02349e-07, ||r||/||r_0|| = 1.85088e-05
+LBFGS iteration 65 : ||r|| = 2.67276e-07, ||r||/||r_0|| = 5.48231e-06
+LBFGS iteration 66 : ||r|| = 1.73874e-07, ||r||/||r_0|| = 3.56647e-06
+LBFGS iteration 67 : ||r|| = 1.67946e-07, ||r||/||r_0|| = 3.44488e-06
+LBFGS iteration 68 : ||r|| = 2.39486e-07, ||r||/||r_0|| = 4.91227e-06
+LBFGS iteration 69 : ||r|| = 1.74799e-07, ||r||/||r_0|| = 3.58544e-06
+LBFGS iteration 70 : ||r|| = 1.38108e-07, ||r||/||r_0|| = 2.83284e-06
+LBFGS iteration 71 : ||r|| = 1.5727e-07, ||r||/||r_0|| = 3.22588e-06
+LBFGS iteration 72 : ||r|| = 1.69831e-07, ||r||/||r_0|| = 3.48354e-06
+LBFGS iteration 73 : ||r|| = 1.44929e-07, ||r||/||r_0|| = 2.97275e-06
+LBFGS iteration 74 : ||r|| = 9.706e-08, ||r||/||r_0|| = 1.99087e-06
+LBFGS iteration 75 : ||r|| = 9.15601e-08, ||r||/||r_0|| = 1.87806e-06
+LBFGS iteration 76 : ||r|| = 1.55269e-07, ||r||/||r_0|| = 3.18485e-06
+LBFGS iteration 77 : ||r|| = 7.85595e-08, ||r||/||r_0|| = 1.6114e-06
+LBFGS iteration 78 : ||r|| = 3.44741e-08, ||r||/||r_0|| = 7.07125e-07
+LBFGS/Newton+GMRES converged in 78 iterations with a residual norm of 3.44741e-08.
+solver took 10.3609s.
+|| q_h - q_ex || / || q_ex || = 0.000103258
+|| t_h - t_ex || / || t_ex || = 6.13896e-05

examples/regress_test/p2_o2_dg_hb_nl_newton.txt

@@ -0,0 +1,86 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00638558s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.00964168s.
+Preconditioner took 3.6389e-05s.
+Newton iteration  0 : ||r|| = 0.102997
+Newton iteration  1 : ||r|| = 0.000212358, ||r||/||r_0|| = 0.00206179
+Newton iteration  2 : ||r|| = 7.28894e-05, ||r||/||r_0|| = 0.000707684
+Newton iteration  3 : ||r|| = 3.17779e-05, ||r||/||r_0|| = 0.000308532
+Newton iteration  4 : ||r|| = 2.76903e-05, ||r||/||r_0|| = 0.000268845
+Newton iteration  5 : ||r|| = 2.17462e-05, ||r||/||r_0|| = 0.000211134
+Newton iteration  6 : ||r|| = 1.7992e-05, ||r||/||r_0|| = 0.000174684
+Newton iteration  7 : ||r|| = 1.50151e-05, ||r||/||r_0|| = 0.000145781
+Newton iteration  8 : ||r|| = 1.26765e-05, ||r||/||r_0|| = 0.000123076
+Newton iteration  9 : ||r|| = 1.07699e-05, ||r||/||r_0|| = 0.000104565
+Newton iteration 10 : ||r|| = 9.18746e-06, ||r||/||r_0|| = 8.92011e-05
+Newton iteration 11 : ||r|| = 7.85578e-06, ||r||/||r_0|| = 7.62718e-05
+Newton iteration 12 : ||r|| = 6.72573e-06, ||r||/||r_0|| = 6.53002e-05
+Newton iteration 13 : ||r|| = 5.76189e-06, ||r||/||r_0|| = 5.59422e-05
+Newton iteration 14 : ||r|| = 4.93744e-06, ||r||/||r_0|| = 4.79377e-05
+Newton iteration 15 : ||r|| = 4.23115e-06, ||r||/||r_0|| = 4.10802e-05
+Newton iteration 16 : ||r|| = 3.62564e-06, ||r||/||r_0|| = 3.52014e-05
+Newton iteration 17 : ||r|| = 3.10642e-06, ||r||/||r_0|| = 3.01602e-05
+Newton iteration 18 : ||r|| = 2.66118e-06, ||r||/||r_0|| = 2.58375e-05
+Newton iteration 19 : ||r|| = 2.27945e-06, ||r||/||r_0|| = 2.21312e-05
+Newton iteration 20 : ||r|| = 1.95223e-06, ||r||/||r_0|| = 1.89543e-05
+Newton iteration 21 : ||r|| = 1.6718e-06, ||r||/||r_0|| = 1.62315e-05
+Newton iteration 22 : ||r|| = 1.43151e-06, ||r||/||r_0|| = 1.38985e-05
+Newton iteration 23 : ||r|| = 1.22566e-06, ||r||/||r_0|| = 1.18999e-05
+Newton iteration 24 : ||r|| = 1.04934e-06, ||r||/||r_0|| = 1.0188e-05
+Newton iteration 25 : ||r|| = 8.98328e-07, ||r||/||r_0|| = 8.72188e-06
+Newton iteration 26 : ||r|| = 7.69016e-07, ||r||/||r_0|| = 7.46639e-06
+Newton iteration 27 : ||r|| = 6.58293e-07, ||r||/||r_0|| = 6.39137e-06
+Newton iteration 28 : ||r|| = 5.63494e-07, ||r||/||r_0|| = 5.47097e-06
+Newton iteration 29 : ||r|| = 4.82335e-07, ||r||/||r_0|| = 4.68299e-06
+Newton iteration 30 : ||r|| = 4.12856e-07, ||r||/||r_0|| = 4.00842e-06
+Newton iteration 31 : ||r|| = 3.5338e-07, ||r||/||r_0|| = 3.43096e-06
+Newton iteration 32 : ||r|| = 3.02467e-07, ||r||/||r_0|| = 2.93666e-06
+Newton iteration 33 : ||r|| = 2.58889e-07, ||r||/||r_0|| = 2.51355e-06
+Newton iteration 34 : ||r|| = 2.21585e-07, ||r||/||r_0|| = 2.15137e-06
+Newton iteration 35 : ||r|| = 1.89656e-07, ||r||/||r_0|| = 1.84137e-06
+Newton iteration 36 : ||r|| = 1.62327e-07, ||r||/||r_0|| = 1.57603e-06
+Newton iteration 37 : ||r|| = 1.38934e-07, ||r||/||r_0|| = 1.34891e-06
+Newton iteration 38 : ||r|| = 1.18913e-07, ||r||/||r_0|| = 1.15453e-06
+Newton iteration 39 : ||r|| = 1.01775e-07, ||r||/||r_0|| = 9.88139e-07
+Newton+GMRES+GS/Newton+GMRES converged in 39 iterations with a residual norm of 1.01775e-07.
+solver took 13.3521s.
+|| q_h - q_ex || / || q_ex || = 0.000108111
+|| t_h - t_ex || / || t_ex || = 1.8685e-05

examples/regress_test/p2_o2_dg_hb_nlc_hdg1.txt

@@ -0,0 +1,244 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0099388s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.0143097s.
+Preconditioner took 5.4394e-05s.
+LBFGS iteration 0 : ||r|| = 0.102998
+LBFGS iteration 1 : ||r|| = 0.271172, ||r||/||r_0|| = 2.63278
+LBFGS iteration 2 : ||r|| = 0.0841892, ||r||/||r_0|| = 0.817385
+LBFGS iteration 3 : ||r|| = 0.0784426, ||r||/||r_0|| = 0.761592
+LBFGS iteration 4 : ||r|| = 0.22129, ||r||/||r_0|| = 2.14848
+LBFGS iteration 5 : ||r|| = 0.0742401, ||r||/||r_0|| = 0.72079
+LBFGS iteration 6 : ||r|| = 0.0453347, ||r||/||r_0|| = 0.44015
+LBFGS iteration 7 : ||r|| = 0.0381501, ||r||/||r_0|| = 0.370396
+LBFGS iteration 8 : ||r|| = 0.0938069, ||r||/||r_0|| = 0.910763
+LBFGS iteration 9 : ||r|| = 0.0531746, ||r||/||r_0|| = 0.516268
+LBFGS iteration 10 : ||r|| = 0.0343101, ||r||/||r_0|| = 0.333114
+LBFGS iteration 11 : ||r|| = 0.0337266, ||r||/||r_0|| = 0.327448
+LBFGS iteration 12 : ||r|| = 0.0551221, ||r||/||r_0|| = 0.535176
+LBFGS iteration 13 : ||r|| = 0.0321613, ||r||/||r_0|| = 0.312251
+LBFGS iteration 14 : ||r|| = 0.0228749, ||r||/||r_0|| = 0.22209
+LBFGS iteration 15 : ||r|| = 0.0247366, ||r||/||r_0|| = 0.240165
+LBFGS iteration 16 : ||r|| = 0.0297442, ||r||/||r_0|| = 0.288783
+LBFGS iteration 17 : ||r|| = 0.0226467, ||r||/||r_0|| = 0.219874
+LBFGS iteration 18 : ||r|| = 0.0171502, ||r||/||r_0|| = 0.16651
+LBFGS iteration 19 : ||r|| = 0.0165138, ||r||/||r_0|| = 0.160331
+LBFGS iteration 20 : ||r|| = 0.0330431, ||r||/||r_0|| = 0.320813
+LBFGS iteration 21 : ||r|| = 0.0162798, ||r||/||r_0|| = 0.15806
+LBFGS iteration 22 : ||r|| = 0.0125702, ||r||/||r_0|| = 0.122043
+LBFGS iteration 23 : ||r|| = 0.0127564, ||r||/||r_0|| = 0.12385
+LBFGS iteration 24 : ||r|| = 0.0463668, ||r||/||r_0|| = 0.450171
+LBFGS iteration 25 : ||r|| = 0.00995276, ||r||/||r_0|| = 0.0966305
+LBFGS iteration 26 : ||r|| = 0.00773456, ||r||/||r_0|| = 0.0750941
+LBFGS iteration 27 : ||r|| = 0.00877639, ||r||/||r_0|| = 0.0852091
+LBFGS iteration 28 : ||r|| = 0.0198403, ||r||/||r_0|| = 0.192628
+LBFGS iteration 29 : ||r|| = 0.00966618, ||r||/||r_0|| = 0.093848
+LBFGS iteration 30 : ||r|| = 0.00822464, ||r||/||r_0|| = 0.0798523
+LBFGS iteration 31 : ||r|| = 0.010455, ||r||/||r_0|| = 0.101506
+LBFGS iteration 32 : ||r|| = 0.0170397, ||r||/||r_0|| = 0.165437
+LBFGS iteration 33 : ||r|| = 0.011009, ||r||/||r_0|| = 0.106885
+LBFGS iteration 34 : ||r|| = 0.00973205, ||r||/||r_0|| = 0.0944876
+LBFGS iteration 35 : ||r|| = 0.0180064, ||r||/||r_0|| = 0.174823
+LBFGS iteration 36 : ||r|| = 0.0262695, ||r||/||r_0|| = 0.255048
+LBFGS iteration 37 : ||r|| = 0.0153731, ||r||/||r_0|| = 0.149256
+LBFGS iteration 38 : ||r|| = 0.0124318, ||r||/||r_0|| = 0.120699
+LBFGS iteration 39 : ||r|| = 0.0161489, ||r||/||r_0|| = 0.156788
+LBFGS iteration 40 : ||r|| = 0.0231595, ||r||/||r_0|| = 0.224853
+LBFGS iteration 41 : ||r|| = 0.0351379, ||r||/||r_0|| = 0.34115
+LBFGS iteration 42 : ||r|| = 0.0127315, ||r||/||r_0|| = 0.123609
+LBFGS iteration 43 : ||r|| = 0.00946017, ||r||/||r_0|| = 0.0918479
+LBFGS iteration 44 : ||r|| = 0.0120456, ||r||/||r_0|| = 0.116949
+LBFGS iteration 45 : ||r|| = 0.0118487, ||r||/||r_0|| = 0.115038
+LBFGS iteration 46 : ||r|| = 0.0477269, ||r||/||r_0|| = 0.463376
+LBFGS iteration 47 : ||r|| = 0.00548645, ||r||/||r_0|| = 0.0532675
+LBFGS iteration 48 : ||r|| = 0.00415111, ||r||/||r_0|| = 0.0403028
+LBFGS iteration 49 : ||r|| = 0.00529017, ||r||/||r_0|| = 0.0513618
+LBFGS iteration 50 : ||r|| = 0.00672447, ||r||/||r_0|| = 0.0652872
+LBFGS iteration 51 : ||r|| = 0.0156403, ||r||/||r_0|| = 0.15185
+LBFGS iteration 52 : ||r|| = 0.00424167, ||r||/||r_0|| = 0.041182
+LBFGS iteration 53 : ||r|| = 0.00301382, ||r||/||r_0|| = 0.0292609
+LBFGS iteration 54 : ||r|| = 0.00318902, ||r||/||r_0|| = 0.0309619
+LBFGS iteration 55 : ||r|| = 0.00685096, ||r||/||r_0|| = 0.0665153
+LBFGS iteration 56 : ||r|| = 0.00322596, ||r||/||r_0|| = 0.0313205
+LBFGS iteration 57 : ||r|| = 0.00283775, ||r||/||r_0|| = 0.0275514
+LBFGS iteration 58 : ||r|| = 0.00387597, ||r||/||r_0|| = 0.0376315
+LBFGS iteration 59 : ||r|| = 0.00513989, ||r||/||r_0|| = 0.0499027
+LBFGS iteration 60 : ||r|| = 0.00776876, ||r||/||r_0|| = 0.0754262
+LBFGS iteration 61 : ||r|| = 0.00244952, ||r||/||r_0|| = 0.0237821
+LBFGS iteration 62 : ||r|| = 0.00183117, ||r||/||r_0|| = 0.0177786
+LBFGS iteration 63 : ||r|| = 0.00227826, ||r||/||r_0|| = 0.0221194
+LBFGS iteration 64 : ||r|| = 0.00332178, ||r||/||r_0|| = 0.0322509
+LBFGS iteration 65 : ||r|| = 0.00415374, ||r||/||r_0|| = 0.0403283
+LBFGS iteration 66 : ||r|| = 0.00181323, ||r||/||r_0|| = 0.0176045
+LBFGS iteration 67 : ||r|| = 0.00174389, ||r||/||r_0|| = 0.0169313
+LBFGS iteration 68 : ||r|| = 0.0020263, ||r||/||r_0|| = 0.0196732
+LBFGS iteration 69 : ||r|| = 0.00568839, ||r||/||r_0|| = 0.0552281
+LBFGS iteration 70 : ||r|| = 0.00189302, ||r||/||r_0|| = 0.0183792
+LBFGS iteration 71 : ||r|| = 0.00132959, ||r||/||r_0|| = 0.0129088
+LBFGS iteration 72 : ||r|| = 0.00136831, ||r||/||r_0|| = 0.0132848
+LBFGS iteration 73 : ||r|| = 0.00166149, ||r||/||r_0|| = 0.0161312
+LBFGS iteration 74 : ||r|| = 0.00379668, ||r||/||r_0|| = 0.0368616
+LBFGS iteration 75 : ||r|| = 0.00105996, ||r||/||r_0|| = 0.010291
+LBFGS iteration 76 : ||r|| = 0.000884205, ||r||/||r_0|| = 0.00858467
+LBFGS iteration 77 : ||r|| = 0.00120409, ||r||/||r_0|| = 0.0116904
+LBFGS iteration 78 : ||r|| = 0.00165343, ||r||/||r_0|| = 0.016053
+LBFGS iteration 79 : ||r|| = 0.00314008, ||r||/||r_0|| = 0.0304867
+LBFGS iteration 80 : ||r|| = 0.0014337, ||r||/||r_0|| = 0.0139196
+LBFGS iteration 81 : ||r|| = 0.00140075, ||r||/||r_0|| = 0.0135998
+LBFGS iteration 82 : ||r|| = 0.0018572, ||r||/||r_0|| = 0.0180314
+LBFGS iteration 83 : ||r|| = 0.00376407, ||r||/||r_0|| = 0.036545
+LBFGS iteration 84 : ||r|| = 0.00226196, ||r||/||r_0|| = 0.0219612
+LBFGS iteration 85 : ||r|| = 0.00163059, ||r||/||r_0|| = 0.0158312
+LBFGS iteration 86 : ||r|| = 0.00180682, ||r||/||r_0|| = 0.0175422
+LBFGS iteration 87 : ||r|| = 0.00329049, ||r||/||r_0|| = 0.0319471
+LBFGS iteration 88 : ||r|| = 0.0010264, ||r||/||r_0|| = 0.00996521
+LBFGS iteration 89 : ||r|| = 0.000702226, ||r||/||r_0|| = 0.00681785
+LBFGS iteration 90 : ||r|| = 0.000669535, ||r||/||r_0|| = 0.00650046
+LBFGS iteration 91 : ||r|| = 0.00115642, ||r||/||r_0|| = 0.0112276
+LBFGS iteration 92 : ||r|| = 0.000397287, ||r||/||r_0|| = 0.00385722
+LBFGS iteration 93 : ||r|| = 0.000312461, ||r||/||r_0|| = 0.00303366
+LBFGS iteration 94 : ||r|| = 0.000372996, ||r||/||r_0|| = 0.00362138
+LBFGS iteration 95 : ||r|| = 0.000783238, ||r||/||r_0|| = 0.00760439
+LBFGS iteration 96 : ||r|| = 0.000281058, ||r||/||r_0|| = 0.00272876
+LBFGS iteration 97 : ||r|| = 0.000213155, ||r||/||r_0|| = 0.0020695
+LBFGS iteration 98 : ||r|| = 0.000243323, ||r||/||r_0|| = 0.0023624
+LBFGS iteration 99 : ||r|| = 0.000313185, ||r||/||r_0|| = 0.00304068
+LBFGS iteration 100 : ||r|| = 0.000665351, ||r||/||r_0|| = 0.00645983
+LBFGS iteration 101 : ||r|| = 0.000111608, ||r||/||r_0|| = 0.00108359
+LBFGS iteration 102 : ||r|| = 9.33731e-05, ||r||/||r_0|| = 0.000906551
+LBFGS iteration 103 : ||r|| = 0.000144744, ||r||/||r_0|| = 0.00140531
+LBFGS iteration 104 : ||r|| = 0.000225511, ||r||/||r_0|| = 0.00218947
+LBFGS iteration 105 : ||r|| = 0.000102313, ||r||/||r_0|| = 0.000993346
+LBFGS iteration 106 : ||r|| = 9.13002e-05, ||r||/||r_0|| = 0.000886425
+LBFGS iteration 107 : ||r|| = 8.62169e-05, ||r||/||r_0|| = 0.000837072
+LBFGS iteration 108 : ||r|| = 0.000295226, ||r||/||r_0|| = 0.00286633
+LBFGS iteration 109 : ||r|| = 4.8086e-05, ||r||/||r_0|| = 0.000466862
+LBFGS iteration 110 : ||r|| = 3.23783e-05, ||r||/||r_0|| = 0.000314358
+LBFGS iteration 111 : ||r|| = 3.07194e-05, ||r||/||r_0|| = 0.000298252
+LBFGS iteration 112 : ||r|| = 4.16119e-05, ||r||/||r_0|| = 0.000404006
+LBFGS iteration 113 : ||r|| = 0.000109023, ||r||/||r_0|| = 0.00105849
+LBFGS iteration 114 : ||r|| = 4.01945e-05, ||r||/||r_0|| = 0.000390245
+LBFGS iteration 115 : ||r|| = 2.86779e-05, ||r||/||r_0|| = 0.000278431
+LBFGS iteration 116 : ||r|| = 4.35855e-05, ||r||/||r_0|| = 0.000423168
+LBFGS iteration 117 : ||r|| = 5.12247e-05, ||r||/||r_0|| = 0.000497336
+LBFGS iteration 118 : ||r|| = 0.000127964, ||r||/||r_0|| = 0.00124239
+LBFGS iteration 119 : ||r|| = 5.92462e-05, ||r||/||r_0|| = 0.000575216
+LBFGS iteration 120 : ||r|| = 4.2893e-05, ||r||/||r_0|| = 0.000416444
+LBFGS iteration 121 : ||r|| = 6.63128e-05, ||r||/||r_0|| = 0.000643825
+LBFGS iteration 122 : ||r|| = 9.14301e-05, ||r||/||r_0|| = 0.000887687
+LBFGS iteration 123 : ||r|| = 0.00010506, ||r||/||r_0|| = 0.00102001
+LBFGS iteration 124 : ||r|| = 5.09164e-05, ||r||/||r_0|| = 0.000494343
+LBFGS iteration 125 : ||r|| = 6.28054e-05, ||r||/||r_0|| = 0.000609772
+LBFGS iteration 126 : ||r|| = 7.11059e-05, ||r||/||r_0|| = 0.000690361
+LBFGS iteration 127 : ||r|| = 0.000193586, ||r||/||r_0|| = 0.00187951
+LBFGS iteration 128 : ||r|| = 5.63144e-05, ||r||/||r_0|| = 0.000546751
+LBFGS iteration 129 : ||r|| = 3.61646e-05, ||r||/||r_0|| = 0.000351119
+LBFGS iteration 130 : ||r|| = 4.1231e-05, ||r||/||r_0|| = 0.000400308
+LBFGS iteration 131 : ||r|| = 4.59783e-05, ||r||/||r_0|| = 0.000446399
+LBFGS iteration 132 : ||r|| = 0.000153525, ||r||/||r_0|| = 0.00149056
+LBFGS iteration 133 : ||r|| = 2.93105e-05, ||r||/||r_0|| = 0.000284573
+LBFGS iteration 134 : ||r|| = 1.80206e-05, ||r||/||r_0|| = 0.00017496
+LBFGS iteration 135 : ||r|| = 1.76399e-05, ||r||/||r_0|| = 0.000171264
+LBFGS iteration 136 : ||r|| = 2.14596e-05, ||r||/||r_0|| = 0.000208349
+LBFGS iteration 137 : ||r|| = 4.18038e-05, ||r||/||r_0|| = 0.000405869
+LBFGS iteration 138 : ||r|| = 1.23309e-05, ||r||/||r_0|| = 0.000119719
+LBFGS iteration 139 : ||r|| = 1.10831e-05, ||r||/||r_0|| = 0.000107605
+LBFGS iteration 140 : ||r|| = 1.25287e-05, ||r||/||r_0|| = 0.00012164
+LBFGS iteration 141 : ||r|| = 4.05171e-05, ||r||/||r_0|| = 0.000393377
+LBFGS iteration 142 : ||r|| = 1.15912e-05, ||r||/||r_0|| = 0.000112538
+LBFGS iteration 143 : ||r|| = 8.42843e-06, ||r||/||r_0|| = 8.18309e-05
+LBFGS iteration 144 : ||r|| = 9.62354e-06, ||r||/||r_0|| = 9.34341e-05
+LBFGS iteration 145 : ||r|| = 9.97105e-06, ||r||/||r_0|| = 9.6808e-05
+LBFGS iteration 146 : ||r|| = 3.44715e-05, ||r||/||r_0|| = 0.000334681
+LBFGS iteration 147 : ||r|| = 5.88102e-06, ||r||/||r_0|| = 5.70982e-05
+LBFGS iteration 148 : ||r|| = 5.02618e-06, ||r||/||r_0|| = 4.87987e-05
+LBFGS iteration 149 : ||r|| = 6.00365e-06, ||r||/||r_0|| = 5.82889e-05
+LBFGS iteration 150 : ||r|| = 1.43151e-05, ||r||/||r_0|| = 0.000138984
+LBFGS iteration 151 : ||r|| = 5.69353e-06, ||r||/||r_0|| = 5.52779e-05
+LBFGS iteration 152 : ||r|| = 3.7348e-06, ||r||/||r_0|| = 3.62609e-05
+LBFGS iteration 153 : ||r|| = 3.8149e-06, ||r||/||r_0|| = 3.70385e-05
+LBFGS iteration 154 : ||r|| = 3.58341e-06, ||r||/||r_0|| = 3.4791e-05
+LBFGS iteration 155 : ||r|| = 1.43055e-05, ||r||/||r_0|| = 0.000138891
+LBFGS iteration 156 : ||r|| = 2.27484e-06, ||r||/||r_0|| = 2.20862e-05
+LBFGS iteration 157 : ||r|| = 1.80614e-06, ||r||/||r_0|| = 1.75356e-05
+LBFGS iteration 158 : ||r|| = 1.93981e-06, ||r||/||r_0|| = 1.88335e-05
+LBFGS iteration 159 : ||r|| = 4.57294e-06, ||r||/||r_0|| = 4.43983e-05
+LBFGS iteration 160 : ||r|| = 1.84275e-06, ||r||/||r_0|| = 1.78911e-05
+LBFGS iteration 161 : ||r|| = 1.45863e-06, ||r||/||r_0|| = 1.41617e-05
+LBFGS iteration 162 : ||r|| = 1.68099e-06, ||r||/||r_0|| = 1.63206e-05
+LBFGS iteration 163 : ||r|| = 1.82306e-06, ||r||/||r_0|| = 1.77e-05
+LBFGS iteration 164 : ||r|| = 6.21111e-06, ||r||/||r_0|| = 6.03031e-05
+LBFGS iteration 165 : ||r|| = 9.80448e-07, ||r||/||r_0|| = 9.51908e-06
+LBFGS iteration 166 : ||r|| = 8.22413e-07, ||r||/||r_0|| = 7.98474e-06
+LBFGS iteration 167 : ||r|| = 1.1065e-06, ||r||/||r_0|| = 1.07429e-05
+LBFGS iteration 168 : ||r|| = 1.62654e-06, ||r||/||r_0|| = 1.57919e-05
+LBFGS iteration 169 : ||r|| = 1.86364e-06, ||r||/||r_0|| = 1.8094e-05
+LBFGS iteration 170 : ||r|| = 1.48631e-06, ||r||/||r_0|| = 1.44305e-05
+LBFGS iteration 171 : ||r|| = 2.36915e-06, ||r||/||r_0|| = 2.30018e-05
+LBFGS iteration 172 : ||r|| = 3.33242e-06, ||r||/||r_0|| = 3.23541e-05
+LBFGS iteration 173 : ||r|| = 2.87959e-06, ||r||/||r_0|| = 2.79577e-05
+LBFGS iteration 174 : ||r|| = 3.38872e-06, ||r||/||r_0|| = 3.29008e-05
+LBFGS iteration 175 : ||r|| = 3.05819e-06, ||r||/||r_0|| = 2.96917e-05
+LBFGS iteration 176 : ||r|| = 2.0389e-06, ||r||/||r_0|| = 1.97955e-05
+LBFGS iteration 177 : ||r|| = 1.67249e-06, ||r||/||r_0|| = 1.6238e-05
+LBFGS iteration 178 : ||r|| = 2.24282e-06, ||r||/||r_0|| = 2.17753e-05
+LBFGS iteration 179 : ||r|| = 1.20688e-06, ||r||/||r_0|| = 1.17175e-05
+LBFGS iteration 180 : ||r|| = 9.09721e-07, ||r||/||r_0|| = 8.8324e-06
+LBFGS iteration 181 : ||r|| = 9.95028e-07, ||r||/||r_0|| = 9.66063e-06
+LBFGS iteration 182 : ||r|| = 7.30319e-07, ||r||/||r_0|| = 7.0906e-06
+LBFGS iteration 183 : ||r|| = 1.10231e-06, ||r||/||r_0|| = 1.07022e-05
+LBFGS iteration 184 : ||r|| = 6.43652e-07, ||r||/||r_0|| = 6.24916e-06
+LBFGS iteration 185 : ||r|| = 5.21105e-07, ||r||/||r_0|| = 5.05936e-06
+LBFGS iteration 186 : ||r|| = 6.4775e-07, ||r||/||r_0|| = 6.28895e-06
+LBFGS iteration 187 : ||r|| = 9.73777e-07, ||r||/||r_0|| = 9.45431e-06
+LBFGS iteration 188 : ||r|| = 3.7301e-07, ||r||/||r_0|| = 3.62152e-06
+LBFGS iteration 189 : ||r|| = 2.67637e-07, ||r||/||r_0|| = 2.59846e-06
+LBFGS iteration 190 : ||r|| = 3.23775e-07, ||r||/||r_0|| = 3.1435e-06
+LBFGS iteration 191 : ||r|| = 3.63364e-07, ||r||/||r_0|| = 3.52787e-06
+LBFGS iteration 192 : ||r|| = 7.60241e-07, ||r||/||r_0|| = 7.38111e-06
+LBFGS iteration 193 : ||r|| = 1.29302e-07, ||r||/||r_0|| = 1.25538e-06
+LBFGS iteration 194 : ||r|| = 1.05663e-07, ||r||/||r_0|| = 1.02587e-06
+LBFGS iteration 195 : ||r|| = 1.33219e-07, ||r||/||r_0|| = 1.29341e-06
+LBFGS iteration 196 : ||r|| = 2.77704e-07, ||r||/||r_0|| = 2.6962e-06
+LBFGS iteration 197 : ||r|| = 9.65259e-08, ||r||/||r_0|| = 9.37161e-07
+LBFGS/Newton+GMRES converged in 197 iterations with a residual norm of 9.65259e-08.
+solver took 27.8513s.
+|| q_h - q_ex || / || q_ex || = 0.000108101
+|| t_h - t_ex || / || t_ex || = 1.85985e-05

examples/regress_test/p2_o2_dg_hb_nlc_hdg2.txt

@@ -0,0 +1,151 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 2
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00819804s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.0182912s.
+Preconditioner took 8.5342e-05s.
+LBFGS iteration 0 : ||r|| = 0.0487627
+LBFGS iteration 1 : ||r|| = 0.0692614, ||r||/||r_0|| = 1.42037
+LBFGS iteration 2 : ||r|| = 0.0822781, ||r||/||r_0|| = 1.68731
+LBFGS iteration 3 : ||r|| = 0.118922, ||r||/||r_0|| = 2.43879
+LBFGS iteration 4 : ||r|| = 0.107647, ||r||/||r_0|| = 2.20756
+LBFGS iteration 5 : ||r|| = 0.123669, ||r||/||r_0|| = 2.53613
+LBFGS iteration 6 : ||r|| = 0.0329542, ||r||/||r_0|| = 0.675807
+LBFGS iteration 7 : ||r|| = 0.0282146, ||r||/||r_0|| = 0.57861
+LBFGS iteration 8 : ||r|| = 0.0342989, ||r||/||r_0|| = 0.703384
+LBFGS iteration 9 : ||r|| = 0.0671743, ||r||/||r_0|| = 1.37757
+LBFGS iteration 10 : ||r|| = 0.0208077, ||r||/||r_0|| = 0.426714
+LBFGS iteration 11 : ||r|| = 0.0117098, ||r||/||r_0|| = 0.240138
+LBFGS iteration 12 : ||r|| = 0.0130887, ||r||/||r_0|| = 0.268415
+LBFGS iteration 13 : ||r|| = 0.0189146, ||r||/||r_0|| = 0.387891
+LBFGS iteration 14 : ||r|| = 0.00899461, ||r||/||r_0|| = 0.184457
+LBFGS iteration 15 : ||r|| = 0.00396105, ||r||/||r_0|| = 0.0812312
+LBFGS iteration 16 : ||r|| = 0.00314709, ||r||/||r_0|| = 0.0645388
+LBFGS iteration 17 : ||r|| = 0.00253435, ||r||/||r_0|| = 0.0519731
+LBFGS iteration 18 : ||r|| = 0.00290809, ||r||/||r_0|| = 0.0596376
+LBFGS iteration 19 : ||r|| = 0.000829381, ||r||/||r_0|| = 0.0170085
+LBFGS iteration 20 : ||r|| = 0.000618104, ||r||/||r_0|| = 0.0126757
+LBFGS iteration 21 : ||r|| = 0.000547119, ||r||/||r_0|| = 0.01122
+LBFGS iteration 22 : ||r|| = 0.000814219, ||r||/||r_0|| = 0.0166976
+LBFGS iteration 23 : ||r|| = 0.000509959, ||r||/||r_0|| = 0.010458
+LBFGS iteration 24 : ||r|| = 0.000460691, ||r||/||r_0|| = 0.00944761
+LBFGS iteration 25 : ||r|| = 0.000604138, ||r||/||r_0|| = 0.0123893
+LBFGS iteration 26 : ||r|| = 0.00127908, ||r||/||r_0|| = 0.0262308
+LBFGS iteration 27 : ||r|| = 0.000287425, ||r||/||r_0|| = 0.00589435
+LBFGS iteration 28 : ||r|| = 0.000172595, ||r||/||r_0|| = 0.00353948
+LBFGS iteration 29 : ||r|| = 0.000175317, ||r||/||r_0|| = 0.0035953
+LBFGS iteration 30 : ||r|| = 0.000247047, ||r||/||r_0|| = 0.0050663
+LBFGS iteration 31 : ||r|| = 0.000265188, ||r||/||r_0|| = 0.00543832
+LBFGS iteration 32 : ||r|| = 0.000162164, ||r||/||r_0|| = 0.00332557
+LBFGS iteration 33 : ||r|| = 9.46401e-05, ||r||/||r_0|| = 0.00194083
+LBFGS iteration 34 : ||r|| = 7.53712e-05, ||r||/||r_0|| = 0.00154567
+LBFGS iteration 35 : ||r|| = 7.6147e-05, ||r||/||r_0|| = 0.00156158
+LBFGS iteration 36 : ||r|| = 0.000115679, ||r||/||r_0|| = 0.00237228
+LBFGS iteration 37 : ||r|| = 0.000112865, ||r||/||r_0|| = 0.00231457
+LBFGS iteration 38 : ||r|| = 9.58335e-05, ||r||/||r_0|| = 0.0019653
+LBFGS iteration 39 : ||r|| = 0.000119291, ||r||/||r_0|| = 0.00244635
+LBFGS iteration 40 : ||r|| = 9.94457e-05, ||r||/||r_0|| = 0.00203938
+LBFGS iteration 41 : ||r|| = 4.50672e-05, ||r||/||r_0|| = 0.000924213
+LBFGS iteration 42 : ||r|| = 3.14627e-05, ||r||/||r_0|| = 0.000645219
+LBFGS iteration 43 : ||r|| = 3.69188e-05, ||r||/||r_0|| = 0.000757111
+LBFGS iteration 44 : ||r|| = 5.81826e-05, ||r||/||r_0|| = 0.00119318
+LBFGS iteration 45 : ||r|| = 3.94574e-05, ||r||/||r_0|| = 0.000809171
+LBFGS iteration 46 : ||r|| = 2.62179e-05, ||r||/||r_0|| = 0.000537663
+LBFGS iteration 47 : ||r|| = 3.36251e-05, ||r||/||r_0|| = 0.000689566
+LBFGS iteration 48 : ||r|| = 4.42556e-05, ||r||/||r_0|| = 0.00090757
+LBFGS iteration 49 : ||r|| = 8.51674e-05, ||r||/||r_0|| = 0.00174657
+LBFGS iteration 50 : ||r|| = 3.88016e-05, ||r||/||r_0|| = 0.000795723
+LBFGS iteration 51 : ||r|| = 2.54703e-05, ||r||/||r_0|| = 0.000522331
+LBFGS iteration 52 : ||r|| = 3.04912e-05, ||r||/||r_0|| = 0.000625296
+LBFGS iteration 53 : ||r|| = 3.55765e-05, ||r||/||r_0|| = 0.000729583
+LBFGS iteration 54 : ||r|| = 2.66586e-05, ||r||/||r_0|| = 0.0005467
+LBFGS iteration 55 : ||r|| = 3.52237e-05, ||r||/||r_0|| = 0.000722349
+LBFGS iteration 56 : ||r|| = 1.9746e-05, ||r||/||r_0|| = 0.000404939
+LBFGS iteration 57 : ||r|| = 1.13281e-05, ||r||/||r_0|| = 0.00023231
+LBFGS iteration 58 : ||r|| = 8.83885e-06, ||r||/||r_0|| = 0.000181262
+LBFGS iteration 59 : ||r|| = 9.66527e-06, ||r||/||r_0|| = 0.00019821
+LBFGS iteration 60 : ||r|| = 4.37068e-06, ||r||/||r_0|| = 8.96315e-05
+LBFGS iteration 61 : ||r|| = 3.47367e-06, ||r||/||r_0|| = 7.12362e-05
+LBFGS iteration 62 : ||r|| = 4.20141e-06, ||r||/||r_0|| = 8.61602e-05
+LBFGS iteration 63 : ||r|| = 5.19229e-06, ||r||/||r_0|| = 0.000106481
+LBFGS iteration 64 : ||r|| = 1.03245e-05, ||r||/||r_0|| = 0.00021173
+LBFGS iteration 65 : ||r|| = 2.88111e-06, ||r||/||r_0|| = 5.90842e-05
+LBFGS iteration 66 : ||r|| = 2.609e-06, ||r||/||r_0|| = 5.3504e-05
+LBFGS iteration 67 : ||r|| = 3.35885e-06, ||r||/||r_0|| = 6.88814e-05
+LBFGS iteration 68 : ||r|| = 7.93043e-06, ||r||/||r_0|| = 0.000162633
+LBFGS iteration 69 : ||r|| = 2.95862e-06, ||r||/||r_0|| = 6.06737e-05
+LBFGS iteration 70 : ||r|| = 2.2214e-06, ||r||/||r_0|| = 4.55553e-05
+LBFGS iteration 71 : ||r|| = 2.10929e-06, ||r||/||r_0|| = 4.32561e-05
+LBFGS iteration 72 : ||r|| = 5.13069e-06, ||r||/||r_0|| = 0.000105218
+LBFGS iteration 73 : ||r|| = 1.89629e-06, ||r||/||r_0|| = 3.88881e-05
+LBFGS iteration 74 : ||r|| = 1.33534e-06, ||r||/||r_0|| = 2.73844e-05
+LBFGS iteration 75 : ||r|| = 1.29834e-06, ||r||/||r_0|| = 2.66257e-05
+LBFGS iteration 76 : ||r|| = 1.56187e-06, ||r||/||r_0|| = 3.203e-05
+LBFGS iteration 77 : ||r|| = 2.06506e-06, ||r||/||r_0|| = 4.23492e-05
+LBFGS iteration 78 : ||r|| = 8.49287e-07, ||r||/||r_0|| = 1.74167e-05
+LBFGS iteration 79 : ||r|| = 8.12393e-07, ||r||/||r_0|| = 1.66601e-05
+LBFGS iteration 80 : ||r|| = 1.16061e-06, ||r||/||r_0|| = 2.38011e-05
+LBFGS iteration 81 : ||r|| = 1.34494e-06, ||r||/||r_0|| = 2.75813e-05
+LBFGS iteration 82 : ||r|| = 3.20001e-06, ||r||/||r_0|| = 6.56242e-05
+LBFGS iteration 83 : ||r|| = 5.09758e-07, ||r||/||r_0|| = 1.04538e-05
+LBFGS iteration 84 : ||r|| = 3.68324e-07, ||r||/||r_0|| = 7.55339e-06
+LBFGS iteration 85 : ||r|| = 4.03531e-07, ||r||/||r_0|| = 8.27539e-06
+LBFGS iteration 86 : ||r|| = 6.71093e-07, ||r||/||r_0|| = 1.37624e-05
+LBFGS iteration 87 : ||r|| = 3.11575e-07, ||r||/||r_0|| = 6.38962e-06
+LBFGS iteration 88 : ||r|| = 2.38873e-07, ||r||/||r_0|| = 4.89868e-06
+LBFGS iteration 89 : ||r|| = 2.79015e-07, ||r||/||r_0|| = 5.72189e-06
+LBFGS iteration 90 : ||r|| = 6.17594e-07, ||r||/||r_0|| = 1.26653e-05
+LBFGS iteration 91 : ||r|| = 2.44804e-07, ||r||/||r_0|| = 5.02031e-06
+LBFGS iteration 92 : ||r|| = 1.90112e-07, ||r||/||r_0|| = 3.89872e-06
+LBFGS iteration 93 : ||r|| = 2.14709e-07, ||r||/||r_0|| = 4.40313e-06
+LBFGS iteration 94 : ||r|| = 3.41317e-07, ||r||/||r_0|| = 6.99954e-06
+LBFGS iteration 95 : ||r|| = 2.61445e-07, ||r||/||r_0|| = 5.36157e-06
+LBFGS iteration 96 : ||r|| = 1.24679e-07, ||r||/||r_0|| = 2.55686e-06
+LBFGS iteration 97 : ||r|| = 1.2566e-07, ||r||/||r_0|| = 2.57696e-06
+LBFGS iteration 98 : ||r|| = 1.70687e-07, ||r||/||r_0|| = 3.50037e-06
+LBFGS iteration 99 : ||r|| = 2.42928e-07, ||r||/||r_0|| = 4.98184e-06
+LBFGS iteration 100 : ||r|| = 1.16163e-07, ||r||/||r_0|| = 2.38221e-06
+LBFGS iteration 101 : ||r|| = 7.31961e-08, ||r||/||r_0|| = 1.50107e-06
+LBFGS iteration 102 : ||r|| = 6.66993e-08, ||r||/||r_0|| = 1.36783e-06
+LBFGS iteration 103 : ||r|| = 7.54501e-08, ||r||/||r_0|| = 1.54729e-06
+LBFGS iteration 104 : ||r|| = 4.24685e-08, ||r||/||r_0|| = 8.70922e-07
+LBFGS/Newton+GMRES converged in 104 iterations with a residual norm of 4.24685e-08.
+solver took 14.4801s.
+|| q_h - q_ex || / || q_ex || = 0.000104382
+|| t_h - t_ex || / || t_ex || = 6.30557e-05

examples/regress_test/p2_o2_dg_hb_nlc_hdg2_newton.txt

@@ -0,0 +1,49 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 2
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00949233s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.0336414s.
+Preconditioner took 3.4259e-05s.
+Newton iteration  0 : ||r|| = 0.0487627
+Newton iteration  1 : ||r|| = 3.23457e-08, ||r||/||r_0|| = 6.63328e-07
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 3.23457e-08.
+solver took 0.626314s.
+|| q_h - q_ex || / || q_ex || = 0.000104381
+|| t_h - t_ex || / || t_ex || = 6.30592e-05

examples/regress_test/p2_o2_dg_hb_nlc_hdg3.txt

@@ -0,0 +1,261 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-flux
+   --no-nonlinear-pot
+   --nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 3
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0151292s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.0112321s.
+Preconditioner took 8.8196e-05s.
+LBFGS iteration 0 : ||r|| = 0.102852
+LBFGS iteration 1 : ||r|| = 0.269732, ||r||/||r_0|| = 2.62252
+LBFGS iteration 2 : ||r|| = 0.0843298, ||r||/||r_0|| = 0.819915
+LBFGS iteration 3 : ||r|| = 0.0781518, ||r||/||r_0|| = 0.759847
+LBFGS iteration 4 : ||r|| = 0.20701, ||r||/||r_0|| = 2.0127
+LBFGS iteration 5 : ||r|| = 0.0806524, ||r||/||r_0|| = 0.784161
+LBFGS iteration 6 : ||r|| = 0.0449547, ||r||/||r_0|| = 0.437082
+LBFGS iteration 7 : ||r|| = 0.0369292, ||r||/||r_0|| = 0.359052
+LBFGS iteration 8 : ||r|| = 0.0785845, ||r||/||r_0|| = 0.764054
+LBFGS iteration 9 : ||r|| = 0.0750852, ||r||/||r_0|| = 0.730032
+LBFGS iteration 10 : ||r|| = 0.0354019, ||r||/||r_0|| = 0.344203
+LBFGS iteration 11 : ||r|| = 0.0286791, ||r||/||r_0|| = 0.278839
+LBFGS iteration 12 : ||r|| = 0.0356425, ||r||/||r_0|| = 0.346542
+LBFGS iteration 13 : ||r|| = 0.0812469, ||r||/||r_0|| = 0.78994
+LBFGS iteration 14 : ||r|| = 0.023582, ||r||/||r_0|| = 0.229281
+LBFGS iteration 15 : ||r|| = 0.0189154, ||r||/||r_0|| = 0.183909
+LBFGS iteration 16 : ||r|| = 0.0225094, ||r||/||r_0|| = 0.218853
+LBFGS iteration 17 : ||r|| = 0.0376246, ||r||/||r_0|| = 0.365813
+LBFGS iteration 18 : ||r|| = 0.0162902, ||r||/||r_0|| = 0.158385
+LBFGS iteration 19 : ||r|| = 0.0143154, ||r||/||r_0|| = 0.139185
+LBFGS iteration 20 : ||r|| = 0.0206985, ||r||/||r_0|| = 0.201245
+LBFGS iteration 21 : ||r|| = 0.0359734, ||r||/||r_0|| = 0.349759
+LBFGS iteration 22 : ||r|| = 0.0151558, ||r||/||r_0|| = 0.147355
+LBFGS iteration 23 : ||r|| = 0.0120115, ||r||/||r_0|| = 0.116784
+LBFGS iteration 24 : ||r|| = 0.0146992, ||r||/||r_0|| = 0.142917
+LBFGS iteration 25 : ||r|| = 0.020302, ||r||/||r_0|| = 0.197391
+LBFGS iteration 26 : ||r|| = 0.0123491, ||r||/||r_0|| = 0.120067
+LBFGS iteration 27 : ||r|| = 0.00789921, ||r||/||r_0|| = 0.0768017
+LBFGS iteration 28 : ||r|| = 0.00915428, ||r||/||r_0|| = 0.0890044
+LBFGS iteration 29 : ||r|| = 0.0114089, ||r||/||r_0|| = 0.110925
+LBFGS iteration 30 : ||r|| = 0.0175121, ||r||/||r_0|| = 0.170265
+LBFGS iteration 31 : ||r|| = 0.00854982, ||r||/||r_0|| = 0.0831274
+LBFGS iteration 32 : ||r|| = 0.00885541, ||r||/||r_0|| = 0.0860986
+LBFGS iteration 33 : ||r|| = 0.0126803, ||r||/||r_0|| = 0.123287
+LBFGS iteration 34 : ||r|| = 0.0204225, ||r||/||r_0|| = 0.198562
+LBFGS iteration 35 : ||r|| = 0.0152173, ||r||/||r_0|| = 0.147954
+LBFGS iteration 36 : ||r|| = 0.0124808, ||r||/||r_0|| = 0.121347
+LBFGS iteration 37 : ||r|| = 0.0166343, ||r||/||r_0|| = 0.161731
+LBFGS iteration 38 : ||r|| = 0.018105, ||r||/||r_0|| = 0.17603
+LBFGS iteration 39 : ||r|| = 0.0179652, ||r||/||r_0|| = 0.17467
+LBFGS iteration 40 : ||r|| = 0.0410257, ||r||/||r_0|| = 0.398881
+LBFGS iteration 41 : ||r|| = 0.015195, ||r||/||r_0|| = 0.147736
+LBFGS iteration 42 : ||r|| = 0.0131814, ||r||/||r_0|| = 0.128159
+LBFGS iteration 43 : ||r|| = 0.0160678, ||r||/||r_0|| = 0.156223
+LBFGS iteration 44 : ||r|| = 0.020502, ||r||/||r_0|| = 0.199335
+LBFGS iteration 45 : ||r|| = 0.030545, ||r||/||r_0|| = 0.296981
+LBFGS iteration 46 : ||r|| = 0.00645858, ||r||/||r_0|| = 0.0627949
+LBFGS iteration 47 : ||r|| = 0.00513159, ||r||/||r_0|| = 0.0498929
+LBFGS iteration 48 : ||r|| = 0.00740027, ||r||/||r_0|| = 0.0719507
+LBFGS iteration 49 : ||r|| = 0.0112287, ||r||/||r_0|| = 0.109174
+LBFGS iteration 50 : ||r|| = 0.00480891, ||r||/||r_0|| = 0.0467557
+LBFGS iteration 51 : ||r|| = 0.00375757, ||r||/||r_0|| = 0.0365338
+LBFGS iteration 52 : ||r|| = 0.00426416, ||r||/||r_0|| = 0.0414592
+LBFGS iteration 53 : ||r|| = 0.00508323, ||r||/||r_0|| = 0.0494228
+LBFGS iteration 54 : ||r|| = 0.0138726, ||r||/||r_0|| = 0.134879
+LBFGS iteration 55 : ||r|| = 0.00196441, ||r||/||r_0|| = 0.0190994
+LBFGS iteration 56 : ||r|| = 0.00149658, ||r||/||r_0|| = 0.0145508
+LBFGS iteration 57 : ||r|| = 0.00165282, ||r||/||r_0|| = 0.0160699
+LBFGS iteration 58 : ||r|| = 0.00243986, ||r||/||r_0|| = 0.0237221
+LBFGS iteration 59 : ||r|| = 0.00163018, ||r||/||r_0|| = 0.0158498
+LBFGS iteration 60 : ||r|| = 0.00125956, ||r||/||r_0|| = 0.0122464
+LBFGS iteration 61 : ||r|| = 0.00177104, ||r||/||r_0|| = 0.0172193
+LBFGS iteration 62 : ||r|| = 0.00385749, ||r||/||r_0|| = 0.0375053
+LBFGS iteration 63 : ||r|| = 0.00144156, ||r||/||r_0|| = 0.0140159
+LBFGS iteration 64 : ||r|| = 0.000836277, ||r||/||r_0|| = 0.00813088
+LBFGS iteration 65 : ||r|| = 0.000909021, ||r||/||r_0|| = 0.00883816
+LBFGS iteration 66 : ||r|| = 0.00109422, ||r||/||r_0|| = 0.0106388
+LBFGS iteration 67 : ||r|| = 0.00299816, ||r||/||r_0|| = 0.0291503
+LBFGS iteration 68 : ||r|| = 0.000918464, ||r||/||r_0|| = 0.00892997
+LBFGS iteration 69 : ||r|| = 0.000790941, ||r||/||r_0|| = 0.00769009
+LBFGS iteration 70 : ||r|| = 0.000944827, ||r||/||r_0|| = 0.00918628
+LBFGS iteration 71 : ||r|| = 0.00310802, ||r||/||r_0|| = 0.0302184
+LBFGS iteration 72 : ||r|| = 0.000863815, ||r||/||r_0|| = 0.00839863
+LBFGS iteration 73 : ||r|| = 0.000633538, ||r||/||r_0|| = 0.00615971
+LBFGS iteration 74 : ||r|| = 0.000802629, ||r||/||r_0|| = 0.00780373
+LBFGS iteration 75 : ||r|| = 0.00085514, ||r||/||r_0|| = 0.00831428
+LBFGS iteration 76 : ||r|| = 0.00480643, ||r||/||r_0|| = 0.0467316
+LBFGS iteration 77 : ||r|| = 0.000599871, ||r||/||r_0|| = 0.00583237
+LBFGS iteration 78 : ||r|| = 0.000478311, ||r||/||r_0|| = 0.00465048
+LBFGS iteration 79 : ||r|| = 0.000579719, ||r||/||r_0|| = 0.00563644
+LBFGS iteration 80 : ||r|| = 0.00112557, ||r||/||r_0|| = 0.0109436
+LBFGS iteration 81 : ||r|| = 0.00116702, ||r||/||r_0|| = 0.0113466
+LBFGS iteration 82 : ||r|| = 0.00103924, ||r||/||r_0|| = 0.0101042
+LBFGS iteration 83 : ||r|| = 0.00180429, ||r||/||r_0|| = 0.0175426
+LBFGS iteration 84 : ||r|| = 0.00101235, ||r||/||r_0|| = 0.00984277
+LBFGS iteration 85 : ||r|| = 0.00105991, ||r||/||r_0|| = 0.0103052
+LBFGS iteration 86 : ||r|| = 0.00131042, ||r||/||r_0|| = 0.0127409
+LBFGS iteration 87 : ||r|| = 0.00373243, ||r||/||r_0|| = 0.0362893
+LBFGS iteration 88 : ||r|| = 0.000711079, ||r||/||r_0|| = 0.00691361
+LBFGS iteration 89 : ||r|| = 0.00049266, ||r||/||r_0|| = 0.00478999
+LBFGS iteration 90 : ||r|| = 0.000508025, ||r||/||r_0|| = 0.00493938
+LBFGS iteration 91 : ||r|| = 0.000757281, ||r||/||r_0|| = 0.00736283
+LBFGS iteration 92 : ||r|| = 0.000414084, ||r||/||r_0|| = 0.00402602
+LBFGS iteration 93 : ||r|| = 0.000411871, ||r||/||r_0|| = 0.00400451
+LBFGS iteration 94 : ||r|| = 0.000553323, ||r||/||r_0|| = 0.0053798
+LBFGS iteration 95 : ||r|| = 0.000369447, ||r||/||r_0|| = 0.00359202
+LBFGS iteration 96 : ||r|| = 0.000248359, ||r||/||r_0|| = 0.00241472
+LBFGS iteration 97 : ||r|| = 0.0002959, ||r||/||r_0|| = 0.00287695
+LBFGS iteration 98 : ||r|| = 0.000208774, ||r||/||r_0|| = 0.00202985
+LBFGS iteration 99 : ||r|| = 0.00017392, ||r||/||r_0|| = 0.00169097
+LBFGS iteration 100 : ||r|| = 0.000181768, ||r||/||r_0|| = 0.00176728
+LBFGS iteration 101 : ||r|| = 0.000262822, ||r||/||r_0|| = 0.00255534
+LBFGS iteration 102 : ||r|| = 0.000115737, ||r||/||r_0|| = 0.00112528
+LBFGS iteration 103 : ||r|| = 0.000109631, ||r||/||r_0|| = 0.00106591
+LBFGS iteration 104 : ||r|| = 0.000126351, ||r||/||r_0|| = 0.00122847
+LBFGS iteration 105 : ||r|| = 0.000255899, ||r||/||r_0|| = 0.00248804
+LBFGS iteration 106 : ||r|| = 0.000101702, ||r||/||r_0|| = 0.000988817
+LBFGS iteration 107 : ||r|| = 6.26341e-05, ||r||/||r_0|| = 0.000608973
+LBFGS iteration 108 : ||r|| = 7.6409e-05, ||r||/||r_0|| = 0.000742902
+LBFGS iteration 109 : ||r|| = 0.000110439, ||r||/||r_0|| = 0.00107377
+LBFGS iteration 110 : ||r|| = 9.0711e-05, ||r||/||r_0|| = 0.000881957
+LBFGS iteration 111 : ||r|| = 0.000150645, ||r||/||r_0|| = 0.00146468
+LBFGS iteration 112 : ||r|| = 0.000106021, ||r||/||r_0|| = 0.00103081
+LBFGS iteration 113 : ||r|| = 6.77155e-05, ||r||/||r_0|| = 0.000658379
+LBFGS iteration 114 : ||r|| = 5.27681e-05, ||r||/||r_0|| = 0.000513049
+LBFGS iteration 115 : ||r|| = 8.68939e-05, ||r||/||r_0|| = 0.000844845
+LBFGS iteration 116 : ||r|| = 6.04294e-05, ||r||/||r_0|| = 0.000587538
+LBFGS iteration 117 : ||r|| = 6.0226e-05, ||r||/||r_0|| = 0.00058556
+LBFGS iteration 118 : ||r|| = 7.39482e-05, ||r||/||r_0|| = 0.000718977
+LBFGS iteration 119 : ||r|| = 5.39151e-05, ||r||/||r_0|| = 0.000524201
+LBFGS iteration 120 : ||r|| = 4.92494e-05, ||r||/||r_0|| = 0.000478838
+LBFGS iteration 121 : ||r|| = 7.88362e-05, ||r||/||r_0|| = 0.000766502
+LBFGS iteration 122 : ||r|| = 4.41549e-05, ||r||/||r_0|| = 0.000429306
+LBFGS iteration 123 : ||r|| = 3.62518e-05, ||r||/||r_0|| = 0.000352466
+LBFGS iteration 124 : ||r|| = 4.27624e-05, ||r||/||r_0|| = 0.000415766
+LBFGS iteration 125 : ||r|| = 3.87193e-05, ||r||/||r_0|| = 0.000376457
+LBFGS iteration 126 : ||r|| = 3.00126e-05, ||r||/||r_0|| = 0.000291804
+LBFGS iteration 127 : ||r|| = 3.08843e-05, ||r||/||r_0|| = 0.000300279
+LBFGS iteration 128 : ||r|| = 4.26319e-05, ||r||/||r_0|| = 0.000414497
+LBFGS iteration 129 : ||r|| = 1.9177e-05, ||r||/||r_0|| = 0.000186453
+LBFGS iteration 130 : ||r|| = 1.51799e-05, ||r||/||r_0|| = 0.00014759
+LBFGS iteration 131 : ||r|| = 2.01545e-05, ||r||/||r_0|| = 0.000195957
+LBFGS iteration 132 : ||r|| = 2.12162e-05, ||r||/||r_0|| = 0.00020628
+LBFGS iteration 133 : ||r|| = 1.39944e-05, ||r||/||r_0|| = 0.000136063
+LBFGS iteration 134 : ||r|| = 1.4108e-05, ||r||/||r_0|| = 0.000137168
+LBFGS iteration 135 : ||r|| = 1.85294e-05, ||r||/||r_0|| = 0.000180156
+LBFGS iteration 136 : ||r|| = 2.36465e-05, ||r||/||r_0|| = 0.000229908
+LBFGS iteration 137 : ||r|| = 3.12811e-05, ||r||/||r_0|| = 0.000304137
+LBFGS iteration 138 : ||r|| = 2.07414e-05, ||r||/||r_0|| = 0.000201662
+LBFGS iteration 139 : ||r|| = 1.93988e-05, ||r||/||r_0|| = 0.000188609
+LBFGS iteration 140 : ||r|| = 3.02654e-05, ||r||/||r_0|| = 0.000294262
+LBFGS iteration 141 : ||r|| = 1.28032e-05, ||r||/||r_0|| = 0.000124482
+LBFGS iteration 142 : ||r|| = 7.87628e-06, ||r||/||r_0|| = 7.65788e-05
+LBFGS iteration 143 : ||r|| = 8.16385e-06, ||r||/||r_0|| = 7.93748e-05
+LBFGS iteration 144 : ||r|| = 1.52151e-05, ||r||/||r_0|| = 0.000147932
+LBFGS iteration 145 : ||r|| = 6.99362e-06, ||r||/||r_0|| = 6.7997e-05
+LBFGS iteration 146 : ||r|| = 4.56467e-06, ||r||/||r_0|| = 4.43809e-05
+LBFGS iteration 147 : ||r|| = 3.29005e-06, ||r||/||r_0|| = 3.19882e-05
+LBFGS iteration 148 : ||r|| = 6.79475e-06, ||r||/||r_0|| = 6.60634e-05
+LBFGS iteration 149 : ||r|| = 2.86175e-06, ||r||/||r_0|| = 2.7824e-05
+LBFGS iteration 150 : ||r|| = 1.89227e-06, ||r||/||r_0|| = 1.8398e-05
+LBFGS iteration 151 : ||r|| = 2.02504e-06, ||r||/||r_0|| = 1.96889e-05
+LBFGS iteration 152 : ||r|| = 2.72502e-06, ||r||/||r_0|| = 2.64946e-05
+LBFGS iteration 153 : ||r|| = 2.42998e-06, ||r||/||r_0|| = 2.3626e-05
+LBFGS iteration 154 : ||r|| = 1.4431e-06, ||r||/||r_0|| = 1.40308e-05
+LBFGS iteration 155 : ||r|| = 1.49854e-06, ||r||/||r_0|| = 1.45698e-05
+LBFGS iteration 156 : ||r|| = 1.79221e-06, ||r||/||r_0|| = 1.74252e-05
+LBFGS iteration 157 : ||r|| = 3.87845e-06, ||r||/||r_0|| = 3.7709e-05
+LBFGS iteration 158 : ||r|| = 1.32684e-06, ||r||/||r_0|| = 1.29005e-05
+LBFGS iteration 159 : ||r|| = 1.00696e-06, ||r||/||r_0|| = 9.79041e-06
+LBFGS iteration 160 : ||r|| = 1.21341e-06, ||r||/||r_0|| = 1.17976e-05
+LBFGS iteration 161 : ||r|| = 1.51095e-06, ||r||/||r_0|| = 1.46905e-05
+LBFGS iteration 162 : ||r|| = 1.84277e-06, ||r||/||r_0|| = 1.79167e-05
+LBFGS iteration 163 : ||r|| = 8.42172e-07, ||r||/||r_0|| = 8.1882e-06
+LBFGS iteration 164 : ||r|| = 7.666e-07, ||r||/||r_0|| = 7.45343e-06
+LBFGS iteration 165 : ||r|| = 8.63428e-07, ||r||/||r_0|| = 8.39486e-06
+LBFGS iteration 166 : ||r|| = 2.24014e-06, ||r||/||r_0|| = 2.17802e-05
+LBFGS iteration 167 : ||r|| = 6.93619e-07, ||r||/||r_0|| = 6.74386e-06
+LBFGS iteration 168 : ||r|| = 6.01868e-07, ||r||/||r_0|| = 5.85179e-06
+LBFGS iteration 169 : ||r|| = 8.42312e-07, ||r||/||r_0|| = 8.18956e-06
+LBFGS iteration 170 : ||r|| = 1.21665e-06, ||r||/||r_0|| = 1.18292e-05
+LBFGS iteration 171 : ||r|| = 1.93991e-06, ||r||/||r_0|| = 1.88612e-05
+LBFGS iteration 172 : ||r|| = 9.63484e-07, ||r||/||r_0|| = 9.36768e-06
+LBFGS iteration 173 : ||r|| = 7.85247e-07, ||r||/||r_0|| = 7.63473e-06
+LBFGS iteration 174 : ||r|| = 8.24173e-07, ||r||/||r_0|| = 8.01319e-06
+LBFGS iteration 175 : ||r|| = 1.45075e-06, ||r||/||r_0|| = 1.41052e-05
+LBFGS iteration 176 : ||r|| = 6.69464e-07, ||r||/||r_0|| = 6.50901e-06
+LBFGS iteration 177 : ||r|| = 6.73884e-07, ||r||/||r_0|| = 6.55199e-06
+LBFGS iteration 178 : ||r|| = 8.57037e-07, ||r||/||r_0|| = 8.33272e-06
+LBFGS iteration 179 : ||r|| = 1.5586e-06, ||r||/||r_0|| = 1.51538e-05
+LBFGS iteration 180 : ||r|| = 1.07719e-06, ||r||/||r_0|| = 1.04732e-05
+LBFGS iteration 181 : ||r|| = 7.70795e-07, ||r||/||r_0|| = 7.49422e-06
+LBFGS iteration 182 : ||r|| = 1.098e-06, ||r||/||r_0|| = 1.06755e-05
+LBFGS iteration 183 : ||r|| = 1.02764e-06, ||r||/||r_0|| = 9.99144e-06
+LBFGS iteration 184 : ||r|| = 8.36347e-07, ||r||/||r_0|| = 8.13156e-06
+LBFGS iteration 185 : ||r|| = 1.10066e-06, ||r||/||r_0|| = 1.07014e-05
+LBFGS iteration 186 : ||r|| = 7.56056e-07, ||r||/||r_0|| = 7.35092e-06
+LBFGS iteration 187 : ||r|| = 3.34517e-07, ||r||/||r_0|| = 3.25241e-06
+LBFGS iteration 188 : ||r|| = 2.59719e-07, ||r||/||r_0|| = 2.52517e-06
+LBFGS iteration 189 : ||r|| = 3.54648e-07, ||r||/||r_0|| = 3.44814e-06
+LBFGS iteration 190 : ||r|| = 4.69366e-07, ||r||/||r_0|| = 4.56351e-06
+LBFGS iteration 191 : ||r|| = 1.06595e-06, ||r||/||r_0|| = 1.0364e-05
+LBFGS iteration 192 : ||r|| = 3.09342e-07, ||r||/||r_0|| = 3.00765e-06
+LBFGS iteration 193 : ||r|| = 2.63774e-07, ||r||/||r_0|| = 2.5646e-06
+LBFGS iteration 194 : ||r|| = 2.90094e-07, ||r||/||r_0|| = 2.8205e-06
+LBFGS iteration 195 : ||r|| = 7.36248e-07, ||r||/||r_0|| = 7.15833e-06
+LBFGS iteration 196 : ||r|| = 1.89643e-07, ||r||/||r_0|| = 1.84384e-06
+LBFGS iteration 197 : ||r|| = 1.43344e-07, ||r||/||r_0|| = 1.3937e-06
+LBFGS iteration 198 : ||r|| = 1.63917e-07, ||r||/||r_0|| = 1.59372e-06
+LBFGS iteration 199 : ||r|| = 3.05848e-07, ||r||/||r_0|| = 2.97367e-06
+LBFGS iteration 200 : ||r|| = 1.7486e-07, ||r||/||r_0|| = 1.70012e-06
+LBFGS iteration 201 : ||r|| = 1.24007e-07, ||r||/||r_0|| = 1.20569e-06
+LBFGS iteration 202 : ||r|| = 1.9057e-07, ||r||/||r_0|| = 1.85286e-06
+LBFGS iteration 203 : ||r|| = 1.88729e-07, ||r||/||r_0|| = 1.83496e-06
+LBFGS iteration 204 : ||r|| = 1.21561e-07, ||r||/||r_0|| = 1.1819e-06
+LBFGS iteration 205 : ||r|| = 1.2193e-07, ||r||/||r_0|| = 1.18549e-06
+LBFGS iteration 206 : ||r|| = 1.80472e-07, ||r||/||r_0|| = 1.75468e-06
+LBFGS iteration 207 : ||r|| = 1.35772e-07, ||r||/||r_0|| = 1.32008e-06
+LBFGS iteration 208 : ||r|| = 1.47567e-07, ||r||/||r_0|| = 1.43476e-06
+LBFGS iteration 209 : ||r|| = 2.27832e-07, ||r||/||r_0|| = 2.21514e-06
+LBFGS iteration 210 : ||r|| = 1.17267e-07, ||r||/||r_0|| = 1.14015e-06
+LBFGS iteration 211 : ||r|| = 6.96351e-08, ||r||/||r_0|| = 6.77043e-07
+LBFGS/Newton+GMRES converged in 211 iterations with a residual norm of 6.96351e-08.
+solver took 21.7164s.
+|| q_h - q_ex || / || q_ex || = 8.59626e-05
+|| t_h - t_ex || / || t_ex || = 1.84229e-05

examples/regress_test/p2_o2_dg_hb_nlc_hdg4.txt

@@ -0,0 +1,168 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-flux
+   --no-nonlinear-pot
+   --nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 4
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+
+
+MFEM Warning: Upwinded flux is implemented only component-wise.
+ ... in function: mfem::ComponentwiseUpwindFlux::ComponentwiseUpwindFlux(const mfem::FluxFunction&)
+ ... in file: fem/hyperbolic.cpp:904
+
+Hybridization init took 0.0148386s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.0442283s.
+Preconditioner took 7.5799e-05s.
+LBFGS iteration 0 : ||r|| = 0.0484297
+LBFGS iteration 1 : ||r|| = 0.0660736, ||r||/||r_0|| = 1.36432
+LBFGS iteration 2 : ||r|| = 0.0832317, ||r||/||r_0|| = 1.71861
+LBFGS iteration 3 : ||r|| = 0.143821, ||r||/||r_0|| = 2.9697
+LBFGS iteration 4 : ||r|| = 0.0960827, ||r||/||r_0|| = 1.98396
+LBFGS iteration 5 : ||r|| = 0.0577718, ||r||/||r_0|| = 1.1929
+LBFGS iteration 6 : ||r|| = 0.0320765, ||r||/||r_0|| = 0.662332
+LBFGS iteration 7 : ||r|| = 0.0316769, ||r||/||r_0|| = 0.65408
+LBFGS iteration 8 : ||r|| = 0.0478375, ||r||/||r_0|| = 0.987772
+LBFGS iteration 9 : ||r|| = 0.0616466, ||r||/||r_0|| = 1.27291
+LBFGS iteration 10 : ||r|| = 0.0168704, ||r||/||r_0|| = 0.348348
+LBFGS iteration 11 : ||r|| = 0.0116486, ||r||/||r_0|| = 0.240526
+LBFGS iteration 12 : ||r|| = 0.0145305, ||r||/||r_0|| = 0.300034
+LBFGS iteration 13 : ||r|| = 0.0238124, ||r||/||r_0|| = 0.491691
+LBFGS iteration 14 : ||r|| = 0.00735104, ||r||/||r_0|| = 0.151788
+LBFGS iteration 15 : ||r|| = 0.00410267, ||r||/||r_0|| = 0.0847139
+LBFGS iteration 16 : ||r|| = 0.00376678, ||r||/||r_0|| = 0.0777783
+LBFGS iteration 17 : ||r|| = 0.00631038, ||r||/||r_0|| = 0.1303
+LBFGS iteration 18 : ||r|| = 0.00177791, ||r||/||r_0|| = 0.0367111
+LBFGS iteration 19 : ||r|| = 0.000556176, ||r||/||r_0|| = 0.0114842
+LBFGS iteration 20 : ||r|| = 0.000582371, ||r||/||r_0|| = 0.0120251
+LBFGS iteration 21 : ||r|| = 0.000830775, ||r||/||r_0|| = 0.0171543
+LBFGS iteration 22 : ||r|| = 0.000739226, ||r||/||r_0|| = 0.0152639
+LBFGS iteration 23 : ||r|| = 0.000474997, ||r||/||r_0|| = 0.00980797
+LBFGS iteration 24 : ||r|| = 0.000523104, ||r||/||r_0|| = 0.0108013
+LBFGS iteration 25 : ||r|| = 0.000674829, ||r||/||r_0|| = 0.0139342
+LBFGS iteration 26 : ||r|| = 0.000424443, ||r||/||r_0|| = 0.00876411
+LBFGS iteration 27 : ||r|| = 0.000260063, ||r||/||r_0|| = 0.00536991
+LBFGS iteration 28 : ||r|| = 0.000258311, ||r||/||r_0|| = 0.00533373
+LBFGS iteration 29 : ||r|| = 0.00020167, ||r||/||r_0|| = 0.00416418
+LBFGS iteration 30 : ||r|| = 0.000186482, ||r||/||r_0|| = 0.00385057
+LBFGS iteration 31 : ||r|| = 0.000154389, ||r||/||r_0|| = 0.0031879
+LBFGS iteration 32 : ||r|| = 0.000135307, ||r||/||r_0|| = 0.00279389
+LBFGS iteration 33 : ||r|| = 0.00011094, ||r||/||r_0|| = 0.00229074
+LBFGS iteration 34 : ||r|| = 0.00013026, ||r||/||r_0|| = 0.00268968
+LBFGS iteration 35 : ||r|| = 0.000186965, ||r||/||r_0|| = 0.00386054
+LBFGS iteration 36 : ||r|| = 9.61453e-05, ||r||/||r_0|| = 0.00198526
+LBFGS iteration 37 : ||r|| = 7.00898e-05, ||r||/||r_0|| = 0.00144725
+LBFGS iteration 38 : ||r|| = 6.911e-05, ||r||/||r_0|| = 0.00142702
+LBFGS iteration 39 : ||r|| = 9.90733e-05, ||r||/||r_0|| = 0.00204571
+LBFGS iteration 40 : ||r|| = 2.7209e-05, ||r||/||r_0|| = 0.000561824
+LBFGS iteration 41 : ||r|| = 2.06825e-05, ||r||/||r_0|| = 0.000427062
+LBFGS iteration 42 : ||r|| = 2.34929e-05, ||r||/||r_0|| = 0.000485094
+LBFGS iteration 43 : ||r|| = 3.59468e-05, ||r||/||r_0|| = 0.000742247
+LBFGS iteration 44 : ||r|| = 1.5112e-05, ||r||/||r_0|| = 0.000312039
+LBFGS iteration 45 : ||r|| = 7.90826e-06, ||r||/||r_0|| = 0.000163294
+LBFGS iteration 46 : ||r|| = 8.39579e-06, ||r||/||r_0|| = 0.00017336
+LBFGS iteration 47 : ||r|| = 1.20051e-05, ||r||/||r_0|| = 0.000247887
+LBFGS iteration 48 : ||r|| = 1.534e-05, ||r||/||r_0|| = 0.000316748
+LBFGS iteration 49 : ||r|| = 1.77569e-05, ||r||/||r_0|| = 0.000366654
+LBFGS iteration 50 : ||r|| = 1.08359e-05, ||r||/||r_0|| = 0.000223745
+LBFGS iteration 51 : ||r|| = 1.02129e-05, ||r||/||r_0|| = 0.00021088
+LBFGS iteration 52 : ||r|| = 1.30101e-05, ||r||/||r_0|| = 0.000268639
+LBFGS iteration 53 : ||r|| = 1.1584e-05, ||r||/||r_0|| = 0.000239191
+LBFGS iteration 54 : ||r|| = 1.64202e-05, ||r||/||r_0|| = 0.000339052
+LBFGS iteration 55 : ||r|| = 8.1508e-06, ||r||/||r_0|| = 0.000168302
+LBFGS iteration 56 : ||r|| = 6.31368e-06, ||r||/||r_0|| = 0.000130368
+LBFGS iteration 57 : ||r|| = 7.25881e-06, ||r||/||r_0|| = 0.000149883
+LBFGS iteration 58 : ||r|| = 1.44318e-05, ||r||/||r_0|| = 0.000297994
+LBFGS iteration 59 : ||r|| = 4.98022e-06, ||r||/||r_0|| = 0.000102834
+LBFGS iteration 60 : ||r|| = 3.36145e-06, ||r||/||r_0|| = 6.94089e-05
+LBFGS iteration 61 : ||r|| = 3.73417e-06, ||r||/||r_0|| = 7.7105e-05
+LBFGS iteration 62 : ||r|| = 7.49255e-06, ||r||/||r_0|| = 0.00015471
+LBFGS iteration 63 : ||r|| = 3.05329e-06, ||r||/||r_0|| = 6.30459e-05
+LBFGS iteration 64 : ||r|| = 2.40472e-06, ||r||/||r_0|| = 4.96538e-05
+LBFGS iteration 65 : ||r|| = 3.12871e-06, ||r||/||r_0|| = 6.46032e-05
+LBFGS iteration 66 : ||r|| = 4.84728e-06, ||r||/||r_0|| = 0.000100089
+LBFGS iteration 67 : ||r|| = 4.61982e-06, ||r||/||r_0|| = 9.53923e-05
+LBFGS iteration 68 : ||r|| = 3.36811e-06, ||r||/||r_0|| = 6.95463e-05
+LBFGS iteration 69 : ||r|| = 4.06208e-06, ||r||/||r_0|| = 8.38759e-05
+LBFGS iteration 70 : ||r|| = 4.25216e-06, ||r||/||r_0|| = 8.78007e-05
+LBFGS iteration 71 : ||r|| = 2.70444e-06, ||r||/||r_0|| = 5.58426e-05
+LBFGS iteration 72 : ||r|| = 2.13665e-06, ||r||/||r_0|| = 4.41185e-05
+LBFGS iteration 73 : ||r|| = 2.01037e-06, ||r||/||r_0|| = 4.15111e-05
+LBFGS iteration 74 : ||r|| = 1.97272e-06, ||r||/||r_0|| = 4.07336e-05
+LBFGS iteration 75 : ||r|| = 3.12448e-06, ||r||/||r_0|| = 6.45158e-05
+LBFGS iteration 76 : ||r|| = 5.77136e-06, ||r||/||r_0|| = 0.00011917
+LBFGS iteration 77 : ||r|| = 1.41934e-06, ||r||/||r_0|| = 2.93072e-05
+LBFGS iteration 78 : ||r|| = 1.01687e-06, ||r||/||r_0|| = 2.09967e-05
+LBFGS iteration 79 : ||r|| = 1.23446e-06, ||r||/||r_0|| = 2.54897e-05
+LBFGS iteration 80 : ||r|| = 1.71986e-06, ||r||/||r_0|| = 3.55126e-05
+LBFGS iteration 81 : ||r|| = 9.44706e-07, ||r||/||r_0|| = 1.95068e-05
+LBFGS iteration 82 : ||r|| = 6.23815e-07, ||r||/||r_0|| = 1.28808e-05
+LBFGS iteration 83 : ||r|| = 9.3261e-07, ||r||/||r_0|| = 1.9257e-05
+LBFGS iteration 84 : ||r|| = 1.03297e-06, ||r||/||r_0|| = 2.13293e-05
+LBFGS iteration 85 : ||r|| = 7.72218e-07, ||r||/||r_0|| = 1.59451e-05
+LBFGS iteration 86 : ||r|| = 1.34837e-06, ||r||/||r_0|| = 2.78419e-05
+LBFGS iteration 87 : ||r|| = 8.40947e-07, ||r||/||r_0|| = 1.73643e-05
+LBFGS iteration 88 : ||r|| = 5.08744e-07, ||r||/||r_0|| = 1.05048e-05
+LBFGS iteration 89 : ||r|| = 4.34125e-07, ||r||/||r_0|| = 8.96403e-06
+LBFGS iteration 90 : ||r|| = 7.17288e-07, ||r||/||r_0|| = 1.48109e-05
+LBFGS iteration 91 : ||r|| = 9.58339e-07, ||r||/||r_0|| = 1.97883e-05
+LBFGS iteration 92 : ||r|| = 1.97426e-06, ||r||/||r_0|| = 4.07656e-05
+LBFGS iteration 93 : ||r|| = 5.06923e-07, ||r||/||r_0|| = 1.04672e-05
+LBFGS iteration 94 : ||r|| = 3.90608e-07, ||r||/||r_0|| = 8.06548e-06
+LBFGS iteration 95 : ||r|| = 4.24309e-07, ||r||/||r_0|| = 8.76135e-06
+LBFGS iteration 96 : ||r|| = 1.07248e-06, ||r||/||r_0|| = 2.21451e-05
+LBFGS iteration 97 : ||r|| = 3.00548e-07, ||r||/||r_0|| = 6.20587e-06
+LBFGS iteration 98 : ||r|| = 2.03456e-07, ||r||/||r_0|| = 4.20105e-06
+LBFGS iteration 99 : ||r|| = 2.4499e-07, ||r||/||r_0|| = 5.05868e-06
+LBFGS iteration 100 : ||r|| = 2.26993e-07, ||r||/||r_0|| = 4.68707e-06
+LBFGS iteration 101 : ||r|| = 5.23722e-07, ||r||/||r_0|| = 1.08141e-05
+LBFGS iteration 102 : ||r|| = 9.62671e-08, ||r||/||r_0|| = 1.98777e-06
+LBFGS iteration 103 : ||r|| = 7.85369e-08, ||r||/||r_0|| = 1.62167e-06
+LBFGS iteration 104 : ||r|| = 9.39425e-08, ||r||/||r_0|| = 1.93977e-06
+LBFGS iteration 105 : ||r|| = 2.22004e-07, ||r||/||r_0|| = 4.58405e-06
+LBFGS iteration 106 : ||r|| = 9.91465e-08, ||r||/||r_0|| = 2.04723e-06
+LBFGS iteration 107 : ||r|| = 7.9714e-08, ||r||/||r_0|| = 1.64598e-06
+LBFGS iteration 108 : ||r|| = 1.07991e-07, ||r||/||r_0|| = 2.22985e-06
+LBFGS iteration 109 : ||r|| = 1.28177e-07, ||r||/||r_0|| = 2.64666e-06
+LBFGS iteration 110 : ||r|| = 3.42996e-07, ||r||/||r_0|| = 7.08235e-06
+LBFGS iteration 111 : ||r|| = 8.76545e-08, ||r||/||r_0|| = 1.80993e-06
+LBFGS iteration 112 : ||r|| = 4.62161e-08, ||r||/||r_0|| = 9.54294e-07
+LBFGS/Newton+GMRES converged in 112 iterations with a residual norm of 4.62161e-08.
+solver took 14.6534s.
+|| q_h - q_ex || / || q_ex || = 8.93027e-05
+|| t_h - t_ex || / || t_ex || = 6.62381e-05

examples/regress_test/p2_o2_dg_hb_nlc_hdg4_newton.txt

@@ -0,0 +1,55 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 4
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+
+
+MFEM Warning: Upwinded flux is implemented only component-wise.
+ ... in function: mfem::ComponentwiseUpwindFlux::ComponentwiseUpwindFlux(const mfem::FluxFunction&)
+ ... in file: fem/hyperbolic.cpp:865
+
+Hybridization init took 0.00678614s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.0168531s.
+Preconditioner took 4.6723e-05s.
+Newton iteration  0 : ||r|| = 0.0484297
+Newton iteration  1 : ||r|| = 4.67701e-08, ||r||/||r_0|| = 9.65732e-07
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 4.67701e-08.
+solver took 0.416255s.
+|| q_h - q_ex || / || q_ex || = 8.93096e-05
+|| t_h - t_ex || / || t_ex || = 6.62475e-05

examples/regress_test/p2_o2_dg_hb_nld.txt

@@ -0,0 +1,125 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 0
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0115329s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.0460493s.
+Preconditioner took 7.3876e-05s.
+LBFGS iteration 0 : ||r|| = 0.0487525
+LBFGS iteration 1 : ||r|| = 0.0692476, ||r||/||r_0|| = 1.42039
+LBFGS iteration 2 : ||r|| = 0.0822451, ||r||/||r_0|| = 1.68699
+LBFGS iteration 3 : ||r|| = 0.118638, ||r||/||r_0|| = 2.43348
+LBFGS iteration 4 : ||r|| = 0.10805, ||r||/||r_0|| = 2.2163
+LBFGS iteration 5 : ||r|| = 0.123018, ||r||/||r_0|| = 2.52331
+LBFGS iteration 6 : ||r|| = 0.0331166, ||r||/||r_0|| = 0.67928
+LBFGS iteration 7 : ||r|| = 0.028239, ||r||/||r_0|| = 0.579233
+LBFGS iteration 8 : ||r|| = 0.0339501, ||r||/||r_0|| = 0.696376
+LBFGS iteration 9 : ||r|| = 0.0632489, ||r||/||r_0|| = 1.29735
+LBFGS iteration 10 : ||r|| = 0.0197064, ||r||/||r_0|| = 0.404214
+LBFGS iteration 11 : ||r|| = 0.0115797, ||r||/||r_0|| = 0.23752
+LBFGS iteration 12 : ||r|| = 0.0132388, ||r||/||r_0|| = 0.271551
+LBFGS iteration 13 : ||r|| = 0.0185307, ||r||/||r_0|| = 0.380098
+LBFGS iteration 14 : ||r|| = 0.00805841, ||r||/||r_0|| = 0.165292
+LBFGS iteration 15 : ||r|| = 0.0039921, ||r||/||r_0|| = 0.0818851
+LBFGS iteration 16 : ||r|| = 0.00336112, ||r||/||r_0|| = 0.0689425
+LBFGS iteration 17 : ||r|| = 0.00385756, ||r||/||r_0|| = 0.0791254
+LBFGS iteration 18 : ||r|| = 0.00192134, ||r||/||r_0|| = 0.0394101
+LBFGS iteration 19 : ||r|| = 0.000721511, ||r||/||r_0|| = 0.0147995
+LBFGS iteration 20 : ||r|| = 0.000602176, ||r||/||r_0|| = 0.0123517
+LBFGS iteration 21 : ||r|| = 0.00065292, ||r||/||r_0|| = 0.0133925
+LBFGS iteration 22 : ||r|| = 0.00115966, ||r||/||r_0|| = 0.0237867
+LBFGS iteration 23 : ||r|| = 0.000458623, ||r||/||r_0|| = 0.00940717
+LBFGS iteration 24 : ||r|| = 0.000389707, ||r||/||r_0|| = 0.00799358
+LBFGS iteration 25 : ||r|| = 0.000556569, ||r||/||r_0|| = 0.0114162
+LBFGS iteration 26 : ||r|| = 0.000629825, ||r||/||r_0|| = 0.0129188
+LBFGS iteration 27 : ||r|| = 0.00235984, ||r||/||r_0|| = 0.0484046
+LBFGS iteration 28 : ||r|| = 0.000319451, ||r||/||r_0|| = 0.00655251
+LBFGS iteration 29 : ||r|| = 0.000182618, ||r||/||r_0|| = 0.00374582
+LBFGS iteration 30 : ||r|| = 0.000134455, ||r||/||r_0|| = 0.0027579
+LBFGS iteration 31 : ||r|| = 0.000165894, ||r||/||r_0|| = 0.00340277
+LBFGS iteration 32 : ||r|| = 0.00026601, ||r||/||r_0|| = 0.00545634
+LBFGS iteration 33 : ||r|| = 0.000247642, ||r||/||r_0|| = 0.00507958
+LBFGS iteration 34 : ||r|| = 8.2696e-05, ||r||/||r_0|| = 0.00169624
+LBFGS iteration 35 : ||r|| = 6.20623e-05, ||r||/||r_0|| = 0.00127301
+LBFGS iteration 36 : ||r|| = 7.09836e-05, ||r||/||r_0|| = 0.001456
+LBFGS iteration 37 : ||r|| = 0.000188172, ||r||/||r_0|| = 0.00385974
+LBFGS iteration 38 : ||r|| = 7.4328e-05, ||r||/||r_0|| = 0.0015246
+LBFGS iteration 39 : ||r|| = 5.84394e-05, ||r||/||r_0|| = 0.0011987
+LBFGS iteration 40 : ||r|| = 6.66841e-05, ||r||/||r_0|| = 0.00136781
+LBFGS iteration 41 : ||r|| = 8.73659e-05, ||r||/||r_0|| = 0.00179203
+LBFGS iteration 42 : ||r|| = 5.70444e-05, ||r||/||r_0|| = 0.00117008
+LBFGS iteration 43 : ||r|| = 1.6698e-05, ||r||/||r_0|| = 0.000342505
+LBFGS iteration 44 : ||r|| = 1.28373e-05, ||r||/||r_0|| = 0.000263316
+LBFGS iteration 45 : ||r|| = 1.44491e-05, ||r||/||r_0|| = 0.000296377
+LBFGS iteration 46 : ||r|| = 2.93999e-05, ||r||/||r_0|| = 0.000603044
+LBFGS iteration 47 : ||r|| = 6.07943e-06, ||r||/||r_0|| = 0.0001247
+LBFGS iteration 48 : ||r|| = 4.09369e-06, ||r||/||r_0|| = 8.39688e-05
+LBFGS iteration 49 : ||r|| = 4.37239e-06, ||r||/||r_0|| = 8.96855e-05
+LBFGS iteration 50 : ||r|| = 5.92606e-06, ||r||/||r_0|| = 0.000121554
+LBFGS iteration 51 : ||r|| = 6.93319e-06, ||r||/||r_0|| = 0.000142212
+LBFGS iteration 52 : ||r|| = 2.81715e-06, ||r||/||r_0|| = 5.77848e-05
+LBFGS iteration 53 : ||r|| = 2.17057e-06, ||r||/||r_0|| = 4.45223e-05
+LBFGS iteration 54 : ||r|| = 2.09908e-06, ||r||/||r_0|| = 4.30559e-05
+LBFGS iteration 55 : ||r|| = 3.16087e-06, ||r||/||r_0|| = 6.48351e-05
+LBFGS iteration 56 : ||r|| = 1.7279e-06, ||r||/||r_0|| = 3.54423e-05
+LBFGS iteration 57 : ||r|| = 1.61034e-06, ||r||/||r_0|| = 3.30309e-05
+LBFGS iteration 58 : ||r|| = 1.83997e-06, ||r||/||r_0|| = 3.77411e-05
+LBFGS iteration 59 : ||r|| = 4.20304e-06, ||r||/||r_0|| = 8.62119e-05
+LBFGS iteration 60 : ||r|| = 8.45043e-07, ||r||/||r_0|| = 1.73333e-05
+LBFGS iteration 61 : ||r|| = 4.7119e-07, ||r||/||r_0|| = 9.66495e-06
+LBFGS iteration 62 : ||r|| = 5.06177e-07, ||r||/||r_0|| = 1.03826e-05
+LBFGS iteration 63 : ||r|| = 5.93133e-07, ||r||/||r_0|| = 1.21662e-05
+LBFGS iteration 64 : ||r|| = 8.79673e-07, ||r||/||r_0|| = 1.80437e-05
+LBFGS iteration 65 : ||r|| = 2.66684e-07, ||r||/||r_0|| = 5.47017e-06
+LBFGS iteration 66 : ||r|| = 1.72537e-07, ||r||/||r_0|| = 3.53905e-06
+LBFGS iteration 67 : ||r|| = 1.68842e-07, ||r||/||r_0|| = 3.46326e-06
+LBFGS iteration 68 : ||r|| = 2.45189e-07, ||r||/||r_0|| = 5.02927e-06
+LBFGS iteration 69 : ||r|| = 1.77019e-07, ||r||/||r_0|| = 3.63098e-06
+LBFGS iteration 70 : ||r|| = 1.34901e-07, ||r||/||r_0|| = 2.76707e-06
+LBFGS iteration 71 : ||r|| = 1.5508e-07, ||r||/||r_0|| = 3.18097e-06
+LBFGS iteration 72 : ||r|| = 1.76064e-07, ||r||/||r_0|| = 3.61138e-06
+LBFGS iteration 73 : ||r|| = 1.26792e-07, ||r||/||r_0|| = 2.60073e-06
+LBFGS iteration 74 : ||r|| = 9.94787e-08, ||r||/||r_0|| = 2.04049e-06
+LBFGS iteration 75 : ||r|| = 9.22266e-08, ||r||/||r_0|| = 1.89173e-06
+LBFGS iteration 76 : ||r|| = 1.36524e-07, ||r||/||r_0|| = 2.80035e-06
+LBFGS iteration 77 : ||r|| = 7.74882e-08, ||r||/||r_0|| = 1.58942e-06
+LBFGS iteration 78 : ||r|| = 3.45993e-08, ||r||/||r_0|| = 7.09694e-07
+LBFGS/Newton+GMRES converged in 78 iterations with a residual norm of 3.45993e-08.
+solver took 5.1499s.
+|| q_h - q_ex || / || q_ex || = 0.000103258
+|| t_h - t_ex || / || t_ex || = 6.13896e-05

examples/regress_test/p2_o2_dg_hb_nld_newton.txt

@@ -0,0 +1,48 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 0
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0127285s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.0427805s.
+Preconditioner took 2.0331e-05s.
+Newton iteration  0 : ||r|| = 0.0487525
+Newton iteration  1 : ||r|| = 2.70229e-08, ||r||/||r_0|| = 5.54287e-07
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 2.70229e-08.
+solver took 0.436097s.
+|| q_h - q_ex || / || q_ex || = 0.00010326
+|| t_h - t_ex || / || t_ex || = 6.13937e-05

examples/regress_test/p2_o2_dg_hb_upwind_nl.txt

@@ -0,0 +1,149 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --upwinded
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0236426s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.021345s.
+Preconditioner took 6.3435e-05s.
+LBFGS iteration 0 : ||r|| = 0.0479048
+LBFGS iteration 1 : ||r|| = 0.0616084, ||r||/||r_0|| = 1.28606
+LBFGS iteration 2 : ||r|| = 0.084747, ||r||/||r_0|| = 1.76907
+LBFGS iteration 3 : ||r|| = 0.215028, ||r||/||r_0|| = 4.48866
+LBFGS iteration 4 : ||r|| = 0.0923703, ||r||/||r_0|| = 1.92821
+LBFGS iteration 5 : ||r|| = 0.040195, ||r||/||r_0|| = 0.83906
+LBFGS iteration 6 : ||r|| = 0.0349554, ||r||/||r_0|| = 0.729685
+LBFGS iteration 7 : ||r|| = 0.064908, ||r||/||r_0|| = 1.35494
+LBFGS iteration 8 : ||r|| = 0.0331042, ||r||/||r_0|| = 0.691042
+LBFGS iteration 9 : ||r|| = 0.0174788, ||r||/||r_0|| = 0.364866
+LBFGS iteration 10 : ||r|| = 0.0248971, ||r||/||r_0|| = 0.519721
+LBFGS iteration 11 : ||r|| = 0.0120826, ||r||/||r_0|| = 0.252221
+LBFGS iteration 12 : ||r|| = 0.0107089, ||r||/||r_0|| = 0.223546
+LBFGS iteration 13 : ||r|| = 0.0114643, ||r||/||r_0|| = 0.239313
+LBFGS iteration 14 : ||r|| = 0.0298765, ||r||/||r_0|| = 0.623664
+LBFGS iteration 15 : ||r|| = 0.00386271, ||r||/||r_0|| = 0.080633
+LBFGS iteration 16 : ||r|| = 0.00259066, ||r||/||r_0|| = 0.0540793
+LBFGS iteration 17 : ||r|| = 0.00212743, ||r||/||r_0|| = 0.0444096
+LBFGS iteration 18 : ||r|| = 0.00324336, ||r||/||r_0|| = 0.0677043
+LBFGS iteration 19 : ||r|| = 0.00102497, ||r||/||r_0|| = 0.021396
+LBFGS iteration 20 : ||r|| = 0.000751072, ||r||/||r_0|| = 0.0156784
+LBFGS iteration 21 : ||r|| = 0.000851405, ||r||/||r_0|| = 0.0177729
+LBFGS iteration 22 : ||r|| = 0.00096888, ||r||/||r_0|| = 0.0202251
+LBFGS iteration 23 : ||r|| = 0.0024082, ||r||/||r_0|| = 0.0502706
+LBFGS iteration 24 : ||r|| = 0.000539827, ||r||/||r_0|| = 0.0112687
+LBFGS iteration 25 : ||r|| = 0.000383843, ||r||/||r_0|| = 0.00801261
+LBFGS iteration 26 : ||r|| = 0.000348655, ||r||/||r_0|| = 0.00727809
+LBFGS iteration 27 : ||r|| = 0.00107688, ||r||/||r_0|| = 0.0224795
+LBFGS iteration 28 : ||r|| = 0.000292123, ||r||/||r_0|| = 0.00609799
+LBFGS iteration 29 : ||r|| = 0.000212752, ||r||/||r_0|| = 0.00444115
+LBFGS iteration 30 : ||r|| = 0.000302863, ||r||/||r_0|| = 0.00632219
+LBFGS iteration 31 : ||r|| = 0.000319195, ||r||/||r_0|| = 0.00666311
+LBFGS iteration 32 : ||r|| = 0.00162415, ||r||/||r_0|| = 0.0339037
+LBFGS iteration 33 : ||r|| = 0.000173184, ||r||/||r_0|| = 0.00361516
+LBFGS iteration 34 : ||r|| = 0.000112543, ||r||/||r_0|| = 0.0023493
+LBFGS iteration 35 : ||r|| = 0.000119018, ||r||/||r_0|| = 0.00248446
+LBFGS iteration 36 : ||r|| = 0.000150008, ||r||/||r_0|| = 0.00313138
+LBFGS iteration 37 : ||r|| = 0.000303811, ||r||/||r_0|| = 0.00634198
+LBFGS iteration 38 : ||r|| = 0.000173008, ||r||/||r_0|| = 0.00361149
+LBFGS iteration 39 : ||r|| = 0.000169492, ||r||/||r_0|| = 0.0035381
+LBFGS iteration 40 : ||r|| = 0.000190126, ||r||/||r_0|| = 0.00396883
+LBFGS iteration 41 : ||r|| = 0.000462501, ||r||/||r_0|| = 0.00965458
+LBFGS iteration 42 : ||r|| = 0.00011831, ||r||/||r_0|| = 0.00246968
+LBFGS iteration 43 : ||r|| = 7.38961e-05, ||r||/||r_0|| = 0.00154256
+LBFGS iteration 44 : ||r|| = 7.46699e-05, ||r||/||r_0|| = 0.00155871
+LBFGS iteration 45 : ||r|| = 5.93494e-05, ||r||/||r_0|| = 0.0012389
+LBFGS iteration 46 : ||r|| = 0.00027262, ||r||/||r_0|| = 0.00569088
+LBFGS iteration 47 : ||r|| = 3.3381e-05, ||r||/||r_0|| = 0.000696821
+LBFGS iteration 48 : ||r|| = 2.70576e-05, ||r||/||r_0|| = 0.00056482
+LBFGS iteration 49 : ||r|| = 2.61724e-05, ||r||/||r_0|| = 0.000546341
+LBFGS iteration 50 : ||r|| = 4.86663e-05, ||r||/||r_0|| = 0.0010159
+LBFGS iteration 51 : ||r|| = 2.69864e-05, ||r||/||r_0|| = 0.000563333
+LBFGS iteration 52 : ||r|| = 2.50576e-05, ||r||/||r_0|| = 0.000523071
+LBFGS iteration 53 : ||r|| = 4.99829e-05, ||r||/||r_0|| = 0.00104338
+LBFGS iteration 54 : ||r|| = 4.34595e-05, ||r||/||r_0|| = 0.000907206
+LBFGS iteration 55 : ||r|| = 2.92315e-05, ||r||/||r_0|| = 0.0006102
+LBFGS iteration 56 : ||r|| = 2.64364e-05, ||r||/||r_0|| = 0.000551852
+LBFGS iteration 57 : ||r|| = 3.00193e-05, ||r||/||r_0|| = 0.000626645
+LBFGS iteration 58 : ||r|| = 1.74462e-05, ||r||/||r_0|| = 0.000364186
+LBFGS iteration 59 : ||r|| = 9.98224e-06, ||r||/||r_0|| = 0.000208377
+LBFGS iteration 60 : ||r|| = 1.17688e-05, ||r||/||r_0|| = 0.000245671
+LBFGS iteration 61 : ||r|| = 1.09008e-05, ||r||/||r_0|| = 0.000227552
+LBFGS iteration 62 : ||r|| = 3.29489e-05, ||r||/||r_0|| = 0.000687801
+LBFGS iteration 63 : ||r|| = 6.35244e-06, ||r||/||r_0|| = 0.000132606
+LBFGS iteration 64 : ||r|| = 4.57206e-06, ||r||/||r_0|| = 9.54407e-05
+LBFGS iteration 65 : ||r|| = 5.70158e-06, ||r||/||r_0|| = 0.000119019
+LBFGS iteration 66 : ||r|| = 1.73482e-05, ||r||/||r_0|| = 0.00036214
+LBFGS iteration 67 : ||r|| = 4.01448e-06, ||r||/||r_0|| = 8.38012e-05
+LBFGS iteration 68 : ||r|| = 3.08078e-06, ||r||/||r_0|| = 6.43104e-05
+LBFGS iteration 69 : ||r|| = 4.19155e-06, ||r||/||r_0|| = 8.74975e-05
+LBFGS iteration 70 : ||r|| = 4.48357e-06, ||r||/||r_0|| = 9.35933e-05
+LBFGS iteration 71 : ||r|| = 7.97758e-06, ||r||/||r_0|| = 0.00016653
+LBFGS iteration 72 : ||r|| = 2.23571e-06, ||r||/||r_0|| = 4.66699e-05
+LBFGS iteration 73 : ||r|| = 2.13489e-06, ||r||/||r_0|| = 4.45652e-05
+LBFGS iteration 74 : ||r|| = 2.93225e-06, ||r||/||r_0|| = 6.121e-05
+LBFGS iteration 75 : ||r|| = 7.09285e-06, ||r||/||r_0|| = 0.000148061
+LBFGS iteration 76 : ||r|| = 1.43997e-06, ||r||/||r_0|| = 3.0059e-05
+LBFGS iteration 77 : ||r|| = 7.43531e-07, ||r||/||r_0|| = 1.5521e-05
+LBFGS iteration 78 : ||r|| = 5.66857e-07, ||r||/||r_0|| = 1.1833e-05
+LBFGS iteration 79 : ||r|| = 6.06591e-07, ||r||/||r_0|| = 1.26624e-05
+LBFGS iteration 80 : ||r|| = 6.65828e-07, ||r||/||r_0|| = 1.3899e-05
+LBFGS iteration 81 : ||r|| = 4.12741e-07, ||r||/||r_0|| = 8.61586e-06
+LBFGS iteration 82 : ||r|| = 4.65903e-07, ||r||/||r_0|| = 9.72561e-06
+LBFGS iteration 83 : ||r|| = 6.28728e-07, ||r||/||r_0|| = 1.31245e-05
+LBFGS iteration 84 : ||r|| = 7.87081e-07, ||r||/||r_0|| = 1.64301e-05
+LBFGS iteration 85 : ||r|| = 3.95964e-07, ||r||/||r_0|| = 8.26564e-06
+LBFGS iteration 86 : ||r|| = 3.58002e-07, ||r||/||r_0|| = 7.47319e-06
+LBFGS iteration 87 : ||r|| = 3.62976e-07, ||r||/||r_0|| = 7.57702e-06
+LBFGS iteration 88 : ||r|| = 7.7039e-07, ||r||/||r_0|| = 1.60817e-05
+LBFGS iteration 89 : ||r|| = 2.16129e-07, ||r||/||r_0|| = 4.51164e-06
+LBFGS iteration 90 : ||r|| = 1.6687e-07, ||r||/||r_0|| = 3.48338e-06
+LBFGS iteration 91 : ||r|| = 1.6022e-07, ||r||/||r_0|| = 3.34455e-06
+LBFGS iteration 92 : ||r|| = 4.01653e-07, ||r||/||r_0|| = 8.38441e-06
+LBFGS iteration 93 : ||r|| = 1.10133e-07, ||r||/||r_0|| = 2.29899e-06
+LBFGS iteration 94 : ||r|| = 7.81633e-08, ||r||/||r_0|| = 1.63164e-06
+LBFGS iteration 95 : ||r|| = 1.09594e-07, ||r||/||r_0|| = 2.28774e-06
+LBFGS iteration 96 : ||r|| = 1.22878e-07, ||r||/||r_0|| = 2.56504e-06
+LBFGS iteration 97 : ||r|| = 2.26778e-07, ||r||/||r_0|| = 4.73393e-06
+LBFGS iteration 98 : ||r|| = 8.83864e-08, ||r||/||r_0|| = 1.84504e-06
+LBFGS iteration 99 : ||r|| = 7.13829e-08, ||r||/||r_0|| = 1.4901e-06
+LBFGS iteration 100 : ||r|| = 6.36646e-08, ||r||/||r_0|| = 1.32898e-06
+LBFGS iteration 101 : ||r|| = 1.42178e-07, ||r||/||r_0|| = 2.96792e-06
+LBFGS iteration 102 : ||r|| = 4.69853e-08, ||r||/||r_0|| = 9.80806e-07
+LBFGS/Newton+GMRES converged in 102 iterations with a residual norm of 4.69853e-08.
+solver took 16.3459s.
+|| q_h - q_ex || / || q_ex || = 5.3741e-05
+|| t_h - t_ex || / || t_ex || = 6.81804e-05

examples/regress_test/p2_o2_dg_hb_upwind_nl_newton.txt

@@ -0,0 +1,48 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --upwinded
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00680956s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.0086565s.
+Preconditioner took 2.3903e-05s.
+Newton iteration  0 : ||r|| = 0.0479048
+Newton iteration  1 : ||r|| = 1.64599e-07, ||r||/||r_0|| = 3.43597e-06
+Newton iteration  2 : ||r|| = 6.93055e-09, ||r||/||r_0|| = 1.44673e-07
+Newton+GMRES+GS/Newton+GMRES converged in 2 iterations with a residual norm of 6.93055e-09.
+solver took 0.740314s.
+|| q_h - q_ex || / || q_ex || = 5.37121e-05
+|| t_h - t_ex || / || t_ex || = 6.81417e-05

examples/regress_test/p2_o2_dg_hb_upwind_nld.txt

@@ -0,0 +1,150 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 0
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --upwinded
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0158488s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.0398068s.
+Preconditioner took 5.8518e-05s.
+LBFGS iteration 0 : ||r|| = 0.0479048
+LBFGS iteration 1 : ||r|| = 0.0616084, ||r||/||r_0|| = 1.28606
+LBFGS iteration 2 : ||r|| = 0.084747, ||r||/||r_0|| = 1.76907
+LBFGS iteration 3 : ||r|| = 0.215028, ||r||/||r_0|| = 4.48866
+LBFGS iteration 4 : ||r|| = 0.0923703, ||r||/||r_0|| = 1.92821
+LBFGS iteration 5 : ||r|| = 0.040195, ||r||/||r_0|| = 0.83906
+LBFGS iteration 6 : ||r|| = 0.0349554, ||r||/||r_0|| = 0.729685
+LBFGS iteration 7 : ||r|| = 0.064908, ||r||/||r_0|| = 1.35494
+LBFGS iteration 8 : ||r|| = 0.0331042, ||r||/||r_0|| = 0.691042
+LBFGS iteration 9 : ||r|| = 0.0174788, ||r||/||r_0|| = 0.364866
+LBFGS iteration 10 : ||r|| = 0.0248971, ||r||/||r_0|| = 0.519721
+LBFGS iteration 11 : ||r|| = 0.0120826, ||r||/||r_0|| = 0.252221
+LBFGS iteration 12 : ||r|| = 0.0107089, ||r||/||r_0|| = 0.223546
+LBFGS iteration 13 : ||r|| = 0.0114643, ||r||/||r_0|| = 0.239313
+LBFGS iteration 14 : ||r|| = 0.0298765, ||r||/||r_0|| = 0.623664
+LBFGS iteration 15 : ||r|| = 0.00386271, ||r||/||r_0|| = 0.080633
+LBFGS iteration 16 : ||r|| = 0.00259066, ||r||/||r_0|| = 0.0540793
+LBFGS iteration 17 : ||r|| = 0.00212743, ||r||/||r_0|| = 0.0444096
+LBFGS iteration 18 : ||r|| = 0.00324336, ||r||/||r_0|| = 0.0677043
+LBFGS iteration 19 : ||r|| = 0.00102497, ||r||/||r_0|| = 0.021396
+LBFGS iteration 20 : ||r|| = 0.000751072, ||r||/||r_0|| = 0.0156784
+LBFGS iteration 21 : ||r|| = 0.000851405, ||r||/||r_0|| = 0.0177729
+LBFGS iteration 22 : ||r|| = 0.00096888, ||r||/||r_0|| = 0.0202251
+LBFGS iteration 23 : ||r|| = 0.0024082, ||r||/||r_0|| = 0.0502706
+LBFGS iteration 24 : ||r|| = 0.000539827, ||r||/||r_0|| = 0.0112687
+LBFGS iteration 25 : ||r|| = 0.000383843, ||r||/||r_0|| = 0.00801261
+LBFGS iteration 26 : ||r|| = 0.000348655, ||r||/||r_0|| = 0.00727809
+LBFGS iteration 27 : ||r|| = 0.00107688, ||r||/||r_0|| = 0.0224795
+LBFGS iteration 28 : ||r|| = 0.000292123, ||r||/||r_0|| = 0.00609799
+LBFGS iteration 29 : ||r|| = 0.000212752, ||r||/||r_0|| = 0.00444115
+LBFGS iteration 30 : ||r|| = 0.000302863, ||r||/||r_0|| = 0.00632219
+LBFGS iteration 31 : ||r|| = 0.000319195, ||r||/||r_0|| = 0.00666311
+LBFGS iteration 32 : ||r|| = 0.00162415, ||r||/||r_0|| = 0.0339037
+LBFGS iteration 33 : ||r|| = 0.000173184, ||r||/||r_0|| = 0.00361516
+LBFGS iteration 34 : ||r|| = 0.000112543, ||r||/||r_0|| = 0.0023493
+LBFGS iteration 35 : ||r|| = 0.000119018, ||r||/||r_0|| = 0.00248446
+LBFGS iteration 36 : ||r|| = 0.000150008, ||r||/||r_0|| = 0.00313138
+LBFGS iteration 37 : ||r|| = 0.000303811, ||r||/||r_0|| = 0.00634198
+LBFGS iteration 38 : ||r|| = 0.000173008, ||r||/||r_0|| = 0.00361149
+LBFGS iteration 39 : ||r|| = 0.000169492, ||r||/||r_0|| = 0.0035381
+LBFGS iteration 40 : ||r|| = 0.000190126, ||r||/||r_0|| = 0.00396883
+LBFGS iteration 41 : ||r|| = 0.000462501, ||r||/||r_0|| = 0.00965458
+LBFGS iteration 42 : ||r|| = 0.00011831, ||r||/||r_0|| = 0.00246968
+LBFGS iteration 43 : ||r|| = 7.38961e-05, ||r||/||r_0|| = 0.00154256
+LBFGS iteration 44 : ||r|| = 7.46699e-05, ||r||/||r_0|| = 0.00155871
+LBFGS iteration 45 : ||r|| = 5.93494e-05, ||r||/||r_0|| = 0.0012389
+LBFGS iteration 46 : ||r|| = 0.00027262, ||r||/||r_0|| = 0.00569088
+LBFGS iteration 47 : ||r|| = 3.3381e-05, ||r||/||r_0|| = 0.000696821
+LBFGS iteration 48 : ||r|| = 2.70576e-05, ||r||/||r_0|| = 0.00056482
+LBFGS iteration 49 : ||r|| = 2.61724e-05, ||r||/||r_0|| = 0.000546341
+LBFGS iteration 50 : ||r|| = 4.86663e-05, ||r||/||r_0|| = 0.0010159
+LBFGS iteration 51 : ||r|| = 2.69864e-05, ||r||/||r_0|| = 0.000563333
+LBFGS iteration 52 : ||r|| = 2.50576e-05, ||r||/||r_0|| = 0.000523071
+LBFGS iteration 53 : ||r|| = 4.99829e-05, ||r||/||r_0|| = 0.00104338
+LBFGS iteration 54 : ||r|| = 4.34595e-05, ||r||/||r_0|| = 0.000907206
+LBFGS iteration 55 : ||r|| = 2.92315e-05, ||r||/||r_0|| = 0.0006102
+LBFGS iteration 56 : ||r|| = 2.64364e-05, ||r||/||r_0|| = 0.000551852
+LBFGS iteration 57 : ||r|| = 3.00193e-05, ||r||/||r_0|| = 0.000626645
+LBFGS iteration 58 : ||r|| = 1.74462e-05, ||r||/||r_0|| = 0.000364186
+LBFGS iteration 59 : ||r|| = 9.98224e-06, ||r||/||r_0|| = 0.000208377
+LBFGS iteration 60 : ||r|| = 1.17688e-05, ||r||/||r_0|| = 0.000245671
+LBFGS iteration 61 : ||r|| = 1.09008e-05, ||r||/||r_0|| = 0.000227552
+LBFGS iteration 62 : ||r|| = 3.29489e-05, ||r||/||r_0|| = 0.0006878
+LBFGS iteration 63 : ||r|| = 6.35244e-06, ||r||/||r_0|| = 0.000132606
+LBFGS iteration 64 : ||r|| = 4.57206e-06, ||r||/||r_0|| = 9.54406e-05
+LBFGS iteration 65 : ||r|| = 5.70157e-06, ||r||/||r_0|| = 0.000119019
+LBFGS iteration 66 : ||r|| = 1.73482e-05, ||r||/||r_0|| = 0.000362139
+LBFGS iteration 67 : ||r|| = 4.01447e-06, ||r||/||r_0|| = 8.3801e-05
+LBFGS iteration 68 : ||r|| = 3.08077e-06, ||r||/||r_0|| = 6.43104e-05
+LBFGS iteration 69 : ||r|| = 4.19154e-06, ||r||/||r_0|| = 8.74974e-05
+LBFGS iteration 70 : ||r|| = 4.48349e-06, ||r||/||r_0|| = 9.35917e-05
+LBFGS iteration 71 : ||r|| = 7.9779e-06, ||r||/||r_0|| = 0.000166537
+LBFGS iteration 72 : ||r|| = 2.23567e-06, ||r||/||r_0|| = 4.66691e-05
+LBFGS iteration 73 : ||r|| = 2.13485e-06, ||r||/||r_0|| = 4.45644e-05
+LBFGS iteration 74 : ||r|| = 2.93193e-06, ||r||/||r_0|| = 6.12033e-05
+LBFGS iteration 75 : ||r|| = 7.09301e-06, ||r||/||r_0|| = 0.000148065
+LBFGS iteration 76 : ||r|| = 1.43987e-06, ||r||/||r_0|| = 3.0057e-05
+LBFGS iteration 77 : ||r|| = 7.43469e-07, ||r||/||r_0|| = 1.55197e-05
+LBFGS iteration 78 : ||r|| = 5.66762e-07, ||r||/||r_0|| = 1.1831e-05
+LBFGS iteration 79 : ||r|| = 6.05654e-07, ||r||/||r_0|| = 1.26429e-05
+LBFGS iteration 80 : ||r|| = 6.67706e-07, ||r||/||r_0|| = 1.39382e-05
+LBFGS iteration 81 : ||r|| = 4.12608e-07, ||r||/||r_0|| = 8.61308e-06
+LBFGS iteration 82 : ||r|| = 4.6572e-07, ||r||/||r_0|| = 9.72179e-06
+LBFGS iteration 83 : ||r|| = 6.24456e-07, ||r||/||r_0|| = 1.30354e-05
+LBFGS iteration 84 : ||r|| = 8.13646e-07, ||r||/||r_0|| = 1.69847e-05
+LBFGS iteration 85 : ||r|| = 3.95763e-07, ||r||/||r_0|| = 8.26146e-06
+LBFGS iteration 86 : ||r|| = 3.57541e-07, ||r||/||r_0|| = 7.46358e-06
+LBFGS iteration 87 : ||r|| = 3.59986e-07, ||r||/||r_0|| = 7.51462e-06
+LBFGS iteration 88 : ||r|| = 8.5842e-07, ||r||/||r_0|| = 1.79193e-05
+LBFGS iteration 89 : ||r|| = 2.1999e-07, ||r||/||r_0|| = 4.59224e-06
+LBFGS iteration 90 : ||r|| = 1.64673e-07, ||r||/||r_0|| = 3.43751e-06
+LBFGS iteration 91 : ||r|| = 1.60953e-07, ||r||/||r_0|| = 3.35985e-06
+LBFGS iteration 92 : ||r|| = 3.82217e-07, ||r||/||r_0|| = 7.97869e-06
+LBFGS iteration 93 : ||r|| = 1.10487e-07, ||r||/||r_0|| = 2.30639e-06
+LBFGS iteration 94 : ||r|| = 7.93734e-08, ||r||/||r_0|| = 1.6569e-06
+LBFGS iteration 95 : ||r|| = 1.10419e-07, ||r||/||r_0|| = 2.30497e-06
+LBFGS iteration 96 : ||r|| = 1.23134e-07, ||r||/||r_0|| = 2.57038e-06
+LBFGS iteration 97 : ||r|| = 2.39511e-07, ||r||/||r_0|| = 4.99973e-06
+LBFGS iteration 98 : ||r|| = 9.00609e-08, ||r||/||r_0|| = 1.88e-06
+LBFGS iteration 99 : ||r|| = 7.14156e-08, ||r||/||r_0|| = 1.49078e-06
+LBFGS iteration 100 : ||r|| = 6.46134e-08, ||r||/||r_0|| = 1.34879e-06
+LBFGS iteration 101 : ||r|| = 1.36875e-07, ||r||/||r_0|| = 2.85722e-06
+LBFGS iteration 102 : ||r|| = 5.16486e-08, ||r||/||r_0|| = 1.07815e-06
+LBFGS iteration 103 : ||r|| = 3.19821e-08, ||r||/||r_0|| = 6.67619e-07
+LBFGS/Newton+GMRES converged in 103 iterations with a residual norm of 3.19821e-08.
+solver took 7.04158s.
+|| q_h - q_ex || / || q_ex || = 5.37375e-05
+|| t_h - t_ex || / || t_ex || = 6.81775e-05

examples/regress_test/p2_o2_dg_hb_upwind_nld_newton.txt

@@ -0,0 +1,49 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 0
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --upwinded
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0170454s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.039347s.
+Preconditioner took 2.0644e-05s.
+Newton iteration  0 : ||r|| = 0.0479048
+Newton iteration  1 : ||r|| = 5.54166e-08, ||r||/||r_0|| = 1.15681e-06
+Newton iteration  2 : ||r|| = 1.91411e-08, ||r||/||r_0|| = 3.99565e-07
+Newton+GMRES+GS/Newton+GMRES converged in 2 iterations with a residual norm of 1.91411e-08.
+solver took 0.791156s.
+|| q_h - q_ex || / || q_ex || = 5.37112e-05
+|| t_h - t_ex || / || t_ex || = 6.8141e-05

examples/regress_test/p2_o2_dg_hb_upwind_nlp_newton.txt

@@ -0,0 +1,51 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --no-broken-RT
+   --upwinded
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --no-nonlinear
+   --no-nonlinear-flux
+   --nonlinear-pot
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00680552s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.0249243s.
+Preconditioner took 3.4989e-05s.
+Newton iteration  0 : ||r|| = 0.0479048
+Newton iteration  1 : ||r|| = 4.49235e-10, ||r||/||r_0|| = 9.37767e-09
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 4.49235e-10.
+solver took 0.34942s.
+|| q_h - q_ex || / || q_ex || = 5.37114e-05
+|| t_h - t_ex || / || t_ex || = 6.81408e-05

examples/regress_test/p2_o2_dg_hb_upwind_nlu_newton.txt

@@ -0,0 +1,52 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --no-broken-RT
+   --upwinded
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --no-nonlinear
+   --nonlinear-flux
+   --no-nonlinear-pot
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0119308s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.044629s.
+Preconditioner took 6.6724e-05s.
+Newton iteration  0 : ||r|| = 0.0479048
+Newton iteration  1 : ||r|| = 5.53006e-08, ||r||/||r_0|| = 1.15439e-06
+Newton iteration  2 : ||r|| = 1.92378e-08, ||r||/||r_0|| = 4.01583e-07
+Newton+GMRES+GS/Newton+GMRES converged in 2 iterations with a residual norm of 1.92378e-08.
+solver took 0.179572s.
+|| q_h - q_ex || / || q_ex || = 5.37111e-05
+|| t_h - t_ex || / || t_ex || = 6.8141e-05

examples/regress_test/p2_o2_dg_nld_newton.txt

@@ -0,0 +1,46 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 0
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(V+W) = 2700
+***********************************************************
+Assembly took 0.0875788s.
+Preconditioner took 1.9397e-05s.
+Newton iteration  0 : ||r|| = 0.0568908
+Newton iteration  1 : ||r|| = 1.31954e-10, ||r||/||r_0|| = 2.31942e-09
+Newton+GMRES+GS converged in 1 iterations with a residual norm of 1.31954e-10.
+solver took 0.682485s.
+|| q_h - q_ex || / || q_ex || = 0.000100377
+|| t_h - t_ex || / || t_ex || = 1.71812e-05

examples/regress_test/p2_o2_dg_nld_newton_umfpack.txt

@@ -0,0 +1,46 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 0
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(V+W) = 2700
+***********************************************************
+Assembly took 0.0892387s.
+Preconditioner took 1.8823e-05s.
+Newton iteration  0 : ||r|| = 0.0568908
+Newton iteration  1 : ||r|| = 2.24174e-09, ||r||/||r_0|| = 3.94042e-08
+Newton+GMRES+UMFPack converged in 1 iterations with a residual norm of 2.24174e-09.
+solver took 0.211705s.
+|| q_h - q_ex || / || q_ex || = 0.000100377
+|| t_h - t_ex || / || t_ex || = 1.71813e-05

examples/regress_test/p2_o2_dg_nld_nl_newton.txt

@@ -0,0 +1,46 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 0
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(V+W) = 2700
+***********************************************************
+Assembly took 0.06038s.
+Preconditioner took 8.988e-06s.
+Newton iteration  0 : ||r|| = 0.0568908
+Newton iteration  1 : ||r|| = 1.31954e-10, ||r||/||r_0|| = 2.31942e-09
+Newton+GMRES+GS converged in 1 iterations with a residual norm of 1.31954e-10.
+solver took 0.831873s.
+|| q_h - q_ex || / || q_ex || = 0.000100377
+|| t_h - t_ex || / || t_ex || = 1.71812e-05

examples/regress_test/p2_o2_dg_nld_nl_newton_umfpack.txt

@@ -0,0 +1,46 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 0
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(V+W) = 2700
+***********************************************************
+Assembly took 0.0623638s.
+Preconditioner took 1.5406e-05s.
+Newton iteration  0 : ||r|| = 0.0568908
+Newton iteration  1 : ||r|| = 2.24174e-09, ||r||/||r_0|| = 3.94042e-08
+Newton+GMRES+UMFPack converged in 1 iterations with a residual norm of 2.24174e-09.
+solver took 0.303314s.
+|| q_h - q_ex || / || q_ex || = 0.000100377
+|| t_h - t_ex || / || t_ex || = 1.71813e-05

examples/regress_test/p2_o2_dg_upwind_nld_newton.txt

@@ -0,0 +1,46 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 0
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --upwinded
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(V+W) = 2700
+***********************************************************
+Assembly took 0.0594011s.
+Preconditioner took 3.0745e-05s.
+Newton iteration  0 : ||r|| = 0.0568908
+Newton iteration  1 : ||r|| = 7.72352e-11, ||r||/||r_0|| = 1.3576e-09
+Newton+GMRES+GS converged in 1 iterations with a residual norm of 7.72352e-11.
+solver took 0.737046s.
+|| q_h - q_ex || / || q_ex || = 7.91877e-05
+|| t_h - t_ex || / || t_ex || = 8.27713e-05

examples/regress_test/p2_o2_dg_upwind_nld_newton_umfpack.txt

@@ -0,0 +1,46 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 0
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --upwinded
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(V+W) = 2700
+***********************************************************
+Assembly took 0.0621302s.
+Preconditioner took 3.0662e-05s.
+Newton iteration  0 : ||r|| = 0.0568908
+Newton iteration  1 : ||r|| = 4.38138e-09, ||r||/||r_0|| = 7.70138e-08
+Newton+GMRES+UMFPack converged in 1 iterations with a residual norm of 4.38138e-09.
+solver took 0.162773s.
+|| q_h - q_ex || / || q_ex || = 7.91878e-05
+|| t_h - t_ex || / || t_ex || = 8.27714e-05

examples/regress_test/p2_o2_dg_upwind_nld_nl_newton.txt

@@ -0,0 +1,46 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 0
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --upwinded
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(V+W) = 2700
+***********************************************************
+Assembly took 0.0509854s.
+Preconditioner took 2.71e-05s.
+Newton iteration  0 : ||r|| = 0.0568908
+Newton iteration  1 : ||r|| = 7.72369e-11, ||r||/||r_0|| = 1.35763e-09
+Newton+GMRES+GS converged in 1 iterations with a residual norm of 7.72369e-11.
+solver took 0.797116s.
+|| q_h - q_ex || / || q_ex || = 7.91877e-05
+|| t_h - t_ex || / || t_ex || = 8.27713e-05

examples/regress_test/p2_o2_dg_upwind_nld_nl_newton_umfpack.txt

@@ -0,0 +1,46 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 0
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --upwinded
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(V+W) = 2700
+***********************************************************
+Assembly took 0.0412338s.
+Preconditioner took 2.9921e-05s.
+Newton iteration  0 : ||r|| = 0.0568908
+Newton iteration  1 : ||r|| = 4.38138e-09, ||r||/||r_0|| = 7.70138e-08
+Newton+GMRES+UMFPack converged in 1 iterations with a residual norm of 4.38138e-09.
+solver took 0.204618s.
+|| q_h - q_ex || / || q_ex || = 7.91878e-05
+|| t_h - t_ex || / || t_ex || = 8.27714e-05

examples/regress_test/p2_o2_hb_nl.txt

@@ -0,0 +1,142 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --no-discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0144651s.
+***********************************************************
+dim(V) = 1860
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3420
+***********************************************************
+Assembly took 0.0143539s.
+Preconditioner took 6.2281e-05s.
+LBFGS iteration 0 : ||r|| = 0.0531438
+LBFGS iteration 1 : ||r|| = 0.133876, ||r||/||r_0|| = 2.51912
+LBFGS iteration 2 : ||r|| = 0.0759381, ||r||/||r_0|| = 1.42892
+LBFGS iteration 3 : ||r|| = 0.0970599, ||r||/||r_0|| = 1.82636
+LBFGS iteration 4 : ||r|| = 0.272306, ||r||/||r_0|| = 5.12395
+LBFGS iteration 5 : ||r|| = 0.33755, ||r||/||r_0|| = 6.35165
+LBFGS iteration 6 : ||r|| = 0.0829767, ||r||/||r_0|| = 1.56136
+LBFGS iteration 7 : ||r|| = 0.0442803, ||r||/||r_0|| = 0.833218
+LBFGS iteration 8 : ||r|| = 0.045927, ||r||/||r_0|| = 0.864203
+LBFGS iteration 9 : ||r|| = 0.0791075, ||r||/||r_0|| = 1.48856
+LBFGS iteration 10 : ||r|| = 0.0597997, ||r||/||r_0|| = 1.12524
+LBFGS iteration 11 : ||r|| = 0.0447909, ||r||/||r_0|| = 0.842825
+LBFGS iteration 12 : ||r|| = 0.11125, ||r||/||r_0|| = 2.09338
+LBFGS iteration 13 : ||r|| = 0.0224584, ||r||/||r_0|| = 0.422597
+LBFGS iteration 14 : ||r|| = 0.0194577, ||r||/||r_0|| = 0.366133
+LBFGS iteration 15 : ||r|| = 0.027276, ||r||/||r_0|| = 0.51325
+LBFGS iteration 16 : ||r|| = 0.0421435, ||r||/||r_0|| = 0.79301
+LBFGS iteration 17 : ||r|| = 0.0119437, ||r||/||r_0|| = 0.224744
+LBFGS iteration 18 : ||r|| = 0.00804609, ||r||/||r_0|| = 0.151402
+LBFGS iteration 19 : ||r|| = 0.00973581, ||r||/||r_0|| = 0.183198
+LBFGS iteration 20 : ||r|| = 0.0133476, ||r||/||r_0|| = 0.251161
+LBFGS iteration 21 : ||r|| = 0.0128898, ||r||/||r_0|| = 0.242545
+LBFGS iteration 22 : ||r|| = 0.00296082, ||r||/||r_0|| = 0.0557133
+LBFGS iteration 23 : ||r|| = 0.00136938, ||r||/||r_0|| = 0.0257674
+LBFGS iteration 24 : ||r|| = 0.00141945, ||r||/||r_0|| = 0.0267097
+LBFGS iteration 25 : ||r|| = 0.0019504, ||r||/||r_0|| = 0.0367005
+LBFGS iteration 26 : ||r|| = 0.00174276, ||r||/||r_0|| = 0.0327933
+LBFGS iteration 27 : ||r|| = 0.000654538, ||r||/||r_0|| = 0.0123164
+LBFGS iteration 28 : ||r|| = 0.000549666, ||r||/||r_0|| = 0.010343
+LBFGS iteration 29 : ||r|| = 0.00063636, ||r||/||r_0|| = 0.0119743
+LBFGS iteration 30 : ||r|| = 0.00194428, ||r||/||r_0|| = 0.0365853
+LBFGS iteration 31 : ||r|| = 0.000733621, ||r||/||r_0|| = 0.0138045
+LBFGS iteration 32 : ||r|| = 0.000639731, ||r||/||r_0|| = 0.0120377
+LBFGS iteration 33 : ||r|| = 0.000682233, ||r||/||r_0|| = 0.0128375
+LBFGS iteration 34 : ||r|| = 0.00117926, ||r||/||r_0|| = 0.02219
+LBFGS iteration 35 : ||r|| = 0.000271555, ||r||/||r_0|| = 0.00510982
+LBFGS iteration 36 : ||r|| = 0.000197911, ||r||/||r_0|| = 0.00372407
+LBFGS iteration 37 : ||r|| = 0.000251875, ||r||/||r_0|| = 0.0047395
+LBFGS iteration 38 : ||r|| = 0.00034856, ||r||/||r_0|| = 0.00655881
+LBFGS iteration 39 : ||r|| = 0.0003601, ||r||/||r_0|| = 0.00677596
+LBFGS iteration 40 : ||r|| = 0.000201069, ||r||/||r_0|| = 0.0037835
+LBFGS iteration 41 : ||r|| = 0.000121634, ||r||/||r_0|| = 0.00228876
+LBFGS iteration 42 : ||r|| = 0.000136064, ||r||/||r_0|| = 0.00256029
+LBFGS iteration 43 : ||r|| = 0.000137738, ||r||/||r_0|| = 0.0025918
+LBFGS iteration 44 : ||r|| = 0.000303993, ||r||/||r_0|| = 0.00572019
+LBFGS iteration 45 : ||r|| = 6.53198e-05, ||r||/||r_0|| = 0.00122912
+LBFGS iteration 46 : ||r|| = 3.50262e-05, ||r||/||r_0|| = 0.000659084
+LBFGS iteration 47 : ||r|| = 3.87647e-05, ||r||/||r_0|| = 0.00072943
+LBFGS iteration 48 : ||r|| = 5.17877e-05, ||r||/||r_0|| = 0.000974483
+LBFGS iteration 49 : ||r|| = 8.52871e-05, ||r||/||r_0|| = 0.00160484
+LBFGS iteration 50 : ||r|| = 2.52465e-05, ||r||/||r_0|| = 0.00047506
+LBFGS iteration 51 : ||r|| = 1.71626e-05, ||r||/||r_0|| = 0.000322946
+LBFGS iteration 52 : ||r|| = 1.69215e-05, ||r||/||r_0|| = 0.00031841
+LBFGS iteration 53 : ||r|| = 2.57148e-05, ||r||/||r_0|| = 0.000483872
+LBFGS iteration 54 : ||r|| = 1.71715e-05, ||r||/||r_0|| = 0.000323115
+LBFGS iteration 55 : ||r|| = 6.32037e-06, ||r||/||r_0|| = 0.00011893
+LBFGS iteration 56 : ||r|| = 3.8541e-06, ||r||/||r_0|| = 7.25222e-05
+LBFGS iteration 57 : ||r|| = 3.51269e-06, ||r||/||r_0|| = 6.60979e-05
+LBFGS iteration 58 : ||r|| = 3.64852e-06, ||r||/||r_0|| = 6.86538e-05
+LBFGS iteration 59 : ||r|| = 6.06824e-06, ||r||/||r_0|| = 0.000114185
+LBFGS iteration 60 : ||r|| = 2.29895e-06, ||r||/||r_0|| = 4.32591e-05
+LBFGS iteration 61 : ||r|| = 2.13464e-06, ||r||/||r_0|| = 4.01673e-05
+LBFGS iteration 62 : ||r|| = 3.23597e-06, ||r||/||r_0|| = 6.08909e-05
+LBFGS iteration 63 : ||r|| = 5.9964e-06, ||r||/||r_0|| = 0.000112834
+LBFGS iteration 64 : ||r|| = 4.60688e-06, ||r||/||r_0|| = 8.66871e-05
+LBFGS iteration 65 : ||r|| = 3.41308e-06, ||r||/||r_0|| = 6.42235e-05
+LBFGS iteration 66 : ||r|| = 3.32465e-06, ||r||/||r_0|| = 6.25595e-05
+LBFGS iteration 67 : ||r|| = 2.52728e-06, ||r||/||r_0|| = 4.75556e-05
+LBFGS iteration 68 : ||r|| = 2.33056e-06, ||r||/||r_0|| = 4.38539e-05
+LBFGS iteration 69 : ||r|| = 3.34582e-06, ||r||/||r_0|| = 6.29578e-05
+LBFGS iteration 70 : ||r|| = 1.00966e-06, ||r||/||r_0|| = 1.89986e-05
+LBFGS iteration 71 : ||r|| = 7.55423e-07, ||r||/||r_0|| = 1.42147e-05
+LBFGS iteration 72 : ||r|| = 1.01069e-06, ||r||/||r_0|| = 1.90181e-05
+LBFGS iteration 73 : ||r|| = 1.23955e-06, ||r||/||r_0|| = 2.33244e-05
+LBFGS iteration 74 : ||r|| = 2.93603e-06, ||r||/||r_0|| = 5.52469e-05
+LBFGS iteration 75 : ||r|| = 5.33099e-07, ||r||/||r_0|| = 1.00313e-05
+LBFGS iteration 76 : ||r|| = 3.21811e-07, ||r||/||r_0|| = 6.05548e-06
+LBFGS iteration 77 : ||r|| = 3.42874e-07, ||r||/||r_0|| = 6.45181e-06
+LBFGS iteration 78 : ||r|| = 3.8029e-07, ||r||/||r_0|| = 7.15586e-06
+LBFGS iteration 79 : ||r|| = 8.26745e-07, ||r||/||r_0|| = 1.55568e-05
+LBFGS iteration 80 : ||r|| = 2.35384e-07, ||r||/||r_0|| = 4.4292e-06
+LBFGS iteration 81 : ||r|| = 2.07108e-07, ||r||/||r_0|| = 3.89712e-06
+LBFGS iteration 82 : ||r|| = 2.73917e-07, ||r||/||r_0|| = 5.15426e-06
+LBFGS iteration 83 : ||r|| = 3.62342e-07, ||r||/||r_0|| = 6.81815e-06
+LBFGS iteration 84 : ||r|| = 4.78669e-07, ||r||/||r_0|| = 9.00706e-06
+LBFGS iteration 85 : ||r|| = 1.48215e-07, ||r||/||r_0|| = 2.78895e-06
+LBFGS iteration 86 : ||r|| = 1.53083e-07, ||r||/||r_0|| = 2.88055e-06
+LBFGS iteration 87 : ||r|| = 2.05383e-07, ||r||/||r_0|| = 3.86466e-06
+LBFGS iteration 88 : ||r|| = 4.45563e-07, ||r||/||r_0|| = 8.38411e-06
+LBFGS iteration 89 : ||r|| = 1.22162e-07, ||r||/||r_0|| = 2.29871e-06
+LBFGS iteration 90 : ||r|| = 7.42999e-08, ||r||/||r_0|| = 1.39809e-06
+LBFGS iteration 91 : ||r|| = 9.30259e-08, ||r||/||r_0|| = 1.75046e-06
+LBFGS iteration 92 : ||r|| = 9.60668e-08, ||r||/||r_0|| = 1.80768e-06
+LBFGS iteration 93 : ||r|| = 3.45812e-07, ||r||/||r_0|| = 6.50711e-06
+LBFGS iteration 94 : ||r|| = 5.6767e-08, ||r||/||r_0|| = 1.06818e-06
+LBFGS iteration 95 : ||r|| = 3.45087e-08, ||r||/||r_0|| = 6.49346e-07
+LBFGS/Newton+GMRES converged in 95 iterations with a residual norm of 3.45087e-08.
+solver took 26.1296s.
+|| q_h - q_ex || / || q_ex || = 1.67201e-05
+|| t_h - t_ex || / || t_ex || = 1.15803e-06

examples/regress_test/p2_o2_hb_nl_newton.txt

@@ -0,0 +1,47 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --no-discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00901714s.
+***********************************************************
+dim(V) = 1860
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3420
+***********************************************************
+Assembly took 0.0123551s.
+Preconditioner took 1.3324e-05s.
+Newton iteration  0 : ||r|| = 0.0531438
+Newton iteration  1 : ||r|| = 2.69684e-08, ||r||/||r_0|| = 5.07462e-07
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 2.69684e-08.
+solver took 0.811168s.
+|| q_h - q_ex || / || q_ex || = 1.67174e-05
+|| t_h - t_ex || / || t_ex || = 1.14191e-06

examples/regress_test/p2_o2_hb_nlp_newton.txt

@@ -0,0 +1,51 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --no-discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --no-nonlinear
+   --no-nonlinear-flux
+   --nonlinear-pot
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.028397s.
+***********************************************************
+dim(V) = 1860
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3420
+***********************************************************
+Assembly took 0.0834947s.
+Preconditioner took 9.7263e-05s.
+Newton iteration  0 : ||r|| = 0.0531438
+Newton iteration  1 : ||r|| = 7.42964e-09, ||r||/||r_0|| = 1.39803e-07
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 7.42964e-09.
+solver took 0.300628s.
+|| q_h - q_ex || / || q_ex || = 1.67163e-05
+|| t_h - t_ex || / || t_ex || = 1.14193e-06

examples/regress_test/p2_o2_hb_nlu_newton.txt

@@ -0,0 +1,51 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --no-discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --no-nonlinear
+   --nonlinear-flux
+   --no-nonlinear-pot
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0120959s.
+***********************************************************
+dim(V) = 1860
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3420
+***********************************************************
+Assembly took 0.0368401s.
+Preconditioner took 2.697e-05s.
+Newton iteration  0 : ||r|| = 0.0531438
+Newton iteration  1 : ||r|| = 1.27508e-08, ||r||/||r_0|| = 2.3993e-07
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 1.27508e-08.
+solver took 0.475256s.
+|| q_h - q_ex || / || q_ex || = 1.67159e-05
+|| t_h - t_ex || / || t_ex || = 1.14189e-06

examples/regress_test/p2_o2_hb_upwind_nl.txt

@@ -0,0 +1,163 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --no-discontinuous
+   --no-broken-RT
+   --upwinded
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-flux
+   --no-nonlinear-pot
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0207091s.
+***********************************************************
+dim(V) = 1860
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3420
+***********************************************************
+Assembly took 0.0190565s.
+Preconditioner took 8.5109e-05s.
+LBFGS iteration 0 : ||r|| = 0.0531419
+LBFGS iteration 1 : ||r|| = 0.133842, ||r||/||r_0|| = 2.51858
+LBFGS iteration 2 : ||r|| = 0.0759453, ||r||/||r_0|| = 1.4291
+LBFGS iteration 3 : ||r|| = 0.0970707, ||r||/||r_0|| = 1.82663
+LBFGS iteration 4 : ||r|| = 0.2712, ||r||/||r_0|| = 5.10333
+LBFGS iteration 5 : ||r|| = 0.339311, ||r||/||r_0|| = 6.385
+LBFGS iteration 6 : ||r|| = 0.0830268, ||r||/||r_0|| = 1.56236
+LBFGS iteration 7 : ||r|| = 0.0443227, ||r||/||r_0|| = 0.834045
+LBFGS iteration 8 : ||r|| = 0.0458863, ||r||/||r_0|| = 0.863468
+LBFGS iteration 9 : ||r|| = 0.0787083, ||r||/||r_0|| = 1.4811
+LBFGS iteration 10 : ||r|| = 0.0597951, ||r||/||r_0|| = 1.1252
+LBFGS iteration 11 : ||r|| = 0.0454929, ||r||/||r_0|| = 0.856065
+LBFGS iteration 12 : ||r|| = 0.110389, ||r||/||r_0|| = 2.07724
+LBFGS iteration 13 : ||r|| = 0.0223646, ||r||/||r_0|| = 0.420848
+LBFGS iteration 14 : ||r|| = 0.0194141, ||r||/||r_0|| = 0.365326
+LBFGS iteration 15 : ||r|| = 0.0274816, ||r||/||r_0|| = 0.517136
+LBFGS iteration 16 : ||r|| = 0.0479984, ||r||/||r_0|| = 0.903213
+LBFGS iteration 17 : ||r|| = 0.0132085, ||r||/||r_0|| = 0.248552
+LBFGS iteration 18 : ||r|| = 0.00813445, ||r||/||r_0|| = 0.15307
+LBFGS iteration 19 : ||r|| = 0.00956826, ||r||/||r_0|| = 0.180051
+LBFGS iteration 20 : ||r|| = 0.0113342, ||r||/||r_0|| = 0.213282
+LBFGS iteration 21 : ||r|| = 0.0319224, ||r||/||r_0|| = 0.600702
+LBFGS iteration 22 : ||r|| = 0.00472632, ||r||/||r_0|| = 0.0889377
+LBFGS iteration 23 : ||r|| = 0.00198453, ||r||/||r_0|| = 0.0373439
+LBFGS iteration 24 : ||r|| = 0.00138465, ||r||/||r_0|| = 0.0260558
+LBFGS iteration 25 : ||r|| = 0.00136984, ||r||/||r_0|| = 0.025777
+LBFGS iteration 26 : ||r|| = 0.00388291, ||r||/||r_0|| = 0.073067
+LBFGS iteration 27 : ||r|| = 0.000898066, ||r||/||r_0|| = 0.0168994
+LBFGS iteration 28 : ||r|| = 0.000545102, ||r||/||r_0|| = 0.0102575
+LBFGS iteration 29 : ||r|| = 0.000532495, ||r||/||r_0|| = 0.0100203
+LBFGS iteration 30 : ||r|| = 0.00093569, ||r||/||r_0|| = 0.0176074
+LBFGS iteration 31 : ||r|| = 0.00099363, ||r||/||r_0|| = 0.0186977
+LBFGS iteration 32 : ||r|| = 0.000852682, ||r||/||r_0|| = 0.0160454
+LBFGS iteration 33 : ||r|| = 0.00136212, ||r||/||r_0|| = 0.0256317
+LBFGS iteration 34 : ||r|| = 0.000380054, ||r||/||r_0|| = 0.00715169
+LBFGS iteration 35 : ||r|| = 0.0002739, ||r||/||r_0|| = 0.00515413
+LBFGS iteration 36 : ||r|| = 0.000252761, ||r||/||r_0|| = 0.00475635
+LBFGS iteration 37 : ||r|| = 0.000450362, ||r||/||r_0|| = 0.00847472
+LBFGS iteration 38 : ||r|| = 0.000194958, ||r||/||r_0|| = 0.00366864
+LBFGS iteration 39 : ||r|| = 0.000160964, ||r||/||r_0|| = 0.00302895
+LBFGS iteration 40 : ||r|| = 0.000238961, ||r||/||r_0|| = 0.00449666
+LBFGS iteration 41 : ||r|| = 0.000232242, ||r||/||r_0|| = 0.00437022
+LBFGS iteration 42 : ||r|| = 0.000794672, ||r||/||r_0|| = 0.0149538
+LBFGS iteration 43 : ||r|| = 0.000109136, ||r||/||r_0|| = 0.00205367
+LBFGS iteration 44 : ||r|| = 6.71649e-05, ||r||/||r_0|| = 0.00126388
+LBFGS iteration 45 : ||r|| = 8.40244e-05, ||r||/||r_0|| = 0.00158113
+LBFGS iteration 46 : ||r|| = 0.000109875, ||r||/||r_0|| = 0.00206757
+LBFGS iteration 47 : ||r|| = 0.000114851, ||r||/||r_0|| = 0.00216121
+LBFGS iteration 48 : ||r|| = 0.00047044, ||r||/||r_0|| = 0.00885254
+LBFGS iteration 49 : ||r|| = 5.71004e-05, ||r||/||r_0|| = 0.00107449
+LBFGS iteration 50 : ||r|| = 3.51095e-05, ||r||/||r_0|| = 0.000660676
+LBFGS iteration 51 : ||r|| = 4.52059e-05, ||r||/||r_0|| = 0.000850666
+LBFGS iteration 52 : ||r|| = 4.69574e-05, ||r||/||r_0|| = 0.000883624
+LBFGS iteration 53 : ||r|| = 0.000160547, ||r||/||r_0|| = 0.0030211
+LBFGS iteration 54 : ||r|| = 1.85204e-05, ||r||/||r_0|| = 0.00034851
+LBFGS iteration 55 : ||r|| = 1.20412e-05, ||r||/||r_0|| = 0.000226587
+LBFGS iteration 56 : ||r|| = 1.42105e-05, ||r||/||r_0|| = 0.000267408
+LBFGS iteration 57 : ||r|| = 1.54396e-05, ||r||/||r_0|| = 0.000290535
+LBFGS iteration 58 : ||r|| = 3.9195e-05, ||r||/||r_0|| = 0.000737555
+LBFGS iteration 59 : ||r|| = 5.67039e-06, ||r||/||r_0|| = 0.000106703
+LBFGS iteration 60 : ||r|| = 3.02313e-06, ||r||/||r_0|| = 5.68879e-05
+LBFGS iteration 61 : ||r|| = 2.62658e-06, ||r||/||r_0|| = 4.94259e-05
+LBFGS iteration 62 : ||r|| = 3.84725e-06, ||r||/||r_0|| = 7.23959e-05
+LBFGS iteration 63 : ||r|| = 5.03825e-06, ||r||/||r_0|| = 9.48076e-05
+LBFGS iteration 64 : ||r|| = 2.30241e-06, ||r||/||r_0|| = 4.33257e-05
+LBFGS iteration 65 : ||r|| = 1.56604e-06, ||r||/||r_0|| = 2.9469e-05
+LBFGS iteration 66 : ||r|| = 1.92223e-06, ||r||/||r_0|| = 3.61716e-05
+LBFGS iteration 67 : ||r|| = 2.41125e-06, ||r||/||r_0|| = 4.53738e-05
+LBFGS iteration 68 : ||r|| = 3.53202e-06, ||r||/||r_0|| = 6.64639e-05
+LBFGS iteration 69 : ||r|| = 4.05461e-06, ||r||/||r_0|| = 7.6298e-05
+LBFGS iteration 70 : ||r|| = 1.68181e-06, ||r||/||r_0|| = 3.16476e-05
+LBFGS iteration 71 : ||r|| = 1.4349e-06, ||r||/||r_0|| = 2.70014e-05
+LBFGS iteration 72 : ||r|| = 1.77394e-06, ||r||/||r_0|| = 3.33812e-05
+LBFGS iteration 73 : ||r|| = 2.55595e-06, ||r||/||r_0|| = 4.80968e-05
+LBFGS iteration 74 : ||r|| = 2.6632e-06, ||r||/||r_0|| = 5.01149e-05
+LBFGS iteration 75 : ||r|| = 7.06769e-07, ||r||/||r_0|| = 1.32997e-05
+LBFGS iteration 76 : ||r|| = 6.59467e-07, ||r||/||r_0|| = 1.24096e-05
+LBFGS iteration 77 : ||r|| = 1.07492e-06, ||r||/||r_0|| = 2.02274e-05
+LBFGS iteration 78 : ||r|| = 1.51174e-06, ||r||/||r_0|| = 2.84473e-05
+LBFGS iteration 79 : ||r|| = 2.34339e-06, ||r||/||r_0|| = 4.40969e-05
+LBFGS iteration 80 : ||r|| = 6.43127e-07, ||r||/||r_0|| = 1.21021e-05
+LBFGS iteration 81 : ||r|| = 4.29095e-07, ||r||/||r_0|| = 8.07453e-06
+LBFGS iteration 82 : ||r|| = 4.75945e-07, ||r||/||r_0|| = 8.95613e-06
+LBFGS iteration 83 : ||r|| = 7.07686e-07, ||r||/||r_0|| = 1.33169e-05
+LBFGS iteration 84 : ||r|| = 6.54364e-07, ||r||/||r_0|| = 1.23135e-05
+LBFGS iteration 85 : ||r|| = 3.03114e-07, ||r||/||r_0|| = 5.70387e-06
+LBFGS iteration 86 : ||r|| = 3.25921e-07, ||r||/||r_0|| = 6.13304e-06
+LBFGS iteration 87 : ||r|| = 3.77353e-07, ||r||/||r_0|| = 7.10087e-06
+LBFGS iteration 88 : ||r|| = 9.24639e-07, ||r||/||r_0|| = 1.73994e-05
+LBFGS iteration 89 : ||r|| = 3.01237e-07, ||r||/||r_0|| = 5.66854e-06
+LBFGS iteration 90 : ||r|| = 2.83878e-07, ||r||/||r_0|| = 5.3419e-06
+LBFGS iteration 91 : ||r|| = 3.54051e-07, ||r||/||r_0|| = 6.66238e-06
+LBFGS iteration 92 : ||r|| = 5.59386e-07, ||r||/||r_0|| = 1.05263e-05
+LBFGS iteration 93 : ||r|| = 2.83778e-07, ||r||/||r_0|| = 5.34e-06
+LBFGS iteration 94 : ||r|| = 1.82994e-07, ||r||/||r_0|| = 3.4435e-06
+LBFGS iteration 95 : ||r|| = 2.23884e-07, ||r||/||r_0|| = 4.21295e-06
+LBFGS iteration 96 : ||r|| = 3.18008e-07, ||r||/||r_0|| = 5.98413e-06
+LBFGS iteration 97 : ||r|| = 1.91314e-07, ||r||/||r_0|| = 3.60007e-06
+LBFGS iteration 98 : ||r|| = 1.63122e-07, ||r||/||r_0|| = 3.06956e-06
+LBFGS iteration 99 : ||r|| = 1.99567e-07, ||r||/||r_0|| = 3.75536e-06
+LBFGS iteration 100 : ||r|| = 1.72744e-07, ||r||/||r_0|| = 3.25062e-06
+LBFGS iteration 101 : ||r|| = 2.81951e-07, ||r||/||r_0|| = 5.30563e-06
+LBFGS iteration 102 : ||r|| = 3.08839e-07, ||r||/||r_0|| = 5.8116e-06
+LBFGS iteration 103 : ||r|| = 8.75563e-08, ||r||/||r_0|| = 1.6476e-06
+LBFGS iteration 104 : ||r|| = 7.01442e-08, ||r||/||r_0|| = 1.31994e-06
+LBFGS iteration 105 : ||r|| = 1.1338e-07, ||r||/||r_0|| = 2.13354e-06
+LBFGS iteration 106 : ||r|| = 1.25183e-07, ||r||/||r_0|| = 2.35563e-06
+LBFGS iteration 107 : ||r|| = 4.71349e-07, ||r||/||r_0|| = 8.86964e-06
+LBFGS iteration 108 : ||r|| = 9.63201e-08, ||r||/||r_0|| = 1.81251e-06
+LBFGS iteration 109 : ||r|| = 6.51618e-08, ||r||/||r_0|| = 1.22619e-06
+LBFGS iteration 110 : ||r|| = 9.2279e-08, ||r||/||r_0|| = 1.73646e-06
+LBFGS iteration 111 : ||r|| = 9.22611e-08, ||r||/||r_0|| = 1.73613e-06
+LBFGS iteration 112 : ||r|| = 4.46008e-07, ||r||/||r_0|| = 8.39279e-06
+LBFGS iteration 113 : ||r|| = 3.27318e-08, ||r||/||r_0|| = 6.15933e-07
+LBFGS/Newton+GMRES converged in 113 iterations with a residual norm of 3.27318e-08.
+solver took 28.314s.
+|| q_h - q_ex || / || q_ex || = 1.34145e-05
+|| t_h - t_ex || / || t_ex || = 1.10603e-06

examples/regress_test/p2_o2_hb_upwind_nl_newton.txt

@@ -0,0 +1,47 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --no-discontinuous
+   --upwinded
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00883478s.
+***********************************************************
+dim(V) = 1860
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3420
+***********************************************************
+Assembly took 0.0110992s.
+Preconditioner took 1.1893e-05s.
+Newton iteration  0 : ||r|| = 0.0531419
+Newton iteration  1 : ||r|| = 2.68122e-08, ||r||/||r_0|| = 5.0454e-07
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 2.68122e-08.
+solver took 0.822133s.
+|| q_h - q_ex || / || q_ex || = 1.34064e-05
+|| t_h - t_ex || / || t_ex || = 1.07239e-06

examples/regress_test/p2_o3.txt

@@ -0,0 +1,616 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --bc-neumann
+   --no-reduction
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 3280
+dim(W) = 1600
+dim(V+W) = 4880
+***********************************************************
+Assembly took 0.263944s.
+Preconditioner took 0.0134081s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.0844182
+   Pass :  1   Iteration :   1  ||B r|| = 0.0842305
+   Pass :  1   Iteration :   2  ||B r|| = 0.0533204
+   Pass :  1   Iteration :   3  ||B r|| = 0.0531529
+   Pass :  1   Iteration :   4  ||B r|| = 0.0324337
+   Pass :  1   Iteration :   5  ||B r|| = 0.0323915
+   Pass :  1   Iteration :   6  ||B r|| = 0.0260935
+   Pass :  1   Iteration :   7  ||B r|| = 0.0259252
+   Pass :  1   Iteration :   8  ||B r|| = 0.0245196
+   Pass :  1   Iteration :   9  ||B r|| = 0.0237252
+   Pass :  1   Iteration :  10  ||B r|| = 0.0232376
+   Pass :  1   Iteration :  11  ||B r|| = 0.0213144
+   Pass :  1   Iteration :  12  ||B r|| = 0.0205782
+   Pass :  1   Iteration :  13  ||B r|| = 0.018296
+   Pass :  1   Iteration :  14  ||B r|| = 0.0176434
+   Pass :  1   Iteration :  15  ||B r|| = 0.0154692
+   Pass :  1   Iteration :  16  ||B r|| = 0.0152422
+   Pass :  1   Iteration :  17  ||B r|| = 0.0143615
+   Pass :  1   Iteration :  18  ||B r|| = 0.0142898
+   Pass :  1   Iteration :  19  ||B r|| = 0.0133708
+   Pass :  1   Iteration :  20  ||B r|| = 0.0132149
+   Pass :  1   Iteration :  21  ||B r|| = 0.0127582
+   Pass :  1   Iteration :  22  ||B r|| = 0.0119787
+   Pass :  1   Iteration :  23  ||B r|| = 0.0117468
+   Pass :  1   Iteration :  24  ||B r|| = 0.0107266
+   Pass :  1   Iteration :  25  ||B r|| = 0.0106606
+   Pass :  1   Iteration :  26  ||B r|| = 0.00972712
+   Pass :  1   Iteration :  27  ||B r|| = 0.00971982
+   Pass :  1   Iteration :  28  ||B r|| = 0.00893487
+   Pass :  1   Iteration :  29  ||B r|| = 0.00886412
+   Pass :  1   Iteration :  30  ||B r|| = 0.00836113
+   Pass :  1   Iteration :  31  ||B r|| = 0.00781054
+   Pass :  1   Iteration :  32  ||B r|| = 0.00766531
+   Pass :  1   Iteration :  33  ||B r|| = 0.00703097
+   Pass :  1   Iteration :  34  ||B r|| = 0.00700576
+   Pass :  1   Iteration :  35  ||B r|| = 0.00626115
+   Pass :  1   Iteration :  36  ||B r|| = 0.00625433
+   Pass :  1   Iteration :  37  ||B r|| = 0.00569501
+   Pass :  1   Iteration :  38  ||B r|| = 0.00558192
+   Pass :  1   Iteration :  39  ||B r|| = 0.0052889
+   Pass :  1   Iteration :  40  ||B r|| = 0.00503018
+   Pass :  1   Iteration :  41  ||B r|| = 0.00498759
+   Pass :  1   Iteration :  42  ||B r|| = 0.00473463
+   Pass :  1   Iteration :  43  ||B r|| = 0.00473439
+   Pass :  1   Iteration :  44  ||B r|| = 0.00445589
+   Pass :  1   Iteration :  45  ||B r|| = 0.00442247
+   Pass :  1   Iteration :  46  ||B r|| = 0.00418493
+   Pass :  1   Iteration :  47  ||B r|| = 0.0040762
+   Pass :  1   Iteration :  48  ||B r|| = 0.00400314
+   Pass :  1   Iteration :  49  ||B r|| = 0.00386496
+   Pass :  1   Iteration :  50  ||B r|| = 0.00384145
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 0.00383715
+   Pass :  2   Iteration :  52  ||B r|| = 0.00380579
+   Pass :  2   Iteration :  53  ||B r|| = 0.00377932
+   Pass :  2   Iteration :  54  ||B r|| = 0.0037667
+   Pass :  2   Iteration :  55  ||B r|| = 0.00371225
+   Pass :  2   Iteration :  56  ||B r|| = 0.00370811
+   Pass :  2   Iteration :  57  ||B r|| = 0.00360243
+   Pass :  2   Iteration :  58  ||B r|| = 0.00360237
+   Pass :  2   Iteration :  59  ||B r|| = 0.00348464
+   Pass :  2   Iteration :  60  ||B r|| = 0.00346445
+   Pass :  2   Iteration :  61  ||B r|| = 0.00340369
+   Pass :  2   Iteration :  62  ||B r|| = 0.00335407
+   Pass :  2   Iteration :  63  ||B r|| = 0.00332572
+   Pass :  2   Iteration :  64  ||B r|| = 0.00323357
+   Pass :  2   Iteration :  65  ||B r|| = 0.00323277
+   Pass :  2   Iteration :  66  ||B r|| = 0.00316161
+   Pass :  2   Iteration :  67  ||B r|| = 0.0031608
+   Pass :  2   Iteration :  68  ||B r|| = 0.00310695
+   Pass :  2   Iteration :  69  ||B r|| = 0.00307802
+   Pass :  2   Iteration :  70  ||B r|| = 0.00303149
+   Pass :  2   Iteration :  71  ||B r|| = 0.00297838
+   Pass :  2   Iteration :  72  ||B r|| = 0.00296109
+   Pass :  2   Iteration :  73  ||B r|| = 0.00290145
+   Pass :  2   Iteration :  74  ||B r|| = 0.00290141
+   Pass :  2   Iteration :  75  ||B r|| = 0.00285951
+   Pass :  2   Iteration :  76  ||B r|| = 0.00285754
+   Pass :  2   Iteration :  77  ||B r|| = 0.00278492
+   Pass :  2   Iteration :  78  ||B r|| = 0.00275713
+   Pass :  2   Iteration :  79  ||B r|| = 0.0027127
+   Pass :  2   Iteration :  80  ||B r|| = 0.00264911
+   Pass :  2   Iteration :  81  ||B r|| = 0.0026474
+   Pass :  2   Iteration :  82  ||B r|| = 0.00259002
+   Pass :  2   Iteration :  83  ||B r|| = 0.0025898
+   Pass :  2   Iteration :  84  ||B r|| = 0.00253224
+   Pass :  2   Iteration :  85  ||B r|| = 0.00252698
+   Pass :  2   Iteration :  86  ||B r|| = 0.00248454
+   Pass :  2   Iteration :  87  ||B r|| = 0.0024636
+   Pass :  2   Iteration :  88  ||B r|| = 0.00244664
+   Pass :  2   Iteration :  89  ||B r|| = 0.00238551
+   Pass :  2   Iteration :  90  ||B r|| = 0.00238414
+   Pass :  2   Iteration :  91  ||B r|| = 0.00229093
+   Pass :  2   Iteration :  92  ||B r|| = 0.00228532
+   Pass :  2   Iteration :  93  ||B r|| = 0.00219052
+   Pass :  2   Iteration :  94  ||B r|| = 0.00216507
+   Pass :  2   Iteration :  95  ||B r|| = 0.00210571
+   Pass :  2   Iteration :  96  ||B r|| = 0.00203385
+   Pass :  2   Iteration :  97  ||B r|| = 0.00202392
+   Pass :  2   Iteration :  98  ||B r|| = 0.0018361
+   Pass :  2   Iteration :  99  ||B r|| = 0.00183569
+   Pass :  2   Iteration : 100  ||B r|| = 0.00166983
+Restarting...
+   Pass :  3   Iteration : 101  ||B r|| = 0.00166417
+   Pass :  3   Iteration : 102  ||B r|| = 0.00163733
+   Pass :  3   Iteration : 103  ||B r|| = 0.00162139
+   Pass :  3   Iteration : 104  ||B r|| = 0.00160726
+   Pass :  3   Iteration : 105  ||B r|| = 0.00155064
+   Pass :  3   Iteration : 106  ||B r|| = 0.00154641
+   Pass :  3   Iteration : 107  ||B r|| = 0.00149055
+   Pass :  3   Iteration : 108  ||B r|| = 0.00149034
+   Pass :  3   Iteration : 109  ||B r|| = 0.0014152
+   Pass :  3   Iteration : 110  ||B r|| = 0.00141274
+   Pass :  3   Iteration : 111  ||B r|| = 0.00136809
+   Pass :  3   Iteration : 112  ||B r|| = 0.00134905
+   Pass :  3   Iteration : 113  ||B r|| = 0.00133432
+   Pass :  3   Iteration : 114  ||B r|| = 0.00126373
+   Pass :  3   Iteration : 115  ||B r|| = 0.00126345
+   Pass :  3   Iteration : 116  ||B r|| = 0.00119501
+   Pass :  3   Iteration : 117  ||B r|| = 0.00119232
+   Pass :  3   Iteration : 118  ||B r|| = 0.0011302
+   Pass :  3   Iteration : 119  ||B r|| = 0.00110278
+   Pass :  3   Iteration : 120  ||B r|| = 0.00107176
+   Pass :  3   Iteration : 121  ||B r|| = 0.00101958
+   Pass :  3   Iteration : 122  ||B r|| = 0.00101623
+   Pass :  3   Iteration : 123  ||B r|| = 0.000958328
+   Pass :  3   Iteration : 124  ||B r|| = 0.000957895
+   Pass :  3   Iteration : 125  ||B r|| = 0.000928497
+   Pass :  3   Iteration : 126  ||B r|| = 0.000919787
+   Pass :  3   Iteration : 127  ||B r|| = 0.000884568
+   Pass :  3   Iteration : 128  ||B r|| = 0.00085613
+   Pass :  3   Iteration : 129  ||B r|| = 0.000842104
+   Pass :  3   Iteration : 130  ||B r|| = 0.000794869
+   Pass :  3   Iteration : 131  ||B r|| = 0.000794073
+   Pass :  3   Iteration : 132  ||B r|| = 0.000749975
+   Pass :  3   Iteration : 133  ||B r|| = 0.000745168
+   Pass :  3   Iteration : 134  ||B r|| = 0.00071719
+   Pass :  3   Iteration : 135  ||B r|| = 0.000701547
+   Pass :  3   Iteration : 136  ||B r|| = 0.000691544
+   Pass :  3   Iteration : 137  ||B r|| = 0.000672063
+   Pass :  3   Iteration : 138  ||B r|| = 0.000664616
+   Pass :  3   Iteration : 139  ||B r|| = 0.000638266
+   Pass :  3   Iteration : 140  ||B r|| = 0.000638265
+   Pass :  3   Iteration : 141  ||B r|| = 0.000614645
+   Pass :  3   Iteration : 142  ||B r|| = 0.000610156
+   Pass :  3   Iteration : 143  ||B r|| = 0.000587965
+   Pass :  3   Iteration : 144  ||B r|| = 0.000570909
+   Pass :  3   Iteration : 145  ||B r|| = 0.00055819
+   Pass :  3   Iteration : 146  ||B r|| = 0.00053149
+   Pass :  3   Iteration : 147  ||B r|| = 0.000530662
+   Pass :  3   Iteration : 148  ||B r|| = 0.00050453
+   Pass :  3   Iteration : 149  ||B r|| = 0.000503216
+   Pass :  3   Iteration : 150  ||B r|| = 0.000483403
+Restarting...
+   Pass :  4   Iteration : 151  ||B r|| = 0.000476643
+   Pass :  4   Iteration : 152  ||B r|| = 0.000471618
+   Pass :  4   Iteration : 153  ||B r|| = 0.00046308
+   Pass :  4   Iteration : 154  ||B r|| = 0.000460615
+   Pass :  4   Iteration : 155  ||B r|| = 0.000448007
+   Pass :  4   Iteration : 156  ||B r|| = 0.000447942
+   Pass :  4   Iteration : 157  ||B r|| = 0.000436652
+   Pass :  4   Iteration : 158  ||B r|| = 0.000435443
+   Pass :  4   Iteration : 159  ||B r|| = 0.000426768
+   Pass :  4   Iteration : 160  ||B r|| = 0.000423684
+   Pass :  4   Iteration : 161  ||B r|| = 0.000420009
+   Pass :  4   Iteration : 162  ||B r|| = 0.000413497
+   Pass :  4   Iteration : 163  ||B r|| = 0.000412876
+   Pass :  4   Iteration : 164  ||B r|| = 0.000406041
+   Pass :  4   Iteration : 165  ||B r|| = 0.000406036
+   Pass :  4   Iteration : 166  ||B r|| = 0.000397412
+   Pass :  4   Iteration : 167  ||B r|| = 0.000396406
+   Pass :  4   Iteration : 168  ||B r|| = 0.000388399
+   Pass :  4   Iteration : 169  ||B r|| = 0.000384226
+   Pass :  4   Iteration : 170  ||B r|| = 0.000380544
+   Pass :  4   Iteration : 171  ||B r|| = 0.000374423
+   Pass :  4   Iteration : 172  ||B r|| = 0.000374101
+   Pass :  4   Iteration : 173  ||B r|| = 0.000363142
+   Pass :  4   Iteration : 174  ||B r|| = 0.000363022
+   Pass :  4   Iteration : 175  ||B r|| = 0.000352963
+   Pass :  4   Iteration : 176  ||B r|| = 0.000351495
+   Pass :  4   Iteration : 177  ||B r|| = 0.000344573
+   Pass :  4   Iteration : 178  ||B r|| = 0.000339375
+   Pass :  4   Iteration : 179  ||B r|| = 0.000337602
+   Pass :  4   Iteration : 180  ||B r|| = 0.000329586
+   Pass :  4   Iteration : 181  ||B r|| = 0.000329479
+   Pass :  4   Iteration : 182  ||B r|| = 0.000321449
+   Pass :  4   Iteration : 183  ||B r|| = 0.000321348
+   Pass :  4   Iteration : 184  ||B r|| = 0.00031658
+   Pass :  4   Iteration : 185  ||B r|| = 0.0003147
+   Pass :  4   Iteration : 186  ||B r|| = 0.000312155
+   Pass :  4   Iteration : 187  ||B r|| = 0.000305774
+   Pass :  4   Iteration : 188  ||B r|| = 0.000304569
+   Pass :  4   Iteration : 189  ||B r|| = 0.000295303
+   Pass :  4   Iteration : 190  ||B r|| = 0.000295221
+   Pass :  4   Iteration : 191  ||B r|| = 0.000288295
+   Pass :  4   Iteration : 192  ||B r|| = 0.000288053
+   Pass :  4   Iteration : 193  ||B r|| = 0.000281204
+   Pass :  4   Iteration : 194  ||B r|| = 0.000275367
+   Pass :  4   Iteration : 195  ||B r|| = 0.000272409
+   Pass :  4   Iteration : 196  ||B r|| = 0.000262233
+   Pass :  4   Iteration : 197  ||B r|| = 0.000261862
+   Pass :  4   Iteration : 198  ||B r|| = 0.00024455
+   Pass :  4   Iteration : 199  ||B r|| = 0.000243359
+   Pass :  4   Iteration : 200  ||B r|| = 0.000220587
+Restarting...
+   Pass :  5   Iteration : 201  ||B r|| = 0.000215055
+   Pass :  5   Iteration : 202  ||B r|| = 0.000210167
+   Pass :  5   Iteration : 203  ||B r|| = 0.000205479
+   Pass :  5   Iteration : 204  ||B r|| = 0.000204352
+   Pass :  5   Iteration : 205  ||B r|| = 0.000192827
+   Pass :  5   Iteration : 206  ||B r|| = 0.000192823
+   Pass :  5   Iteration : 207  ||B r|| = 0.000185339
+   Pass :  5   Iteration : 208  ||B r|| = 0.000184762
+   Pass :  5   Iteration : 209  ||B r|| = 0.000178785
+   Pass :  5   Iteration : 210  ||B r|| = 0.000176437
+   Pass :  5   Iteration : 211  ||B r|| = 0.000174204
+   Pass :  5   Iteration : 212  ||B r|| = 0.000171542
+   Pass :  5   Iteration : 213  ||B r|| = 0.000170855
+   Pass :  5   Iteration : 214  ||B r|| = 0.000166245
+   Pass :  5   Iteration : 215  ||B r|| = 0.000166177
+   Pass :  5   Iteration : 216  ||B r|| = 0.000162244
+   Pass :  5   Iteration : 217  ||B r|| = 0.000161452
+   Pass :  5   Iteration : 218  ||B r|| = 0.000158479
+   Pass :  5   Iteration : 219  ||B r|| = 0.000156711
+   Pass :  5   Iteration : 220  ||B r|| = 0.000155696
+   Pass :  5   Iteration : 221  ||B r|| = 0.000152222
+   Pass :  5   Iteration : 222  ||B r|| = 0.000152164
+   Pass :  5   Iteration : 223  ||B r|| = 0.000147163
+   Pass :  5   Iteration : 224  ||B r|| = 0.000146819
+   Pass :  5   Iteration : 225  ||B r|| = 0.000141823
+   Pass :  5   Iteration : 226  ||B r|| = 0.000140915
+   Pass :  5   Iteration : 227  ||B r|| = 0.000137546
+   Pass :  5   Iteration : 228  ||B r|| = 0.000133512
+   Pass :  5   Iteration : 229  ||B r|| = 0.000132627
+   Pass :  5   Iteration : 230  ||B r|| = 0.000123285
+   Pass :  5   Iteration : 231  ||B r|| = 0.00012326
+   Pass :  5   Iteration : 232  ||B r|| = 0.000113477
+   Pass :  5   Iteration : 233  ||B r|| = 0.000111836
+   Pass :  5   Iteration : 234  ||B r|| = 0.000104852
+   Pass :  5   Iteration : 235  ||B r|| = 0.000101777
+   Pass :  5   Iteration : 236  ||B r|| = 9.86043e-05
+   Pass :  5   Iteration : 237  ||B r|| = 9.11604e-05
+   Pass :  5   Iteration : 238  ||B r|| = 9.0706e-05
+   Pass :  5   Iteration : 239  ||B r|| = 8.39772e-05
+   Pass :  5   Iteration : 240  ||B r|| = 8.39371e-05
+   Pass :  5   Iteration : 241  ||B r|| = 7.93621e-05
+   Pass :  5   Iteration : 242  ||B r|| = 7.82914e-05
+   Pass :  5   Iteration : 243  ||B r|| = 7.6767e-05
+   Pass :  5   Iteration : 244  ||B r|| = 7.2773e-05
+   Pass :  5   Iteration : 245  ||B r|| = 7.23065e-05
+   Pass :  5   Iteration : 246  ||B r|| = 6.91859e-05
+   Pass :  5   Iteration : 247  ||B r|| = 6.90643e-05
+   Pass :  5   Iteration : 248  ||B r|| = 6.73012e-05
+   Pass :  5   Iteration : 249  ||B r|| = 6.71644e-05
+   Pass :  5   Iteration : 250  ||B r|| = 6.63627e-05
+Restarting...
+   Pass :  6   Iteration : 251  ||B r|| = 6.60942e-05
+   Pass :  6   Iteration : 252  ||B r|| = 6.5902e-05
+   Pass :  6   Iteration : 253  ||B r|| = 6.54677e-05
+   Pass :  6   Iteration : 254  ||B r|| = 6.54037e-05
+   Pass :  6   Iteration : 255  ||B r|| = 6.31372e-05
+   Pass :  6   Iteration : 256  ||B r|| = 6.3135e-05
+   Pass :  6   Iteration : 257  ||B r|| = 6.03388e-05
+   Pass :  6   Iteration : 258  ||B r|| = 6.02857e-05
+   Pass :  6   Iteration : 259  ||B r|| = 5.83777e-05
+   Pass :  6   Iteration : 260  ||B r|| = 5.76222e-05
+   Pass :  6   Iteration : 261  ||B r|| = 5.70643e-05
+   Pass :  6   Iteration : 262  ||B r|| = 5.52441e-05
+   Pass :  6   Iteration : 263  ||B r|| = 5.5242e-05
+   Pass :  6   Iteration : 264  ||B r|| = 5.26947e-05
+   Pass :  6   Iteration : 265  ||B r|| = 5.26368e-05
+   Pass :  6   Iteration : 266  ||B r|| = 5.05162e-05
+   Pass :  6   Iteration : 267  ||B r|| = 5.01833e-05
+   Pass :  6   Iteration : 268  ||B r|| = 4.90171e-05
+   Pass :  6   Iteration : 269  ||B r|| = 4.80451e-05
+   Pass :  6   Iteration : 270  ||B r|| = 4.76909e-05
+   Pass :  6   Iteration : 271  ||B r|| = 4.66619e-05
+   Pass :  6   Iteration : 272  ||B r|| = 4.66516e-05
+   Pass :  6   Iteration : 273  ||B r|| = 4.55529e-05
+   Pass :  6   Iteration : 274  ||B r|| = 4.54068e-05
+   Pass :  6   Iteration : 275  ||B r|| = 4.4786e-05
+   Pass :  6   Iteration : 276  ||B r|| = 4.45548e-05
+   Pass :  6   Iteration : 277  ||B r|| = 4.39772e-05
+   Pass :  6   Iteration : 278  ||B r|| = 4.3368e-05
+   Pass :  6   Iteration : 279  ||B r|| = 4.32371e-05
+   Pass :  6   Iteration : 280  ||B r|| = 4.23026e-05
+   Pass :  6   Iteration : 281  ||B r|| = 4.23026e-05
+   Pass :  6   Iteration : 282  ||B r|| = 4.16125e-05
+   Pass :  6   Iteration : 283  ||B r|| = 4.15376e-05
+   Pass :  6   Iteration : 284  ||B r|| = 4.10651e-05
+   Pass :  6   Iteration : 285  ||B r|| = 4.07684e-05
+   Pass :  6   Iteration : 286  ||B r|| = 4.04538e-05
+   Pass :  6   Iteration : 287  ||B r|| = 3.95094e-05
+   Pass :  6   Iteration : 288  ||B r|| = 3.92725e-05
+   Pass :  6   Iteration : 289  ||B r|| = 3.73664e-05
+   Pass :  6   Iteration : 290  ||B r|| = 3.73257e-05
+   Pass :  6   Iteration : 291  ||B r|| = 3.61662e-05
+   Pass :  6   Iteration : 292  ||B r|| = 3.58784e-05
+   Pass :  6   Iteration : 293  ||B r|| = 3.51734e-05
+   Pass :  6   Iteration : 294  ||B r|| = 3.37926e-05
+   Pass :  6   Iteration : 295  ||B r|| = 3.3571e-05
+   Pass :  6   Iteration : 296  ||B r|| = 3.13308e-05
+   Pass :  6   Iteration : 297  ||B r|| = 3.13052e-05
+   Pass :  6   Iteration : 298  ||B r|| = 2.933e-05
+   Pass :  6   Iteration : 299  ||B r|| = 2.9112e-05
+   Pass :  6   Iteration : 300  ||B r|| = 2.78565e-05
+Restarting...
+   Pass :  7   Iteration : 301  ||B r|| = 2.72805e-05
+   Pass :  7   Iteration : 302  ||B r|| = 2.70277e-05
+   Pass :  7   Iteration : 303  ||B r|| = 2.64484e-05
+   Pass :  7   Iteration : 304  ||B r|| = 2.63787e-05
+   Pass :  7   Iteration : 305  ||B r|| = 2.49464e-05
+   Pass :  7   Iteration : 306  ||B r|| = 2.49354e-05
+   Pass :  7   Iteration : 307  ||B r|| = 2.39863e-05
+   Pass :  7   Iteration : 308  ||B r|| = 2.38534e-05
+   Pass :  7   Iteration : 309  ||B r|| = 2.33362e-05
+   Pass :  7   Iteration : 310  ||B r|| = 2.30982e-05
+   Pass :  7   Iteration : 311  ||B r|| = 2.2803e-05
+   Pass :  7   Iteration : 312  ||B r|| = 2.22017e-05
+   Pass :  7   Iteration : 313  ||B r|| = 2.21739e-05
+   Pass :  7   Iteration : 314  ||B r|| = 2.1407e-05
+   Pass :  7   Iteration : 315  ||B r|| = 2.13736e-05
+   Pass :  7   Iteration : 316  ||B r|| = 2.08449e-05
+   Pass :  7   Iteration : 317  ||B r|| = 2.06651e-05
+   Pass :  7   Iteration : 318  ||B r|| = 2.03473e-05
+   Pass :  7   Iteration : 319  ||B r|| = 1.98233e-05
+   Pass :  7   Iteration : 320  ||B r|| = 1.96948e-05
+   Pass :  7   Iteration : 321  ||B r|| = 1.91517e-05
+   Pass :  7   Iteration : 322  ||B r|| = 1.91489e-05
+   Pass :  7   Iteration : 323  ||B r|| = 1.86665e-05
+   Pass :  7   Iteration : 324  ||B r|| = 1.85811e-05
+   Pass :  7   Iteration : 325  ||B r|| = 1.82714e-05
+   Pass :  7   Iteration : 326  ||B r|| = 1.7984e-05
+   Pass :  7   Iteration : 327  ||B r|| = 1.76133e-05
+   Pass :  7   Iteration : 328  ||B r|| = 1.70134e-05
+   Pass :  7   Iteration : 329  ||B r|| = 1.69463e-05
+   Pass :  7   Iteration : 330  ||B r|| = 1.61796e-05
+   Pass :  7   Iteration : 331  ||B r|| = 1.61415e-05
+   Pass :  7   Iteration : 332  ||B r|| = 1.54878e-05
+   Pass :  7   Iteration : 333  ||B r|| = 1.52269e-05
+   Pass :  7   Iteration : 334  ||B r|| = 1.46318e-05
+   Pass :  7   Iteration : 335  ||B r|| = 1.40688e-05
+   Pass :  7   Iteration : 336  ||B r|| = 1.40075e-05
+   Pass :  7   Iteration : 337  ||B r|| = 1.33118e-05
+   Pass :  7   Iteration : 338  ||B r|| = 1.33078e-05
+   Pass :  7   Iteration : 339  ||B r|| = 1.23243e-05
+   Pass :  7   Iteration : 340  ||B r|| = 1.22778e-05
+   Pass :  7   Iteration : 341  ||B r|| = 1.16655e-05
+   Pass :  7   Iteration : 342  ||B r|| = 1.13044e-05
+   Pass :  7   Iteration : 343  ||B r|| = 1.11466e-05
+   Pass :  7   Iteration : 344  ||B r|| = 1.06378e-05
+   Pass :  7   Iteration : 345  ||B r|| = 1.06374e-05
+   Pass :  7   Iteration : 346  ||B r|| = 1.01476e-05
+   Pass :  7   Iteration : 347  ||B r|| = 1.01457e-05
+   Pass :  7   Iteration : 348  ||B r|| = 9.69915e-06
+   Pass :  7   Iteration : 349  ||B r|| = 9.58818e-06
+   Pass :  7   Iteration : 350  ||B r|| = 9.33007e-06
+Restarting...
+   Pass :  8   Iteration : 351  ||B r|| = 9.16479e-06
+   Pass :  8   Iteration : 352  ||B r|| = 9.05331e-06
+   Pass :  8   Iteration : 353  ||B r|| = 8.90353e-06
+   Pass :  8   Iteration : 354  ||B r|| = 8.89643e-06
+   Pass :  8   Iteration : 355  ||B r|| = 8.63156e-06
+   Pass :  8   Iteration : 356  ||B r|| = 8.62891e-06
+   Pass :  8   Iteration : 357  ||B r|| = 8.31281e-06
+   Pass :  8   Iteration : 358  ||B r|| = 8.30355e-06
+   Pass :  8   Iteration : 359  ||B r|| = 8.0262e-06
+   Pass :  8   Iteration : 360  ||B r|| = 7.89407e-06
+   Pass :  8   Iteration : 361  ||B r|| = 7.78142e-06
+   Pass :  8   Iteration : 362  ||B r|| = 7.53245e-06
+   Pass :  8   Iteration : 363  ||B r|| = 7.51263e-06
+   Pass :  8   Iteration : 364  ||B r|| = 7.24701e-06
+   Pass :  8   Iteration : 365  ||B r|| = 7.24701e-06
+   Pass :  8   Iteration : 366  ||B r|| = 7.06231e-06
+   Pass :  8   Iteration : 367  ||B r|| = 7.02217e-06
+   Pass :  8   Iteration : 368  ||B r|| = 6.86567e-06
+   Pass :  8   Iteration : 369  ||B r|| = 6.70886e-06
+   Pass :  8   Iteration : 370  ||B r|| = 6.63225e-06
+   Pass :  8   Iteration : 371  ||B r|| = 6.4821e-06
+   Pass :  8   Iteration : 372  ||B r|| = 6.47326e-06
+   Pass :  8   Iteration : 373  ||B r|| = 6.33708e-06
+   Pass :  8   Iteration : 374  ||B r|| = 6.32908e-06
+   Pass :  8   Iteration : 375  ||B r|| = 6.19364e-06
+   Pass :  8   Iteration : 376  ||B r|| = 6.13467e-06
+   Pass :  8   Iteration : 377  ||B r|| = 6.05166e-06
+   Pass :  8   Iteration : 378  ||B r|| = 5.97679e-06
+   Pass :  8   Iteration : 379  ||B r|| = 5.95107e-06
+   Pass :  8   Iteration : 380  ||B r|| = 5.85331e-06
+   Pass :  8   Iteration : 381  ||B r|| = 5.84951e-06
+   Pass :  8   Iteration : 382  ||B r|| = 5.71072e-06
+   Pass :  8   Iteration : 383  ||B r|| = 5.69996e-06
+   Pass :  8   Iteration : 384  ||B r|| = 5.61664e-06
+   Pass :  8   Iteration : 385  ||B r|| = 5.58648e-06
+   Pass :  8   Iteration : 386  ||B r|| = 5.52623e-06
+   Pass :  8   Iteration : 387  ||B r|| = 5.41361e-06
+   Pass :  8   Iteration : 388  ||B r|| = 5.38858e-06
+   Pass :  8   Iteration : 389  ||B r|| = 5.21196e-06
+   Pass :  8   Iteration : 390  ||B r|| = 5.21195e-06
+   Pass :  8   Iteration : 391  ||B r|| = 5.03336e-06
+   Pass :  8   Iteration : 392  ||B r|| = 5.01762e-06
+   Pass :  8   Iteration : 393  ||B r|| = 4.90845e-06
+   Pass :  8   Iteration : 394  ||B r|| = 4.85466e-06
+   Pass :  8   Iteration : 395  ||B r|| = 4.82806e-06
+   Pass :  8   Iteration : 396  ||B r|| = 4.70546e-06
+   Pass :  8   Iteration : 397  ||B r|| = 4.70546e-06
+   Pass :  8   Iteration : 398  ||B r|| = 4.545e-06
+   Pass :  8   Iteration : 399  ||B r|| = 4.54136e-06
+   Pass :  8   Iteration : 400  ||B r|| = 4.40414e-06
+Restarting...
+   Pass :  9   Iteration : 401  ||B r|| = 4.37679e-06
+   Pass :  9   Iteration : 402  ||B r|| = 4.34594e-06
+   Pass :  9   Iteration : 403  ||B r|| = 4.33673e-06
+   Pass :  9   Iteration : 404  ||B r|| = 4.32443e-06
+   Pass :  9   Iteration : 405  ||B r|| = 4.22433e-06
+   Pass :  9   Iteration : 406  ||B r|| = 4.22314e-06
+   Pass :  9   Iteration : 407  ||B r|| = 4.1339e-06
+   Pass :  9   Iteration : 408  ||B r|| = 4.12994e-06
+   Pass :  9   Iteration : 409  ||B r|| = 4.03922e-06
+   Pass :  9   Iteration : 410  ||B r|| = 4.01121e-06
+   Pass :  9   Iteration : 411  ||B r|| = 3.91269e-06
+   Pass :  9   Iteration : 412  ||B r|| = 3.85701e-06
+   Pass :  9   Iteration : 413  ||B r|| = 3.81149e-06
+   Pass :  9   Iteration : 414  ||B r|| = 3.60161e-06
+   Pass :  9   Iteration : 415  ||B r|| = 3.60144e-06
+   Pass :  9   Iteration : 416  ||B r|| = 3.39942e-06
+   Pass :  9   Iteration : 417  ||B r|| = 3.37848e-06
+   Pass :  9   Iteration : 418  ||B r|| = 3.27887e-06
+   Pass :  9   Iteration : 419  ||B r|| = 3.17104e-06
+   Pass :  9   Iteration : 420  ||B r|| = 3.09884e-06
+   Pass :  9   Iteration : 421  ||B r|| = 2.91515e-06
+   Pass :  9   Iteration : 422  ||B r|| = 2.90328e-06
+   Pass :  9   Iteration : 423  ||B r|| = 2.77068e-06
+   Pass :  9   Iteration : 424  ||B r|| = 2.76986e-06
+   Pass :  9   Iteration : 425  ||B r|| = 2.6824e-06
+   Pass :  9   Iteration : 426  ||B r|| = 2.63485e-06
+   Pass :  9   Iteration : 427  ||B r|| = 2.54435e-06
+   Pass :  9   Iteration : 428  ||B r|| = 2.36545e-06
+   Pass :  9   Iteration : 429  ||B r|| = 2.34325e-06
+   Pass :  9   Iteration : 430  ||B r|| = 2.16004e-06
+   Pass :  9   Iteration : 431  ||B r|| = 2.15991e-06
+   Pass :  9   Iteration : 432  ||B r|| = 2.00829e-06
+   Pass :  9   Iteration : 433  ||B r|| = 1.98535e-06
+   Pass :  9   Iteration : 434  ||B r|| = 1.8959e-06
+   Pass :  9   Iteration : 435  ||B r|| = 1.84825e-06
+   Pass :  9   Iteration : 436  ||B r|| = 1.83809e-06
+   Pass :  9   Iteration : 437  ||B r|| = 1.79022e-06
+   Pass :  9   Iteration : 438  ||B r|| = 1.78981e-06
+   Pass :  9   Iteration : 439  ||B r|| = 1.69592e-06
+   Pass :  9   Iteration : 440  ||B r|| = 1.69427e-06
+   Pass :  9   Iteration : 441  ||B r|| = 1.61203e-06
+   Pass :  9   Iteration : 442  ||B r|| = 1.59067e-06
+   Pass :  9   Iteration : 443  ||B r|| = 1.55255e-06
+   Pass :  9   Iteration : 444  ||B r|| = 1.49392e-06
+   Pass :  9   Iteration : 445  ||B r|| = 1.48801e-06
+   Pass :  9   Iteration : 446  ||B r|| = 1.43473e-06
+   Pass :  9   Iteration : 447  ||B r|| = 1.4344e-06
+   Pass :  9   Iteration : 448  ||B r|| = 1.38034e-06
+   Pass :  9   Iteration : 449  ||B r|| = 1.37268e-06
+   Pass :  9   Iteration : 450  ||B r|| = 1.33253e-06
+Restarting...
+   Pass : 10   Iteration : 451  ||B r|| = 1.31521e-06
+   Pass : 10   Iteration : 452  ||B r|| = 1.30574e-06
+   Pass : 10   Iteration : 453  ||B r|| = 1.28918e-06
+   Pass : 10   Iteration : 454  ||B r|| = 1.28862e-06
+   Pass : 10   Iteration : 455  ||B r|| = 1.24724e-06
+   Pass : 10   Iteration : 456  ||B r|| = 1.24671e-06
+   Pass : 10   Iteration : 457  ||B r|| = 1.192e-06
+   Pass : 10   Iteration : 458  ||B r|| = 1.18501e-06
+   Pass : 10   Iteration : 459  ||B r|| = 1.15574e-06
+   Pass : 10   Iteration : 460  ||B r|| = 1.12882e-06
+   Pass : 10   Iteration : 461  ||B r|| = 1.12016e-06
+   Pass : 10   Iteration : 462  ||B r|| = 1.08175e-06
+   Pass : 10   Iteration : 463  ||B r|| = 1.08152e-06
+   Pass : 10   Iteration : 464  ||B r|| = 1.05011e-06
+   Pass : 10   Iteration : 465  ||B r|| = 1.04988e-06
+   Pass : 10   Iteration : 466  ||B r|| = 1.02256e-06
+   Pass : 10   Iteration : 467  ||B r|| = 1.00931e-06
+   Pass : 10   Iteration : 468  ||B r|| = 9.87153e-07
+   Pass : 10   Iteration : 469  ||B r|| = 9.51278e-07
+   Pass : 10   Iteration : 470  ||B r|| = 9.44694e-07
+   Pass : 10   Iteration : 471  ||B r|| = 9.18819e-07
+   Pass : 10   Iteration : 472  ||B r|| = 9.18622e-07
+   Pass : 10   Iteration : 473  ||B r|| = 8.93134e-07
+   Pass : 10   Iteration : 474  ||B r|| = 8.89538e-07
+   Pass : 10   Iteration : 475  ||B r|| = 8.73009e-07
+   Pass : 10   Iteration : 476  ||B r|| = 8.63978e-07
+   Pass : 10   Iteration : 477  ||B r|| = 8.54964e-07
+   Pass : 10   Iteration : 478  ||B r|| = 8.40809e-07
+   Pass : 10   Iteration : 479  ||B r|| = 8.39934e-07
+   Pass : 10   Iteration : 480  ||B r|| = 8.21395e-07
+   Pass : 10   Iteration : 481  ||B r|| = 8.2122e-07
+   Pass : 10   Iteration : 482  ||B r|| = 8.05765e-07
+   Pass : 10   Iteration : 483  ||B r|| = 8.04286e-07
+   Pass : 10   Iteration : 484  ||B r|| = 7.94989e-07
+   Pass : 10   Iteration : 485  ||B r|| = 7.87883e-07
+   Pass : 10   Iteration : 486  ||B r|| = 7.80396e-07
+   Pass : 10   Iteration : 487  ||B r|| = 7.61696e-07
+   Pass : 10   Iteration : 488  ||B r|| = 7.60555e-07
+   Pass : 10   Iteration : 489  ||B r|| = 7.44629e-07
+   Pass : 10   Iteration : 490  ||B r|| = 7.43477e-07
+   Pass : 10   Iteration : 491  ||B r|| = 7.32156e-07
+   Pass : 10   Iteration : 492  ||B r|| = 7.2938e-07
+   Pass : 10   Iteration : 493  ||B r|| = 7.22035e-07
+   Pass : 10   Iteration : 494  ||B r|| = 7.18017e-07
+   Pass : 10   Iteration : 495  ||B r|| = 7.13819e-07
+   Pass : 10   Iteration : 496  ||B r|| = 7.01737e-07
+   Pass : 10   Iteration : 497  ||B r|| = 7.01592e-07
+   Pass : 10   Iteration : 498  ||B r|| = 6.79622e-07
+   Pass : 10   Iteration : 499  ||B r|| = 6.77598e-07
+   Pass : 10   Iteration : 500  ||B r|| = 6.44877e-07
+Restarting...
+   Pass : 11   Iteration : 501  ||B r|| = 6.34635e-07
+   Pass : 11   Iteration : 502  ||B r|| = 6.29397e-07
+   Pass : 11   Iteration : 503  ||B r|| = 6.24697e-07
+   Pass : 11   Iteration : 504  ||B r|| = 6.23519e-07
+   Pass : 11   Iteration : 505  ||B r|| = 6.0908e-07
+   Pass : 11   Iteration : 506  ||B r|| = 6.08996e-07
+   Pass : 11   Iteration : 507  ||B r|| = 5.93527e-07
+   Pass : 11   Iteration : 508  ||B r|| = 5.91799e-07
+   Pass : 11   Iteration : 509  ||B r|| = 5.79602e-07
+   Pass : 11   Iteration : 510  ||B r|| = 5.75784e-07
+   Pass : 11   Iteration : 511  ||B r|| = 5.67023e-07
+   Pass : 11   Iteration : 512  ||B r|| = 5.61611e-07
+   Pass : 11   Iteration : 513  ||B r|| = 5.59179e-07
+   Pass : 11   Iteration : 514  ||B r|| = 5.39416e-07
+   Pass : 11   Iteration : 515  ||B r|| = 5.39228e-07
+   Pass : 11   Iteration : 516  ||B r|| = 5.19868e-07
+   Pass : 11   Iteration : 517  ||B r|| = 5.16938e-07
+   Pass : 11   Iteration : 518  ||B r|| = 5.05106e-07
+   Pass : 11   Iteration : 519  ||B r|| = 4.92772e-07
+   Pass : 11   Iteration : 520  ||B r|| = 4.88959e-07
+   Pass : 11   Iteration : 521  ||B r|| = 4.70329e-07
+   Pass : 11   Iteration : 522  ||B r|| = 4.69329e-07
+   Pass : 11   Iteration : 523  ||B r|| = 4.52224e-07
+   Pass : 11   Iteration : 524  ||B r|| = 4.5215e-07
+   Pass : 11   Iteration : 525  ||B r|| = 4.44092e-07
+   Pass : 11   Iteration : 526  ||B r|| = 4.40834e-07
+   Pass : 11   Iteration : 527  ||B r|| = 4.347e-07
+   Pass : 11   Iteration : 528  ||B r|| = 4.10834e-07
+   Pass : 11   Iteration : 529  ||B r|| = 4.06446e-07
+   Pass : 11   Iteration : 530  ||B r|| = 3.70791e-07
+   Pass : 11   Iteration : 531  ||B r|| = 3.70315e-07
+   Pass : 11   Iteration : 532  ||B r|| = 3.33439e-07
+   Pass : 11   Iteration : 533  ||B r|| = 3.3085e-07
+   Pass : 11   Iteration : 534  ||B r|| = 3.012e-07
+   Pass : 11   Iteration : 535  ||B r|| = 2.89199e-07
+   Pass : 11   Iteration : 536  ||B r|| = 2.76302e-07
+   Pass : 11   Iteration : 537  ||B r|| = 2.47572e-07
+   Pass : 11   Iteration : 538  ||B r|| = 2.47005e-07
+   Pass : 11   Iteration : 539  ||B r|| = 2.11675e-07
+   Pass : 11   Iteration : 540  ||B r|| = 2.11671e-07
+   Pass : 11   Iteration : 541  ||B r|| = 1.82151e-07
+   Pass : 11   Iteration : 542  ||B r|| = 1.74382e-07
+   Pass : 11   Iteration : 543  ||B r|| = 1.59613e-07
+   Pass : 11   Iteration : 544  ||B r|| = 1.37637e-07
+   Pass : 11   Iteration : 545  ||B r|| = 1.36472e-07
+   Pass : 11   Iteration : 546  ||B r|| = 1.21096e-07
+   Pass : 11   Iteration : 547  ||B r|| = 1.20443e-07
+   Pass : 11   Iteration : 548  ||B r|| = 1.13717e-07
+   Pass : 11   Iteration : 549  ||B r|| = 1.10979e-07
+   Pass : 11   Iteration : 550  ||B r|| = 1.09953e-07
+Restarting...
+   Pass : 12   Iteration : 551  ||B r|| = 1.09413e-07
+   Pass : 12   Iteration : 552  ||B r|| = 1.07947e-07
+   Pass : 12   Iteration : 553  ||B r|| = 1.07059e-07
+   Pass : 12   Iteration : 554  ||B r|| = 1.06217e-07
+   Pass : 12   Iteration : 555  ||B r|| = 1.00482e-07
+   Pass : 12   Iteration : 556  ||B r|| = 1.00444e-07
+   Pass : 12   Iteration : 557  ||B r|| = 9.22737e-08
+   Pass : 12   Iteration : 558  ||B r|| = 9.15215e-08
+   Pass : 12   Iteration : 559  ||B r|| = 8.64067e-08
+   Pass : 12   Iteration : 560  ||B r|| = 8.37169e-08
+GMRES+GS converged in 560 iterations with a residual norm of 8.37169e-08.
+solver took 1.5342s.
+|| q_h - q_ex || / || q_ex || = 5.37471e-06
+|| t_h - t_ex || / || t_ex || = 1.0601e-05

examples/regress_test/p2_o3_dg_hb.txt

@@ -0,0 +1,128 @@
+Options used:
+   --mesh 
+   --ncells-x 20
+   --ncells-y 20
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --bc-neumann
+   --no-reduction
+   --hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.092797s.
+***********************************************************
+dim(V) = 12800
+dim(W) = 6400
+dim(M) = 3360
+dim(V+W+M) = 22560
+***********************************************************
+Assembly took 0.372998s.
+Preconditioner took 2.066e-05s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.065472
+   Pass :  1   Iteration :   1  ||B r|| = 0.0388334
+   Pass :  1   Iteration :   2  ||B r|| = 0.0278044
+   Pass :  1   Iteration :   3  ||B r|| = 0.0252541
+   Pass :  1   Iteration :   4  ||B r|| = 0.0195668
+   Pass :  1   Iteration :   5  ||B r|| = 0.0175214
+   Pass :  1   Iteration :   6  ||B r|| = 0.0146266
+   Pass :  1   Iteration :   7  ||B r|| = 0.012881
+   Pass :  1   Iteration :   8  ||B r|| = 0.0113395
+   Pass :  1   Iteration :   9  ||B r|| = 0.00979484
+   Pass :  1   Iteration :  10  ||B r|| = 0.00880061
+   Pass :  1   Iteration :  11  ||B r|| = 0.00765474
+   Pass :  1   Iteration :  12  ||B r|| = 0.00679673
+   Pass :  1   Iteration :  13  ||B r|| = 0.00588253
+   Pass :  1   Iteration :  14  ||B r|| = 0.00541201
+   Pass :  1   Iteration :  15  ||B r|| = 0.00497197
+   Pass :  1   Iteration :  16  ||B r|| = 0.00473461
+   Pass :  1   Iteration :  17  ||B r|| = 0.00441647
+   Pass :  1   Iteration :  18  ||B r|| = 0.00422194
+   Pass :  1   Iteration :  19  ||B r|| = 0.00396753
+   Pass :  1   Iteration :  20  ||B r|| = 0.00379228
+   Pass :  1   Iteration :  21  ||B r|| = 0.00362897
+   Pass :  1   Iteration :  22  ||B r|| = 0.00347745
+   Pass :  1   Iteration :  23  ||B r|| = 0.00334087
+   Pass :  1   Iteration :  24  ||B r|| = 0.00322572
+   Pass :  1   Iteration :  25  ||B r|| = 0.00305259
+   Pass :  1   Iteration :  26  ||B r|| = 0.00291791
+   Pass :  1   Iteration :  27  ||B r|| = 0.0026548
+   Pass :  1   Iteration :  28  ||B r|| = 0.00232244
+   Pass :  1   Iteration :  29  ||B r|| = 0.00198347
+   Pass :  1   Iteration :  30  ||B r|| = 0.00167889
+   Pass :  1   Iteration :  31  ||B r|| = 0.00146962
+   Pass :  1   Iteration :  32  ||B r|| = 0.00126512
+   Pass :  1   Iteration :  33  ||B r|| = 0.00104252
+   Pass :  1   Iteration :  34  ||B r|| = 0.00079785
+   Pass :  1   Iteration :  35  ||B r|| = 0.000642696
+   Pass :  1   Iteration :  36  ||B r|| = 0.000532919
+   Pass :  1   Iteration :  37  ||B r|| = 0.000424416
+   Pass :  1   Iteration :  38  ||B r|| = 0.000315977
+   Pass :  1   Iteration :  39  ||B r|| = 0.000257506
+   Pass :  1   Iteration :  40  ||B r|| = 0.000199244
+   Pass :  1   Iteration :  41  ||B r|| = 0.000149785
+   Pass :  1   Iteration :  42  ||B r|| = 0.000113281
+   Pass :  1   Iteration :  43  ||B r|| = 9.13302e-05
+   Pass :  1   Iteration :  44  ||B r|| = 7.1626e-05
+   Pass :  1   Iteration :  45  ||B r|| = 5.58872e-05
+   Pass :  1   Iteration :  46  ||B r|| = 4.20535e-05
+   Pass :  1   Iteration :  47  ||B r|| = 2.94167e-05
+   Pass :  1   Iteration :  48  ||B r|| = 2.09059e-05
+   Pass :  1   Iteration :  49  ||B r|| = 1.34115e-05
+   Pass :  1   Iteration :  50  ||B r|| = 9.06216e-06
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 6.99008e-06
+   Pass :  2   Iteration :  52  ||B r|| = 4.88885e-06
+   Pass :  2   Iteration :  53  ||B r|| = 3.32648e-06
+   Pass :  2   Iteration :  54  ||B r|| = 2.32036e-06
+   Pass :  2   Iteration :  55  ||B r|| = 1.79629e-06
+   Pass :  2   Iteration :  56  ||B r|| = 1.46896e-06
+   Pass :  2   Iteration :  57  ||B r|| = 1.28666e-06
+   Pass :  2   Iteration :  58  ||B r|| = 1.1565e-06
+   Pass :  2   Iteration :  59  ||B r|| = 1.00838e-06
+   Pass :  2   Iteration :  60  ||B r|| = 8.79667e-07
+   Pass :  2   Iteration :  61  ||B r|| = 7.77748e-07
+   Pass :  2   Iteration :  62  ||B r|| = 6.93451e-07
+   Pass :  2   Iteration :  63  ||B r|| = 6.06337e-07
+   Pass :  2   Iteration :  64  ||B r|| = 5.33214e-07
+   Pass :  2   Iteration :  65  ||B r|| = 4.52657e-07
+   Pass :  2   Iteration :  66  ||B r|| = 3.8744e-07
+   Pass :  2   Iteration :  67  ||B r|| = 3.13515e-07
+   Pass :  2   Iteration :  68  ||B r|| = 2.34746e-07
+   Pass :  2   Iteration :  69  ||B r|| = 1.76843e-07
+   Pass :  2   Iteration :  70  ||B r|| = 1.45838e-07
+   Pass :  2   Iteration :  71  ||B r|| = 1.22815e-07
+   Pass :  2   Iteration :  72  ||B r|| = 1.05045e-07
+   Pass :  2   Iteration :  73  ||B r|| = 9.24836e-08
+   Pass :  2   Iteration :  74  ||B r|| = 8.3753e-08
+   Pass :  2   Iteration :  75  ||B r|| = 7.97572e-08
+   Pass :  2   Iteration :  76  ||B r|| = 7.5414e-08
+   Pass :  2   Iteration :  77  ||B r|| = 7.20257e-08
+   Pass :  2   Iteration :  78  ||B r|| = 6.91908e-08
+   Pass :  2   Iteration :  79  ||B r|| = 6.60233e-08
+   Pass :  2   Iteration :  80  ||B r|| = 6.29475e-08
+GMRES+GS converged in 80 iterations with a residual norm of 6.29475e-08.
+solver took 0.102291s.
+|| q_h - q_ex || / || q_ex || = 3.97124e-06
+|| t_h - t_ex || / || t_ex || = 7.98566e-06

examples/regress_test/p2_o3_dg_hb_upwind.txt

@@ -0,0 +1,132 @@
+Options used:
+   --mesh 
+   --ncells-x 20
+   --ncells-y 20
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --upwinded
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --bc-neumann
+   --no-reduction
+   --hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0947786s.
+***********************************************************
+dim(V) = 12800
+dim(W) = 6400
+dim(M) = 3360
+dim(V+W+M) = 22560
+***********************************************************
+Assembly took 0.339125s.
+Preconditioner took 2.0675e-05s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.0664635
+   Pass :  1   Iteration :   1  ||B r|| = 0.0392329
+   Pass :  1   Iteration :   2  ||B r|| = 0.0284105
+   Pass :  1   Iteration :   3  ||B r|| = 0.025287
+   Pass :  1   Iteration :   4  ||B r|| = 0.0202116
+   Pass :  1   Iteration :   5  ||B r|| = 0.0178666
+   Pass :  1   Iteration :   6  ||B r|| = 0.0147873
+   Pass :  1   Iteration :   7  ||B r|| = 0.0133048
+   Pass :  1   Iteration :   8  ||B r|| = 0.0114991
+   Pass :  1   Iteration :   9  ||B r|| = 0.0103667
+   Pass :  1   Iteration :  10  ||B r|| = 0.00888925
+   Pass :  1   Iteration :  11  ||B r|| = 0.00784177
+   Pass :  1   Iteration :  12  ||B r|| = 0.00697125
+   Pass :  1   Iteration :  13  ||B r|| = 0.00605669
+   Pass :  1   Iteration :  14  ||B r|| = 0.00550247
+   Pass :  1   Iteration :  15  ||B r|| = 0.00499171
+   Pass :  1   Iteration :  16  ||B r|| = 0.00469248
+   Pass :  1   Iteration :  17  ||B r|| = 0.00453217
+   Pass :  1   Iteration :  18  ||B r|| = 0.00414885
+   Pass :  1   Iteration :  19  ||B r|| = 0.00401257
+   Pass :  1   Iteration :  20  ||B r|| = 0.00376803
+   Pass :  1   Iteration :  21  ||B r|| = 0.00363359
+   Pass :  1   Iteration :  22  ||B r|| = 0.00349689
+   Pass :  1   Iteration :  23  ||B r|| = 0.00333516
+   Pass :  1   Iteration :  24  ||B r|| = 0.00322644
+   Pass :  1   Iteration :  25  ||B r|| = 0.00305558
+   Pass :  1   Iteration :  26  ||B r|| = 0.00291691
+   Pass :  1   Iteration :  27  ||B r|| = 0.00265397
+   Pass :  1   Iteration :  28  ||B r|| = 0.00233725
+   Pass :  1   Iteration :  29  ||B r|| = 0.00200603
+   Pass :  1   Iteration :  30  ||B r|| = 0.00167881
+   Pass :  1   Iteration :  31  ||B r|| = 0.00148243
+   Pass :  1   Iteration :  32  ||B r|| = 0.00127395
+   Pass :  1   Iteration :  33  ||B r|| = 0.00104107
+   Pass :  1   Iteration :  34  ||B r|| = 0.000805446
+   Pass :  1   Iteration :  35  ||B r|| = 0.000643581
+   Pass :  1   Iteration :  36  ||B r|| = 0.000533587
+   Pass :  1   Iteration :  37  ||B r|| = 0.0004242
+   Pass :  1   Iteration :  38  ||B r|| = 0.000317968
+   Pass :  1   Iteration :  39  ||B r|| = 0.000252724
+   Pass :  1   Iteration :  40  ||B r|| = 0.000198698
+   Pass :  1   Iteration :  41  ||B r|| = 0.000149294
+   Pass :  1   Iteration :  42  ||B r|| = 0.000112958
+   Pass :  1   Iteration :  43  ||B r|| = 8.93232e-05
+   Pass :  1   Iteration :  44  ||B r|| = 7.11356e-05
+   Pass :  1   Iteration :  45  ||B r|| = 5.45739e-05
+   Pass :  1   Iteration :  46  ||B r|| = 4.1102e-05
+   Pass :  1   Iteration :  47  ||B r|| = 2.88729e-05
+   Pass :  1   Iteration :  48  ||B r|| = 1.98745e-05
+   Pass :  1   Iteration :  49  ||B r|| = 1.31309e-05
+   Pass :  1   Iteration :  50  ||B r|| = 8.6678e-06
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 6.74249e-06
+   Pass :  2   Iteration :  52  ||B r|| = 4.76472e-06
+   Pass :  2   Iteration :  53  ||B r|| = 3.25325e-06
+   Pass :  2   Iteration :  54  ||B r|| = 2.37999e-06
+   Pass :  2   Iteration :  55  ||B r|| = 1.8538e-06
+   Pass :  2   Iteration :  56  ||B r|| = 1.59364e-06
+   Pass :  2   Iteration :  57  ||B r|| = 1.416e-06
+   Pass :  2   Iteration :  58  ||B r|| = 1.26381e-06
+   Pass :  2   Iteration :  59  ||B r|| = 1.13104e-06
+   Pass :  2   Iteration :  60  ||B r|| = 9.70321e-07
+   Pass :  2   Iteration :  61  ||B r|| = 8.62444e-07
+   Pass :  2   Iteration :  62  ||B r|| = 7.71204e-07
+   Pass :  2   Iteration :  63  ||B r|| = 6.652e-07
+   Pass :  2   Iteration :  64  ||B r|| = 5.73199e-07
+   Pass :  2   Iteration :  65  ||B r|| = 4.83644e-07
+   Pass :  2   Iteration :  66  ||B r|| = 4.07507e-07
+   Pass :  2   Iteration :  67  ||B r|| = 3.24629e-07
+   Pass :  2   Iteration :  68  ||B r|| = 2.48764e-07
+   Pass :  2   Iteration :  69  ||B r|| = 1.99923e-07
+   Pass :  2   Iteration :  70  ||B r|| = 1.71949e-07
+   Pass :  2   Iteration :  71  ||B r|| = 1.53571e-07
+   Pass :  2   Iteration :  72  ||B r|| = 1.39562e-07
+   Pass :  2   Iteration :  73  ||B r|| = 1.29668e-07
+   Pass :  2   Iteration :  74  ||B r|| = 1.23321e-07
+   Pass :  2   Iteration :  75  ||B r|| = 1.1908e-07
+   Pass :  2   Iteration :  76  ||B r|| = 1.148e-07
+   Pass :  2   Iteration :  77  ||B r|| = 1.10207e-07
+   Pass :  2   Iteration :  78  ||B r|| = 1.0502e-07
+   Pass :  2   Iteration :  79  ||B r|| = 1.00114e-07
+   Pass :  2   Iteration :  80  ||B r|| = 9.29801e-08
+   Pass :  2   Iteration :  81  ||B r|| = 8.45243e-08
+   Pass :  2   Iteration :  82  ||B r|| = 7.69354e-08
+   Pass :  2   Iteration :  83  ||B r|| = 6.81279e-08
+   Pass :  2   Iteration :  84  ||B r|| = 6.18609e-08
+GMRES+GS converged in 84 iterations with a residual norm of 6.18609e-08.
+solver took 0.120313s.
+|| q_h - q_ex || / || q_ex || = 2.91743e-06
+|| t_h - t_ex || / || t_ex || = 5.38605e-06

examples/regress_test/p2_o3_dg_rd.txt

@@ -0,0 +1,87 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --bc-neumann
+   --reduction
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Reduction init took 0.00030305s.
+***********************************************************
+dim(W) = 1600
+***********************************************************
+Assembly took 0.284917s.
+Preconditioner took 2.1488e-05s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.0595543
+   Pass :  1   Iteration :   1  ||B r|| = 0.0295648
+   Pass :  1   Iteration :   2  ||B r|| = 0.02274
+   Pass :  1   Iteration :   3  ||B r|| = 0.020048
+   Pass :  1   Iteration :   4  ||B r|| = 0.0190169
+   Pass :  1   Iteration :   5  ||B r|| = 0.0176422
+   Pass :  1   Iteration :   6  ||B r|| = 0.0156824
+   Pass :  1   Iteration :   7  ||B r|| = 0.0126397
+   Pass :  1   Iteration :   8  ||B r|| = 0.0100698
+   Pass :  1   Iteration :   9  ||B r|| = 0.00663336
+   Pass :  1   Iteration :  10  ||B r|| = 0.00445083
+   Pass :  1   Iteration :  11  ||B r|| = 0.0035815
+   Pass :  1   Iteration :  12  ||B r|| = 0.0027893
+   Pass :  1   Iteration :  13  ||B r|| = 0.00231255
+   Pass :  1   Iteration :  14  ||B r|| = 0.00188597
+   Pass :  1   Iteration :  15  ||B r|| = 0.00146022
+   Pass :  1   Iteration :  16  ||B r|| = 0.0011475
+   Pass :  1   Iteration :  17  ||B r|| = 0.000796134
+   Pass :  1   Iteration :  18  ||B r|| = 0.000516799
+   Pass :  1   Iteration :  19  ||B r|| = 0.000358033
+   Pass :  1   Iteration :  20  ||B r|| = 0.000273082
+   Pass :  1   Iteration :  21  ||B r|| = 0.000195488
+   Pass :  1   Iteration :  22  ||B r|| = 0.000136892
+   Pass :  1   Iteration :  23  ||B r|| = 8.75159e-05
+   Pass :  1   Iteration :  24  ||B r|| = 4.68569e-05
+   Pass :  1   Iteration :  25  ||B r|| = 2.62121e-05
+   Pass :  1   Iteration :  26  ||B r|| = 1.54574e-05
+   Pass :  1   Iteration :  27  ||B r|| = 9.32176e-06
+   Pass :  1   Iteration :  28  ||B r|| = 5.78434e-06
+   Pass :  1   Iteration :  29  ||B r|| = 3.56524e-06
+   Pass :  1   Iteration :  30  ||B r|| = 2.56435e-06
+   Pass :  1   Iteration :  31  ||B r|| = 1.99563e-06
+   Pass :  1   Iteration :  32  ||B r|| = 1.44708e-06
+   Pass :  1   Iteration :  33  ||B r|| = 1.02745e-06
+   Pass :  1   Iteration :  34  ||B r|| = 7.53507e-07
+   Pass :  1   Iteration :  35  ||B r|| = 5.24316e-07
+   Pass :  1   Iteration :  36  ||B r|| = 3.38631e-07
+   Pass :  1   Iteration :  37  ||B r|| = 2.19631e-07
+   Pass :  1   Iteration :  38  ||B r|| = 1.5732e-07
+   Pass :  1   Iteration :  39  ||B r|| = 1.24975e-07
+   Pass :  1   Iteration :  40  ||B r|| = 9.90772e-08
+   Pass :  1   Iteration :  41  ||B r|| = 7.9514e-08
+   Pass :  1   Iteration :  42  ||B r|| = 6.12828e-08
+   Pass :  1   Iteration :  43  ||B r|| = 4.81615e-08
+GMRES+GS converged in 43 iterations with a residual norm of 4.81615e-08.
+solver took 0.039268s.
+|| q_h - q_ex || / || q_ex || = 1.17008e-05
+|| t_h - t_ex || / || t_ex || = 4.06055e-06

examples/regress_test/p2_o3_dg_rd_umfpack.txt

@@ -0,0 +1,45 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --bc-neumann
+   --reduction
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Reduction init took 0.000224403s.
+***********************************************************
+dim(W) = 1600
+***********************************************************
+Assembly took 0.229536s.
+Preconditioner took 0.0132696s.
+   Pass :  1   Iteration :   0  ||B r|| = 2.10385
+   Pass :  1   Iteration :   1  ||B r|| = 4.68916e-15
+GMRES+UMFPack converged in 1 iterations with a residual norm of 4.68916e-15.
+solver took 0.00531221s.
+|| q_h - q_ex || / || q_ex || = 1.16263e-05
+|| t_h - t_ex || / || t_ex || = 4.01918e-06

examples/regress_test/p2_o3_dg_upwind_rd.txt

@@ -0,0 +1,117 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --upwinded
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --bc-neumann
+   --reduction
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Reduction init took 0.000255944s.
+***********************************************************
+dim(W) = 1600
+***********************************************************
+Assembly took 0.18697s.
+Preconditioner took 3.3748e-05s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.0163145
+   Pass :  1   Iteration :   1  ||B r|| = 0.0115162
+   Pass :  1   Iteration :   2  ||B r|| = 0.011444
+   Pass :  1   Iteration :   3  ||B r|| = 0.0110753
+   Pass :  1   Iteration :   4  ||B r|| = 0.00920566
+   Pass :  1   Iteration :   5  ||B r|| = 0.00798584
+   Pass :  1   Iteration :   6  ||B r|| = 0.0076343
+   Pass :  1   Iteration :   7  ||B r|| = 0.00634399
+   Pass :  1   Iteration :   8  ||B r|| = 0.00546584
+   Pass :  1   Iteration :   9  ||B r|| = 0.00477185
+   Pass :  1   Iteration :  10  ||B r|| = 0.00392019
+   Pass :  1   Iteration :  11  ||B r|| = 0.00306299
+   Pass :  1   Iteration :  12  ||B r|| = 0.00251514
+   Pass :  1   Iteration :  13  ||B r|| = 0.00185507
+   Pass :  1   Iteration :  14  ||B r|| = 0.00128691
+   Pass :  1   Iteration :  15  ||B r|| = 0.000894552
+   Pass :  1   Iteration :  16  ||B r|| = 0.00060419
+   Pass :  1   Iteration :  17  ||B r|| = 0.000448256
+   Pass :  1   Iteration :  18  ||B r|| = 0.000363642
+   Pass :  1   Iteration :  19  ||B r|| = 0.000331316
+   Pass :  1   Iteration :  20  ||B r|| = 0.000300179
+   Pass :  1   Iteration :  21  ||B r|| = 0.000251711
+   Pass :  1   Iteration :  22  ||B r|| = 0.000208637
+   Pass :  1   Iteration :  23  ||B r|| = 0.000171813
+   Pass :  1   Iteration :  24  ||B r|| = 0.000137592
+   Pass :  1   Iteration :  25  ||B r|| = 0.000118575
+   Pass :  1   Iteration :  26  ||B r|| = 0.000101079
+   Pass :  1   Iteration :  27  ||B r|| = 7.50298e-05
+   Pass :  1   Iteration :  28  ||B r|| = 5.65782e-05
+   Pass :  1   Iteration :  29  ||B r|| = 4.52079e-05
+   Pass :  1   Iteration :  30  ||B r|| = 3.85472e-05
+   Pass :  1   Iteration :  31  ||B r|| = 3.40993e-05
+   Pass :  1   Iteration :  32  ||B r|| = 3.11535e-05
+   Pass :  1   Iteration :  33  ||B r|| = 2.79471e-05
+   Pass :  1   Iteration :  34  ||B r|| = 2.30983e-05
+   Pass :  1   Iteration :  35  ||B r|| = 1.89589e-05
+   Pass :  1   Iteration :  36  ||B r|| = 1.51807e-05
+   Pass :  1   Iteration :  37  ||B r|| = 1.21585e-05
+   Pass :  1   Iteration :  38  ||B r|| = 1.00168e-05
+   Pass :  1   Iteration :  39  ||B r|| = 8.25159e-06
+   Pass :  1   Iteration :  40  ||B r|| = 6.72897e-06
+   Pass :  1   Iteration :  41  ||B r|| = 5.40202e-06
+   Pass :  1   Iteration :  42  ||B r|| = 3.96943e-06
+   Pass :  1   Iteration :  43  ||B r|| = 2.86564e-06
+   Pass :  1   Iteration :  44  ||B r|| = 2.23434e-06
+   Pass :  1   Iteration :  45  ||B r|| = 1.77712e-06
+   Pass :  1   Iteration :  46  ||B r|| = 1.44875e-06
+   Pass :  1   Iteration :  47  ||B r|| = 1.18606e-06
+   Pass :  1   Iteration :  48  ||B r|| = 1.00443e-06
+   Pass :  1   Iteration :  49  ||B r|| = 8.29641e-07
+   Pass :  1   Iteration :  50  ||B r|| = 6.84113e-07
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 6.19789e-07
+   Pass :  2   Iteration :  52  ||B r|| = 5.63716e-07
+   Pass :  2   Iteration :  53  ||B r|| = 4.96542e-07
+   Pass :  2   Iteration :  54  ||B r|| = 4.25511e-07
+   Pass :  2   Iteration :  55  ||B r|| = 3.72932e-07
+   Pass :  2   Iteration :  56  ||B r|| = 3.10999e-07
+   Pass :  2   Iteration :  57  ||B r|| = 2.57558e-07
+   Pass :  2   Iteration :  58  ||B r|| = 2.14783e-07
+   Pass :  2   Iteration :  59  ||B r|| = 1.77656e-07
+   Pass :  2   Iteration :  60  ||B r|| = 1.47442e-07
+   Pass :  2   Iteration :  61  ||B r|| = 1.22601e-07
+   Pass :  2   Iteration :  62  ||B r|| = 1.05055e-07
+   Pass :  2   Iteration :  63  ||B r|| = 9.00512e-08
+   Pass :  2   Iteration :  64  ||B r|| = 7.16741e-08
+   Pass :  2   Iteration :  65  ||B r|| = 6.05675e-08
+   Pass :  2   Iteration :  66  ||B r|| = 5.17163e-08
+   Pass :  2   Iteration :  67  ||B r|| = 4.18108e-08
+   Pass :  2   Iteration :  68  ||B r|| = 3.36946e-08
+   Pass :  2   Iteration :  69  ||B r|| = 2.87918e-08
+   Pass :  2   Iteration :  70  ||B r|| = 2.46221e-08
+   Pass :  2   Iteration :  71  ||B r|| = 1.95865e-08
+   Pass :  2   Iteration :  72  ||B r|| = 1.54337e-08
+GMRES+GS converged in 72 iterations with a residual norm of 1.54337e-08.
+solver took 0.0483163s.
+|| q_h - q_ex || / || q_ex || = 5.8937e-07
+|| t_h - t_ex || / || t_ex || = 6.87392e-07

examples/regress_test/p2_o3_dg_upwind_rd_umfpack.txt

@@ -0,0 +1,45 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --upwinded
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --bc-neumann
+   --reduction
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Reduction init took 0.000656228s.
+***********************************************************
+dim(W) = 1600
+***********************************************************
+Assembly took 0.186881s.
+Preconditioner took 0.00652136s.
+   Pass :  1   Iteration :   0  ||B r|| = 2.10384
+   Pass :  1   Iteration :   1  ||B r|| = 1.07425e-14
+GMRES+UMFPack converged in 1 iterations with a residual norm of 1.07425e-14.
+solver took 0.00410399s.
+|| q_h - q_ex || / || q_ex || = 4.87198e-07
+|| t_h - t_ex || / || t_ex || = 6.65782e-07

examples/regress_test/p2_o3_hb.txt

@@ -0,0 +1,79 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --bc-neumann
+   --no-reduction
+   --hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0260873s.
+***********************************************************
+dim(V) = 3280
+dim(W) = 1600
+dim(M) = 880
+dim(V+W+M) = 5760
+***********************************************************
+Assembly took 0.231276s.
+Preconditioner took 1.9305e-05s.
+   Pass :  1   Iteration :   0  ||B r|| = 3.39849
+   Pass :  1   Iteration :   1  ||B r|| = 0.0497973
+   Pass :  1   Iteration :   2  ||B r|| = 0.0290039
+   Pass :  1   Iteration :   3  ||B r|| = 0.0215547
+   Pass :  1   Iteration :   4  ||B r|| = 0.0171677
+   Pass :  1   Iteration :   5  ||B r|| = 0.0134762
+   Pass :  1   Iteration :   6  ||B r|| = 0.0113621
+   Pass :  1   Iteration :   7  ||B r|| = 0.00935178
+   Pass :  1   Iteration :   8  ||B r|| = 0.00774471
+   Pass :  1   Iteration :   9  ||B r|| = 0.00734466
+   Pass :  1   Iteration :  10  ||B r|| = 0.00673245
+   Pass :  1   Iteration :  11  ||B r|| = 0.00636417
+   Pass :  1   Iteration :  12  ||B r|| = 0.00579576
+   Pass :  1   Iteration :  13  ||B r|| = 0.00529263
+   Pass :  1   Iteration :  14  ||B r|| = 0.0042932
+   Pass :  1   Iteration :  15  ||B r|| = 0.00355719
+   Pass :  1   Iteration :  16  ||B r|| = 0.00256598
+   Pass :  1   Iteration :  17  ||B r|| = 0.00139006
+   Pass :  1   Iteration :  18  ||B r|| = 0.000903464
+   Pass :  1   Iteration :  19  ||B r|| = 0.000641531
+   Pass :  1   Iteration :  20  ||B r|| = 0.000483224
+   Pass :  1   Iteration :  21  ||B r|| = 0.000263395
+   Pass :  1   Iteration :  22  ||B r|| = 0.00016559
+   Pass :  1   Iteration :  23  ||B r|| = 9.61118e-05
+   Pass :  1   Iteration :  24  ||B r|| = 6.49821e-05
+   Pass :  1   Iteration :  25  ||B r|| = 3.71899e-05
+   Pass :  1   Iteration :  26  ||B r|| = 2.0518e-05
+   Pass :  1   Iteration :  27  ||B r|| = 1.48709e-05
+   Pass :  1   Iteration :  28  ||B r|| = 9.71717e-06
+   Pass :  1   Iteration :  29  ||B r|| = 6.96074e-06
+   Pass :  1   Iteration :  30  ||B r|| = 5.71704e-06
+   Pass :  1   Iteration :  31  ||B r|| = 4.95969e-06
+   Pass :  1   Iteration :  32  ||B r|| = 3.175e-06
+GMRES+GS converged in 32 iterations with a residual norm of 3.175e-06.
+solver took 0.00956355s.
+|| q_h - q_ex || / || q_ex || = 0.00102764
+|| t_h - t_ex || / || t_ex || = 0.00146825

examples/regress_test/p2_o3_nl.txt

@@ -0,0 +1,245 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --hdg_scheme 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 3280
+dim(W) = 1600
+dim(V+W) = 4880
+***********************************************************
+Assembly took 0.186438s.
+Preconditioner took 0.054954s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.022067
+   Pass :  1   Iteration :   1  ||B r|| = 0.022067
+   Pass :  1   Iteration :   2  ||B r|| = 0.0208806
+   Pass :  1   Iteration :   3  ||B r|| = 0.0207166
+   Pass :  1   Iteration :   4  ||B r|| = 0.0196263
+   Pass :  1   Iteration :   5  ||B r|| = 0.0193127
+   Pass :  1   Iteration :   6  ||B r|| = 0.0193121
+   Pass :  1   Iteration :   7  ||B r|| = 0.0191814
+   Pass :  1   Iteration :   8  ||B r|| = 0.0190947
+   Pass :  1   Iteration :   9  ||B r|| = 0.0181552
+   Pass :  1   Iteration :  10  ||B r|| = 0.0180903
+   Pass :  1   Iteration :  11  ||B r|| = 0.0155652
+   Pass :  1   Iteration :  12  ||B r|| = 0.0155258
+   Pass :  1   Iteration :  13  ||B r|| = 0.014398
+   Pass :  1   Iteration :  14  ||B r|| = 0.0143695
+   Pass :  1   Iteration :  15  ||B r|| = 0.0135542
+   Pass :  1   Iteration :  16  ||B r|| = 0.0135172
+   Pass :  1   Iteration :  17  ||B r|| = 0.013078
+   Pass :  1   Iteration :  18  ||B r|| = 0.0124796
+   Pass :  1   Iteration :  19  ||B r|| = 0.0122545
+   Pass :  1   Iteration :  20  ||B r|| = 0.0108222
+   Pass :  1   Iteration :  21  ||B r|| = 0.0108121
+   Pass :  1   Iteration :  22  ||B r|| = 0.00967796
+   Pass :  1   Iteration :  23  ||B r|| = 0.00965621
+   Pass :  1   Iteration :  24  ||B r|| = 0.00858242
+   Pass :  1   Iteration :  25  ||B r|| = 0.0082878
+   Pass :  1   Iteration :  26  ||B r|| = 0.00776935
+   Pass :  1   Iteration :  27  ||B r|| = 0.00707955
+   Pass :  1   Iteration :  28  ||B r|| = 0.00697587
+   Pass :  1   Iteration :  29  ||B r|| = 0.00602293
+   Pass :  1   Iteration :  30  ||B r|| = 0.00601624
+   Pass :  1   Iteration :  31  ||B r|| = 0.00520713
+   Pass :  1   Iteration :  32  ||B r|| = 0.00510208
+   Pass :  1   Iteration :  33  ||B r|| = 0.0043413
+   Pass :  1   Iteration :  34  ||B r|| = 0.0039158
+   Pass :  1   Iteration :  35  ||B r|| = 0.00357861
+   Pass :  1   Iteration :  36  ||B r|| = 0.00291643
+   Pass :  1   Iteration :  37  ||B r|| = 0.0028874
+   Pass :  1   Iteration :  38  ||B r|| = 0.00212203
+   Pass :  1   Iteration :  39  ||B r|| = 0.00209429
+   Pass :  1   Iteration :  40  ||B r|| = 0.00167641
+   Pass :  1   Iteration :  41  ||B r|| = 0.00148563
+   Pass :  1   Iteration :  42  ||B r|| = 0.00132712
+   Pass :  1   Iteration :  43  ||B r|| = 0.000994524
+   Pass :  1   Iteration :  44  ||B r|| = 0.000994216
+   Pass :  1   Iteration :  45  ||B r|| = 0.000816498
+   Pass :  1   Iteration :  46  ||B r|| = 0.000799419
+   Pass :  1   Iteration :  47  ||B r|| = 0.000732239
+   Pass :  1   Iteration :  48  ||B r|| = 0.000702926
+   Pass :  1   Iteration :  49  ||B r|| = 0.000674539
+   Pass :  1   Iteration :  50  ||B r|| = 0.000627216
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 0.00062193
+   Pass :  2   Iteration :  52  ||B r|| = 0.0005892
+   Pass :  2   Iteration :  53  ||B r|| = 0.000588011
+   Pass :  2   Iteration :  54  ||B r|| = 0.000561997
+   Pass :  2   Iteration :  55  ||B r|| = 0.000543751
+   Pass :  2   Iteration :  56  ||B r|| = 0.000513188
+   Pass :  2   Iteration :  57  ||B r|| = 0.000478002
+   Pass :  2   Iteration :  58  ||B r|| = 0.000465486
+   Pass :  2   Iteration :  59  ||B r|| = 0.000400445
+   Pass :  2   Iteration :  60  ||B r|| = 0.000400246
+   Pass :  2   Iteration :  61  ||B r|| = 0.000352688
+   Pass :  2   Iteration :  62  ||B r|| = 0.000346668
+   Pass :  2   Iteration :  63  ||B r|| = 0.00031797
+   Pass :  2   Iteration :  64  ||B r|| = 0.000298695
+   Pass :  2   Iteration :  65  ||B r|| = 0.000286142
+   Pass :  2   Iteration :  66  ||B r|| = 0.000252347
+   Pass :  2   Iteration :  67  ||B r|| = 0.000250182
+   Pass :  2   Iteration :  68  ||B r|| = 0.000214181
+   Pass :  2   Iteration :  69  ||B r|| = 0.0002141
+   Pass :  2   Iteration :  70  ||B r|| = 0.000182374
+   Pass :  2   Iteration :  71  ||B r|| = 0.000175328
+   Pass :  2   Iteration :  72  ||B r|| = 0.000156797
+   Pass :  2   Iteration :  73  ||B r|| = 0.000132149
+   Pass :  2   Iteration :  74  ||B r|| = 0.000125112
+   Pass :  2   Iteration :  75  ||B r|| = 9.32759e-05
+   Pass :  2   Iteration :  76  ||B r|| = 9.28174e-05
+   Pass :  2   Iteration :  77  ||B r|| = 7.07716e-05
+   Pass :  2   Iteration :  78  ||B r|| = 6.67241e-05
+   Pass :  2   Iteration :  79  ||B r|| = 5.9584e-05
+   Pass :  2   Iteration :  80  ||B r|| = 5.37448e-05
+   Pass :  2   Iteration :  81  ||B r|| = 5.12479e-05
+   Pass :  2   Iteration :  82  ||B r|| = 4.10174e-05
+   Pass :  2   Iteration :  83  ||B r|| = 4.10131e-05
+   Pass :  2   Iteration :  84  ||B r|| = 3.4515e-05
+   Pass :  2   Iteration :  85  ||B r|| = 3.34606e-05
+   Pass :  2   Iteration :  86  ||B r|| = 3.0915e-05
+   Pass :  2   Iteration :  87  ||B r|| = 2.83458e-05
+   Pass :  2   Iteration :  88  ||B r|| = 2.72626e-05
+   Pass :  2   Iteration :  89  ||B r|| = 2.47577e-05
+   Pass :  2   Iteration :  90  ||B r|| = 2.44277e-05
+   Pass :  2   Iteration :  91  ||B r|| = 2.16201e-05
+   Pass :  2   Iteration :  92  ||B r|| = 2.15866e-05
+   Pass :  2   Iteration :  93  ||B r|| = 1.97523e-05
+   Pass :  2   Iteration :  94  ||B r|| = 1.8927e-05
+   Pass :  2   Iteration :  95  ||B r|| = 1.85086e-05
+   Pass :  2   Iteration :  96  ||B r|| = 1.71252e-05
+   Pass :  2   Iteration :  97  ||B r|| = 1.70655e-05
+   Pass :  2   Iteration :  98  ||B r|| = 1.62333e-05
+   Pass :  2   Iteration :  99  ||B r|| = 1.61703e-05
+   Pass :  2   Iteration : 100  ||B r|| = 1.49155e-05
+Restarting...
+   Pass :  3   Iteration : 101  ||B r|| = 1.48969e-05
+   Pass :  3   Iteration : 102  ||B r|| = 1.46428e-05
+   Pass :  3   Iteration : 103  ||B r|| = 1.46181e-05
+   Pass :  3   Iteration : 104  ||B r|| = 1.46045e-05
+   Pass :  3   Iteration : 105  ||B r|| = 1.39796e-05
+   Pass :  3   Iteration : 106  ||B r|| = 1.39764e-05
+   Pass :  3   Iteration : 107  ||B r|| = 1.32178e-05
+   Pass :  3   Iteration : 108  ||B r|| = 1.32131e-05
+   Pass :  3   Iteration : 109  ||B r|| = 1.25714e-05
+   Pass :  3   Iteration : 110  ||B r|| = 1.25594e-05
+   Pass :  3   Iteration : 111  ||B r|| = 1.21126e-05
+   Pass :  3   Iteration : 112  ||B r|| = 1.18562e-05
+   Pass :  3   Iteration : 113  ||B r|| = 1.17378e-05
+   Pass :  3   Iteration : 114  ||B r|| = 1.0941e-05
+   Pass :  3   Iteration : 115  ||B r|| = 1.09339e-05
+   Pass :  3   Iteration : 116  ||B r|| = 9.54335e-06
+   Pass :  3   Iteration : 117  ||B r|| = 9.51161e-06
+   Pass :  3   Iteration : 118  ||B r|| = 8.35379e-06
+   Pass :  3   Iteration : 119  ||B r|| = 8.04087e-06
+   Pass :  3   Iteration : 120  ||B r|| = 7.51408e-06
+   Pass :  3   Iteration : 121  ||B r|| = 6.80584e-06
+   Pass :  3   Iteration : 122  ||B r|| = 6.75339e-06
+   Pass :  3   Iteration : 123  ||B r|| = 5.66556e-06
+   Pass :  3   Iteration : 124  ||B r|| = 5.65505e-06
+   Pass :  3   Iteration : 125  ||B r|| = 4.72256e-06
+   Pass :  3   Iteration : 126  ||B r|| = 4.4958e-06
+   Pass :  3   Iteration : 127  ||B r|| = 3.98298e-06
+   Pass :  3   Iteration : 128  ||B r|| = 3.60389e-06
+   Pass :  3   Iteration : 129  ||B r|| = 3.48606e-06
+   Pass :  3   Iteration : 130  ||B r|| = 3.02899e-06
+   Pass :  3   Iteration : 131  ||B r|| = 3.02877e-06
+   Pass :  3   Iteration : 132  ||B r|| = 2.61592e-06
+   Pass :  3   Iteration : 133  ||B r|| = 2.58403e-06
+   Pass :  3   Iteration : 134  ||B r|| = 2.35026e-06
+   Pass :  3   Iteration : 135  ||B r|| = 2.2251e-06
+   Pass :  3   Iteration : 136  ||B r|| = 2.08811e-06
+   Pass :  3   Iteration : 137  ||B r|| = 1.80365e-06
+   Pass :  3   Iteration : 138  ||B r|| = 1.77968e-06
+   Pass :  3   Iteration : 139  ||B r|| = 1.47939e-06
+   Pass :  3   Iteration : 140  ||B r|| = 1.47722e-06
+   Pass :  3   Iteration : 141  ||B r|| = 1.25568e-06
+   Pass :  3   Iteration : 142  ||B r|| = 1.20881e-06
+   Pass :  3   Iteration : 143  ||B r|| = 1.14307e-06
+   Pass :  3   Iteration : 144  ||B r|| = 1.04547e-06
+   Pass :  3   Iteration : 145  ||B r|| = 1.02875e-06
+   Pass :  3   Iteration : 146  ||B r|| = 9.14727e-07
+   Pass :  3   Iteration : 147  ||B r|| = 9.14676e-07
+   Pass :  3   Iteration : 148  ||B r|| = 8.15389e-07
+   Pass :  3   Iteration : 149  ||B r|| = 7.99485e-07
+   Pass :  3   Iteration : 150  ||B r|| = 7.26065e-07
+Restarting...
+   Pass :  4   Iteration : 151  ||B r|| = 6.99694e-07
+   Pass :  4   Iteration : 152  ||B r|| = 6.84535e-07
+   Pass :  4   Iteration : 153  ||B r|| = 6.45898e-07
+   Pass :  4   Iteration : 154  ||B r|| = 6.43768e-07
+   Pass :  4   Iteration : 155  ||B r|| = 5.83403e-07
+   Pass :  4   Iteration : 156  ||B r|| = 5.8321e-07
+   Pass :  4   Iteration : 157  ||B r|| = 5.24621e-07
+   Pass :  4   Iteration : 158  ||B r|| = 5.19743e-07
+   Pass :  4   Iteration : 159  ||B r|| = 4.7987e-07
+   Pass :  4   Iteration : 160  ||B r|| = 4.51871e-07
+   Pass :  4   Iteration : 161  ||B r|| = 4.41169e-07
+   Pass :  4   Iteration : 162  ||B r|| = 3.9456e-07
+   Pass :  4   Iteration : 163  ||B r|| = 3.93689e-07
+   Pass :  4   Iteration : 164  ||B r|| = 3.34259e-07
+   Pass :  4   Iteration : 165  ||B r|| = 3.28851e-07
+   Pass :  4   Iteration : 166  ||B r|| = 2.90374e-07
+   Pass :  4   Iteration : 167  ||B r|| = 2.77779e-07
+   Pass :  4   Iteration : 168  ||B r|| = 2.62914e-07
+   Pass :  4   Iteration : 169  ||B r|| = 2.36644e-07
+   Pass :  4   Iteration : 170  ||B r|| = 2.32757e-07
+   Pass :  4   Iteration : 171  ||B r|| = 1.99214e-07
+   Pass :  4   Iteration : 172  ||B r|| = 1.98993e-07
+   Pass :  4   Iteration : 173  ||B r|| = 1.63031e-07
+   Pass :  4   Iteration : 174  ||B r|| = 1.56437e-07
+   Pass :  4   Iteration : 175  ||B r|| = 1.35415e-07
+   Pass :  4   Iteration : 176  ||B r|| = 1.17884e-07
+   Pass :  4   Iteration : 177  ||B r|| = 1.14297e-07
+   Pass :  4   Iteration : 178  ||B r|| = 9.45492e-08
+   Pass :  4   Iteration : 179  ||B r|| = 9.45387e-08
+   Pass :  4   Iteration : 180  ||B r|| = 7.49812e-08
+   Pass :  4   Iteration : 181  ||B r|| = 7.2875e-08
+   Pass :  4   Iteration : 182  ||B r|| = 6.20294e-08
+   Pass :  4   Iteration : 183  ||B r|| = 5.70125e-08
+   Pass :  4   Iteration : 184  ||B r|| = 5.34086e-08
+   Pass :  4   Iteration : 185  ||B r|| = 4.71283e-08
+   Pass :  4   Iteration : 186  ||B r|| = 4.69364e-08
+   Pass :  4   Iteration : 187  ||B r|| = 4.02849e-08
+   Pass :  4   Iteration : 188  ||B r|| = 3.9792e-08
+   Pass :  4   Iteration : 189  ||B r|| = 3.52261e-08
+   Pass :  4   Iteration : 190  ||B r|| = 3.36232e-08
+   Pass :  4   Iteration : 191  ||B r|| = 3.07331e-08
+   Pass :  4   Iteration : 192  ||B r|| = 2.82049e-08
+   Pass :  4   Iteration : 193  ||B r|| = 2.78326e-08
+   Pass :  4   Iteration : 194  ||B r|| = 2.53142e-08
+   Pass :  4   Iteration : 195  ||B r|| = 2.52644e-08
+   Pass :  4   Iteration : 196  ||B r|| = 2.37377e-08
+   Pass :  4   Iteration : 197  ||B r|| = 2.31322e-08
+   Pass :  4   Iteration : 198  ||B r|| = 2.26843e-08
+   Pass :  4   Iteration : 199  ||B r|| = 2.21043e-08
+   Pass :  4   Iteration : 200  ||B r|| = 2.16948e-08
+GMRES+GS converged in 200 iterations with a residual norm of 2.16948e-08.
+solver took 7.5115s.
+|| q_h - q_ex || / || q_ex || = 1.09996e-06
+|| t_h - t_ex || / || t_ex || = 1.10664e-06

examples/regress_test/p2_o3_nl_umfpack.txt

@@ -0,0 +1,53 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --hdg_scheme 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 3280
+dim(W) = 1600
+dim(V+W) = 4880
+***********************************************************
+Assembly took 0.190491s.
+Preconditioner took 0.0722513s.
+   Pass :  1   Iteration :   0  ||B r|| = 1.8759
+   Pass :  1   Iteration :   1  ||B r|| = 1.87404
+   Pass :  1   Iteration :   2  ||B r|| = 0.10605
+   Pass :  1   Iteration :   3  ||B r|| = 0.0890947
+   Pass :  1   Iteration :   4  ||B r|| = 0.00999938
+   Pass :  1   Iteration :   5  ||B r|| = 0.00420422
+   Pass :  1   Iteration :   6  ||B r|| = 0.00113566
+   Pass :  1   Iteration :   7  ||B r|| = 0.00016919
+   Pass :  1   Iteration :   8  ||B r|| = 8.64586e-05
+   Pass :  1   Iteration :   9  ||B r|| = 5.74549e-06
+   Pass :  1   Iteration :  10  ||B r|| = 5.21245e-06
+   Pass :  1   Iteration :  11  ||B r|| = 2.97692e-07
+GMRES+UMFPack converged in 11 iterations with a residual norm of 2.97692e-07.
+solver took 0.438948s.
+|| q_h - q_ex || / || q_ex || = 4.12091e-07
+|| t_h - t_ex || / || t_ex || = 1.10557e-07

examples/regress_test/p2_o3_nlc_hdg1.txt

@@ -0,0 +1,244 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --nonlinear
+   --no-nonlinear-flux
+   --no-nonlinear-pot
+   --nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 3280
+dim(W) = 1600
+dim(V+W) = 4880
+***********************************************************
+Assembly took 0.193226s.
+Preconditioner took 0.232254s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.0220032
+   Pass :  1   Iteration :   1  ||B r|| = 0.0220032
+   Pass :  1   Iteration :   2  ||B r|| = 0.0208317
+   Pass :  1   Iteration :   3  ||B r|| = 0.0206802
+   Pass :  1   Iteration :   4  ||B r|| = 0.0196435
+   Pass :  1   Iteration :   5  ||B r|| = 0.0193751
+   Pass :  1   Iteration :   6  ||B r|| = 0.0193644
+   Pass :  1   Iteration :   7  ||B r|| = 0.0192222
+   Pass :  1   Iteration :   8  ||B r|| = 0.0191298
+   Pass :  1   Iteration :   9  ||B r|| = 0.0184188
+   Pass :  1   Iteration :  10  ||B r|| = 0.0182278
+   Pass :  1   Iteration :  11  ||B r|| = 0.0156396
+   Pass :  1   Iteration :  12  ||B r|| = 0.0155674
+   Pass :  1   Iteration :  13  ||B r|| = 0.0143963
+   Pass :  1   Iteration :  14  ||B r|| = 0.0143443
+   Pass :  1   Iteration :  15  ||B r|| = 0.0135627
+   Pass :  1   Iteration :  16  ||B r|| = 0.0135558
+   Pass :  1   Iteration :  17  ||B r|| = 0.0130116
+   Pass :  1   Iteration :  18  ||B r|| = 0.0125869
+   Pass :  1   Iteration :  19  ||B r|| = 0.0122169
+   Pass :  1   Iteration :  20  ||B r|| = 0.0109293
+   Pass :  1   Iteration :  21  ||B r|| = 0.0109181
+   Pass :  1   Iteration :  22  ||B r|| = 0.0097437
+   Pass :  1   Iteration :  23  ||B r|| = 0.00973885
+   Pass :  1   Iteration :  24  ||B r|| = 0.0085645
+   Pass :  1   Iteration :  25  ||B r|| = 0.00844063
+   Pass :  1   Iteration :  26  ||B r|| = 0.00769784
+   Pass :  1   Iteration :  27  ||B r|| = 0.00724603
+   Pass :  1   Iteration :  28  ||B r|| = 0.00696129
+   Pass :  1   Iteration :  29  ||B r|| = 0.00611181
+   Pass :  1   Iteration :  30  ||B r|| = 0.00609183
+   Pass :  1   Iteration :  31  ||B r|| = 0.00522302
+   Pass :  1   Iteration :  32  ||B r|| = 0.00521279
+   Pass :  1   Iteration :  33  ||B r|| = 0.00431424
+   Pass :  1   Iteration :  34  ||B r|| = 0.00413969
+   Pass :  1   Iteration :  35  ||B r|| = 0.0034955
+   Pass :  1   Iteration :  36  ||B r|| = 0.00304203
+   Pass :  1   Iteration :  37  ||B r|| = 0.00289708
+   Pass :  1   Iteration :  38  ||B r|| = 0.00219349
+   Pass :  1   Iteration :  39  ||B r|| = 0.00219047
+   Pass :  1   Iteration :  40  ||B r|| = 0.00163612
+   Pass :  1   Iteration :  41  ||B r|| = 0.00158611
+   Pass :  1   Iteration :  42  ||B r|| = 0.00126672
+   Pass :  1   Iteration :  43  ||B r|| = 0.00105371
+   Pass :  1   Iteration :  44  ||B r|| = 0.00100063
+   Pass :  1   Iteration :  45  ||B r|| = 0.000802595
+   Pass :  1   Iteration :  46  ||B r|| = 0.000801298
+   Pass :  1   Iteration :  47  ||B r|| = 0.000705846
+   Pass :  1   Iteration :  48  ||B r|| = 0.000696003
+   Pass :  1   Iteration :  49  ||B r|| = 0.000646771
+   Pass :  1   Iteration :  50  ||B r|| = 0.000627259
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 0.000621921
+   Pass :  2   Iteration :  52  ||B r|| = 0.000588136
+   Pass :  2   Iteration :  53  ||B r|| = 0.00058774
+   Pass :  2   Iteration :  54  ||B r|| = 0.000558169
+   Pass :  2   Iteration :  55  ||B r|| = 0.000543694
+   Pass :  2   Iteration :  56  ||B r|| = 0.000510469
+   Pass :  2   Iteration :  57  ||B r|| = 0.000470842
+   Pass :  2   Iteration :  58  ||B r|| = 0.000455589
+   Pass :  2   Iteration :  59  ||B r|| = 0.000397025
+   Pass :  2   Iteration :  60  ||B r|| = 0.000396534
+   Pass :  2   Iteration :  61  ||B r|| = 0.000352046
+   Pass :  2   Iteration :  62  ||B r|| = 0.00034964
+   Pass :  2   Iteration :  63  ||B r|| = 0.000316881
+   Pass :  2   Iteration :  64  ||B r|| = 0.000302877
+   Pass :  2   Iteration :  65  ||B r|| = 0.000290048
+   Pass :  2   Iteration :  66  ||B r|| = 0.000259631
+   Pass :  2   Iteration :  67  ||B r|| = 0.000252283
+   Pass :  2   Iteration :  68  ||B r|| = 0.000218729
+   Pass :  2   Iteration :  69  ||B r|| = 0.000218642
+   Pass :  2   Iteration :  70  ||B r|| = 0.000185129
+   Pass :  2   Iteration :  71  ||B r|| = 0.000183245
+   Pass :  2   Iteration :  72  ||B r|| = 0.000159439
+   Pass :  2   Iteration :  73  ||B r|| = 0.000139797
+   Pass :  2   Iteration :  74  ||B r|| = 0.000127418
+   Pass :  2   Iteration :  75  ||B r|| = 9.6403e-05
+   Pass :  2   Iteration :  76  ||B r|| = 9.62446e-05
+   Pass :  2   Iteration :  77  ||B r|| = 7.53468e-05
+   Pass :  2   Iteration :  78  ||B r|| = 7.34374e-05
+   Pass :  2   Iteration :  79  ||B r|| = 6.266e-05
+   Pass :  2   Iteration :  80  ||B r|| = 5.79039e-05
+   Pass :  2   Iteration :  81  ||B r|| = 5.2419e-05
+   Pass :  2   Iteration :  82  ||B r|| = 4.25861e-05
+   Pass :  2   Iteration :  83  ||B r|| = 4.1704e-05
+   Pass :  2   Iteration :  84  ||B r|| = 3.50184e-05
+   Pass :  2   Iteration :  85  ||B r|| = 3.47823e-05
+   Pass :  2   Iteration :  86  ||B r|| = 3.12451e-05
+   Pass :  2   Iteration :  87  ||B r|| = 2.95721e-05
+   Pass :  2   Iteration :  88  ||B r|| = 2.772e-05
+   Pass :  2   Iteration :  89  ||B r|| = 2.59836e-05
+   Pass :  2   Iteration :  90  ||B r|| = 2.4862e-05
+   Pass :  2   Iteration :  91  ||B r|| = 2.21712e-05
+   Pass :  2   Iteration :  92  ||B r|| = 2.20746e-05
+   Pass :  2   Iteration :  93  ||B r|| = 1.9872e-05
+   Pass :  2   Iteration :  94  ||B r|| = 1.9629e-05
+   Pass :  2   Iteration :  95  ||B r|| = 1.85378e-05
+   Pass :  2   Iteration :  96  ||B r|| = 1.77359e-05
+   Pass :  2   Iteration :  97  ||B r|| = 1.74624e-05
+   Pass :  2   Iteration :  98  ||B r|| = 1.66693e-05
+   Pass :  2   Iteration :  99  ||B r|| = 1.6335e-05
+   Pass :  2   Iteration : 100  ||B r|| = 1.51151e-05
+Restarting...
+   Pass :  3   Iteration : 101  ||B r|| = 1.5114e-05
+   Pass :  3   Iteration : 102  ||B r|| = 1.47315e-05
+   Pass :  3   Iteration : 103  ||B r|| = 1.47308e-05
+   Pass :  3   Iteration : 104  ||B r|| = 1.46118e-05
+   Pass :  3   Iteration : 105  ||B r|| = 1.41889e-05
+   Pass :  3   Iteration : 106  ||B r|| = 1.41359e-05
+   Pass :  3   Iteration : 107  ||B r|| = 1.34724e-05
+   Pass :  3   Iteration : 108  ||B r|| = 1.34435e-05
+   Pass :  3   Iteration : 109  ||B r|| = 1.27207e-05
+   Pass :  3   Iteration : 110  ||B r|| = 1.27061e-05
+   Pass :  3   Iteration : 111  ||B r|| = 1.20548e-05
+   Pass :  3   Iteration : 112  ||B r|| = 1.19735e-05
+   Pass :  3   Iteration : 113  ||B r|| = 1.16861e-05
+   Pass :  3   Iteration : 114  ||B r|| = 1.11145e-05
+   Pass :  3   Iteration : 115  ||B r|| = 1.10079e-05
+   Pass :  3   Iteration : 116  ||B r|| = 9.81707e-06
+   Pass :  3   Iteration : 117  ||B r|| = 9.76933e-06
+   Pass :  3   Iteration : 118  ||B r|| = 8.47019e-06
+   Pass :  3   Iteration : 119  ||B r|| = 8.44251e-06
+   Pass :  3   Iteration : 120  ||B r|| = 7.46965e-06
+   Pass :  3   Iteration : 121  ||B r|| = 7.13566e-06
+   Pass :  3   Iteration : 122  ||B r|| = 6.76319e-06
+   Pass :  3   Iteration : 123  ||B r|| = 5.83805e-06
+   Pass :  3   Iteration : 124  ||B r|| = 5.77071e-06
+   Pass :  3   Iteration : 125  ||B r|| = 4.65252e-06
+   Pass :  3   Iteration : 126  ||B r|| = 4.64659e-06
+   Pass :  3   Iteration : 127  ||B r|| = 3.87968e-06
+   Pass :  3   Iteration : 128  ||B r|| = 3.79069e-06
+   Pass :  3   Iteration : 129  ||B r|| = 3.41879e-06
+   Pass :  3   Iteration : 130  ||B r|| = 3.22843e-06
+   Pass :  3   Iteration : 131  ||B r|| = 3.12011e-06
+   Pass :  3   Iteration : 132  ||B r|| = 2.76084e-06
+   Pass :  3   Iteration : 133  ||B r|| = 2.75187e-06
+   Pass :  3   Iteration : 134  ||B r|| = 2.29895e-06
+   Pass :  3   Iteration : 135  ||B r|| = 2.2923e-06
+   Pass :  3   Iteration : 136  ||B r|| = 1.98924e-06
+   Pass :  3   Iteration : 137  ||B r|| = 1.87521e-06
+   Pass :  3   Iteration : 138  ||B r|| = 1.70821e-06
+   Pass :  3   Iteration : 139  ||B r|| = 1.56383e-06
+   Pass :  3   Iteration : 140  ||B r|| = 1.51755e-06
+   Pass :  3   Iteration : 141  ||B r|| = 1.27982e-06
+   Pass :  3   Iteration : 142  ||B r|| = 1.27704e-06
+   Pass :  3   Iteration : 143  ||B r|| = 1.09518e-06
+   Pass :  3   Iteration : 144  ||B r|| = 1.07475e-06
+   Pass :  3   Iteration : 145  ||B r|| = 9.62266e-07
+   Pass :  3   Iteration : 146  ||B r|| = 9.12639e-07
+   Pass :  3   Iteration : 147  ||B r|| = 8.86745e-07
+   Pass :  3   Iteration : 148  ||B r|| = 8.17791e-07
+   Pass :  3   Iteration : 149  ||B r|| = 8.08441e-07
+   Pass :  3   Iteration : 150  ||B r|| = 6.91736e-07
+Restarting...
+   Pass :  4   Iteration : 151  ||B r|| = 6.90683e-07
+   Pass :  4   Iteration : 152  ||B r|| = 6.40767e-07
+   Pass :  4   Iteration : 153  ||B r|| = 6.29071e-07
+   Pass :  4   Iteration : 154  ||B r|| = 6.04991e-07
+   Pass :  4   Iteration : 155  ||B r|| = 5.68926e-07
+   Pass :  4   Iteration : 156  ||B r|| = 5.56556e-07
+   Pass :  4   Iteration : 157  ||B r|| = 5.00241e-07
+   Pass :  4   Iteration : 158  ||B r|| = 4.97432e-07
+   Pass :  4   Iteration : 159  ||B r|| = 4.42326e-07
+   Pass :  4   Iteration : 160  ||B r|| = 4.40108e-07
+   Pass :  4   Iteration : 161  ||B r|| = 4.0534e-07
+   Pass :  4   Iteration : 162  ||B r|| = 3.87866e-07
+   Pass :  4   Iteration : 163  ||B r|| = 3.71339e-07
+   Pass :  4   Iteration : 164  ||B r|| = 3.3364e-07
+   Pass :  4   Iteration : 165  ||B r|| = 3.24578e-07
+   Pass :  4   Iteration : 166  ||B r|| = 2.76839e-07
+   Pass :  4   Iteration : 167  ||B r|| = 2.76614e-07
+   Pass :  4   Iteration : 168  ||B r|| = 2.41385e-07
+   Pass :  4   Iteration : 169  ||B r|| = 2.37068e-07
+   Pass :  4   Iteration : 170  ||B r|| = 2.12812e-07
+   Pass :  4   Iteration : 171  ||B r|| = 1.98566e-07
+   Pass :  4   Iteration : 172  ||B r|| = 1.89446e-07
+   Pass :  4   Iteration : 173  ||B r|| = 1.62576e-07
+   Pass :  4   Iteration : 174  ||B r|| = 1.61144e-07
+   Pass :  4   Iteration : 175  ||B r|| = 1.287e-07
+   Pass :  4   Iteration : 176  ||B r|| = 1.2827e-07
+   Pass :  4   Iteration : 177  ||B r|| = 1.05376e-07
+   Pass :  4   Iteration : 178  ||B r|| = 9.95608e-08
+   Pass :  4   Iteration : 179  ||B r|| = 8.81795e-08
+   Pass :  4   Iteration : 180  ||B r|| = 7.61168e-08
+   Pass :  4   Iteration : 181  ||B r|| = 7.39937e-08
+   Pass :  4   Iteration : 182  ||B r|| = 5.83628e-08
+   Pass :  4   Iteration : 183  ||B r|| = 5.83626e-08
+   Pass :  4   Iteration : 184  ||B r|| = 4.72729e-08
+   Pass :  4   Iteration : 185  ||B r|| = 4.5707e-08
+   Pass :  4   Iteration : 186  ||B r|| = 3.99693e-08
+   Pass :  4   Iteration : 187  ||B r|| = 3.69314e-08
+   Pass :  4   Iteration : 188  ||B r|| = 3.53794e-08
+   Pass :  4   Iteration : 189  ||B r|| = 3.13631e-08
+   Pass :  4   Iteration : 190  ||B r|| = 3.12954e-08
+   Pass :  4   Iteration : 191  ||B r|| = 2.56091e-08
+   Pass :  4   Iteration : 192  ||B r|| = 2.54565e-08
+   Pass :  4   Iteration : 193  ||B r|| = 2.11121e-08
+GMRES+GS converged in 193 iterations with a residual norm of 2.11121e-08.
+solver took 31.1884s.
+|| q_h - q_ex || / || q_ex || = 8.25658e-07
+|| t_h - t_ex || / || t_ex || = 8.18053e-07

examples/regress_test/p2_o3_nlc_hdg1_umfpack.txt

@@ -0,0 +1,69 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --nonlinear
+   --nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 3280
+dim(W) = 1600
+dim(V+W) = 4880
+***********************************************************
+Assembly took 0.184719s.
+Preconditioner took 0.235373s.
+   Pass :  1   Iteration :   0  ||B r|| = 1.87617
+   Pass :  1   Iteration :   1  ||B r|| = 1.87443
+   Pass :  1   Iteration :   2  ||B r|| = 0.18234
+   Pass :  1   Iteration :   3  ||B r|| = 0.171481
+   Pass :  1   Iteration :   4  ||B r|| = 0.0334939
+   Pass :  1   Iteration :   5  ||B r|| = 0.0332163
+   Pass :  1   Iteration :   6  ||B r|| = 0.00818877
+   Pass :  1   Iteration :   7  ||B r|| = 0.00386167
+   Pass :  1   Iteration :   8  ||B r|| = 0.00278074
+   Pass :  1   Iteration :   9  ||B r|| = 0.00137145
+   Pass :  1   Iteration :  10  ||B r|| = 0.00101062
+   Pass :  1   Iteration :  11  ||B r|| = 0.000506094
+   Pass :  1   Iteration :  12  ||B r|| = 0.000238678
+   Pass :  1   Iteration :  13  ||B r|| = 0.000229464
+   Pass :  1   Iteration :  14  ||B r|| = 9.10592e-05
+   Pass :  1   Iteration :  15  ||B r|| = 4.50432e-05
+   Pass :  1   Iteration :  16  ||B r|| = 4.4943e-05
+   Pass :  1   Iteration :  17  ||B r|| = 2.21569e-05
+   Pass :  1   Iteration :  18  ||B r|| = 1.19208e-05
+   Pass :  1   Iteration :  19  ||B r|| = 1.18368e-05
+   Pass :  1   Iteration :  20  ||B r|| = 4.87269e-06
+   Pass :  1   Iteration :  21  ||B r|| = 2.14408e-06
+   Pass :  1   Iteration :  22  ||B r|| = 1.99757e-06
+   Pass :  1   Iteration :  23  ||B r|| = 9.51239e-07
+GMRES+UMFPack converged in 23 iterations with a residual norm of 9.51239e-07.
+solver took 3.05684s.
+|| q_h - q_ex || / || q_ex || = 6.03707e-07
+|| t_h - t_ex || / || t_ex || = 1.08497e-07

examples/regress_test/p2_o3_nlc_hdg2.txt

@@ -0,0 +1,244 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --nonlinear
+   --no-nonlinear-flux
+   --no-nonlinear-pot
+   --nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 2
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 3280
+dim(W) = 1600
+dim(V+W) = 4880
+***********************************************************
+Assembly took 0.195208s.
+Preconditioner took 0.240636s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.0220032
+   Pass :  1   Iteration :   1  ||B r|| = 0.0220032
+   Pass :  1   Iteration :   2  ||B r|| = 0.0208317
+   Pass :  1   Iteration :   3  ||B r|| = 0.0206802
+   Pass :  1   Iteration :   4  ||B r|| = 0.0196435
+   Pass :  1   Iteration :   5  ||B r|| = 0.0193751
+   Pass :  1   Iteration :   6  ||B r|| = 0.0193644
+   Pass :  1   Iteration :   7  ||B r|| = 0.0192222
+   Pass :  1   Iteration :   8  ||B r|| = 0.0191298
+   Pass :  1   Iteration :   9  ||B r|| = 0.0184188
+   Pass :  1   Iteration :  10  ||B r|| = 0.0182278
+   Pass :  1   Iteration :  11  ||B r|| = 0.0156396
+   Pass :  1   Iteration :  12  ||B r|| = 0.0155674
+   Pass :  1   Iteration :  13  ||B r|| = 0.0143963
+   Pass :  1   Iteration :  14  ||B r|| = 0.0143443
+   Pass :  1   Iteration :  15  ||B r|| = 0.0135627
+   Pass :  1   Iteration :  16  ||B r|| = 0.0135558
+   Pass :  1   Iteration :  17  ||B r|| = 0.0130116
+   Pass :  1   Iteration :  18  ||B r|| = 0.0125869
+   Pass :  1   Iteration :  19  ||B r|| = 0.0122169
+   Pass :  1   Iteration :  20  ||B r|| = 0.0109293
+   Pass :  1   Iteration :  21  ||B r|| = 0.0109181
+   Pass :  1   Iteration :  22  ||B r|| = 0.0097437
+   Pass :  1   Iteration :  23  ||B r|| = 0.00973885
+   Pass :  1   Iteration :  24  ||B r|| = 0.0085645
+   Pass :  1   Iteration :  25  ||B r|| = 0.00844063
+   Pass :  1   Iteration :  26  ||B r|| = 0.00769784
+   Pass :  1   Iteration :  27  ||B r|| = 0.00724603
+   Pass :  1   Iteration :  28  ||B r|| = 0.00696129
+   Pass :  1   Iteration :  29  ||B r|| = 0.00611181
+   Pass :  1   Iteration :  30  ||B r|| = 0.00609183
+   Pass :  1   Iteration :  31  ||B r|| = 0.00522302
+   Pass :  1   Iteration :  32  ||B r|| = 0.00521279
+   Pass :  1   Iteration :  33  ||B r|| = 0.00431424
+   Pass :  1   Iteration :  34  ||B r|| = 0.00413969
+   Pass :  1   Iteration :  35  ||B r|| = 0.0034955
+   Pass :  1   Iteration :  36  ||B r|| = 0.00304203
+   Pass :  1   Iteration :  37  ||B r|| = 0.00289708
+   Pass :  1   Iteration :  38  ||B r|| = 0.00219349
+   Pass :  1   Iteration :  39  ||B r|| = 0.00219047
+   Pass :  1   Iteration :  40  ||B r|| = 0.00163612
+   Pass :  1   Iteration :  41  ||B r|| = 0.00158611
+   Pass :  1   Iteration :  42  ||B r|| = 0.00126672
+   Pass :  1   Iteration :  43  ||B r|| = 0.00105371
+   Pass :  1   Iteration :  44  ||B r|| = 0.00100063
+   Pass :  1   Iteration :  45  ||B r|| = 0.000802595
+   Pass :  1   Iteration :  46  ||B r|| = 0.000801298
+   Pass :  1   Iteration :  47  ||B r|| = 0.000705846
+   Pass :  1   Iteration :  48  ||B r|| = 0.000696003
+   Pass :  1   Iteration :  49  ||B r|| = 0.000646771
+   Pass :  1   Iteration :  50  ||B r|| = 0.000627259
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 0.000621921
+   Pass :  2   Iteration :  52  ||B r|| = 0.000588136
+   Pass :  2   Iteration :  53  ||B r|| = 0.00058774
+   Pass :  2   Iteration :  54  ||B r|| = 0.000558169
+   Pass :  2   Iteration :  55  ||B r|| = 0.000543694
+   Pass :  2   Iteration :  56  ||B r|| = 0.000510469
+   Pass :  2   Iteration :  57  ||B r|| = 0.000470842
+   Pass :  2   Iteration :  58  ||B r|| = 0.000455589
+   Pass :  2   Iteration :  59  ||B r|| = 0.000397025
+   Pass :  2   Iteration :  60  ||B r|| = 0.000396534
+   Pass :  2   Iteration :  61  ||B r|| = 0.000352046
+   Pass :  2   Iteration :  62  ||B r|| = 0.00034964
+   Pass :  2   Iteration :  63  ||B r|| = 0.000316881
+   Pass :  2   Iteration :  64  ||B r|| = 0.000302877
+   Pass :  2   Iteration :  65  ||B r|| = 0.000290048
+   Pass :  2   Iteration :  66  ||B r|| = 0.000259631
+   Pass :  2   Iteration :  67  ||B r|| = 0.000252283
+   Pass :  2   Iteration :  68  ||B r|| = 0.000218729
+   Pass :  2   Iteration :  69  ||B r|| = 0.000218642
+   Pass :  2   Iteration :  70  ||B r|| = 0.000185129
+   Pass :  2   Iteration :  71  ||B r|| = 0.000183245
+   Pass :  2   Iteration :  72  ||B r|| = 0.000159439
+   Pass :  2   Iteration :  73  ||B r|| = 0.000139797
+   Pass :  2   Iteration :  74  ||B r|| = 0.000127418
+   Pass :  2   Iteration :  75  ||B r|| = 9.6403e-05
+   Pass :  2   Iteration :  76  ||B r|| = 9.62446e-05
+   Pass :  2   Iteration :  77  ||B r|| = 7.53468e-05
+   Pass :  2   Iteration :  78  ||B r|| = 7.34374e-05
+   Pass :  2   Iteration :  79  ||B r|| = 6.266e-05
+   Pass :  2   Iteration :  80  ||B r|| = 5.79039e-05
+   Pass :  2   Iteration :  81  ||B r|| = 5.2419e-05
+   Pass :  2   Iteration :  82  ||B r|| = 4.25861e-05
+   Pass :  2   Iteration :  83  ||B r|| = 4.1704e-05
+   Pass :  2   Iteration :  84  ||B r|| = 3.50184e-05
+   Pass :  2   Iteration :  85  ||B r|| = 3.47823e-05
+   Pass :  2   Iteration :  86  ||B r|| = 3.12451e-05
+   Pass :  2   Iteration :  87  ||B r|| = 2.95721e-05
+   Pass :  2   Iteration :  88  ||B r|| = 2.772e-05
+   Pass :  2   Iteration :  89  ||B r|| = 2.59836e-05
+   Pass :  2   Iteration :  90  ||B r|| = 2.4862e-05
+   Pass :  2   Iteration :  91  ||B r|| = 2.21712e-05
+   Pass :  2   Iteration :  92  ||B r|| = 2.20746e-05
+   Pass :  2   Iteration :  93  ||B r|| = 1.9872e-05
+   Pass :  2   Iteration :  94  ||B r|| = 1.9629e-05
+   Pass :  2   Iteration :  95  ||B r|| = 1.85378e-05
+   Pass :  2   Iteration :  96  ||B r|| = 1.77359e-05
+   Pass :  2   Iteration :  97  ||B r|| = 1.74624e-05
+   Pass :  2   Iteration :  98  ||B r|| = 1.66693e-05
+   Pass :  2   Iteration :  99  ||B r|| = 1.6335e-05
+   Pass :  2   Iteration : 100  ||B r|| = 1.51151e-05
+Restarting...
+   Pass :  3   Iteration : 101  ||B r|| = 1.5114e-05
+   Pass :  3   Iteration : 102  ||B r|| = 1.47315e-05
+   Pass :  3   Iteration : 103  ||B r|| = 1.47308e-05
+   Pass :  3   Iteration : 104  ||B r|| = 1.46118e-05
+   Pass :  3   Iteration : 105  ||B r|| = 1.41889e-05
+   Pass :  3   Iteration : 106  ||B r|| = 1.41359e-05
+   Pass :  3   Iteration : 107  ||B r|| = 1.34724e-05
+   Pass :  3   Iteration : 108  ||B r|| = 1.34435e-05
+   Pass :  3   Iteration : 109  ||B r|| = 1.27207e-05
+   Pass :  3   Iteration : 110  ||B r|| = 1.27061e-05
+   Pass :  3   Iteration : 111  ||B r|| = 1.20548e-05
+   Pass :  3   Iteration : 112  ||B r|| = 1.19735e-05
+   Pass :  3   Iteration : 113  ||B r|| = 1.16861e-05
+   Pass :  3   Iteration : 114  ||B r|| = 1.11145e-05
+   Pass :  3   Iteration : 115  ||B r|| = 1.10079e-05
+   Pass :  3   Iteration : 116  ||B r|| = 9.81707e-06
+   Pass :  3   Iteration : 117  ||B r|| = 9.76933e-06
+   Pass :  3   Iteration : 118  ||B r|| = 8.47019e-06
+   Pass :  3   Iteration : 119  ||B r|| = 8.44251e-06
+   Pass :  3   Iteration : 120  ||B r|| = 7.46965e-06
+   Pass :  3   Iteration : 121  ||B r|| = 7.13566e-06
+   Pass :  3   Iteration : 122  ||B r|| = 6.76319e-06
+   Pass :  3   Iteration : 123  ||B r|| = 5.83805e-06
+   Pass :  3   Iteration : 124  ||B r|| = 5.77071e-06
+   Pass :  3   Iteration : 125  ||B r|| = 4.65252e-06
+   Pass :  3   Iteration : 126  ||B r|| = 4.64659e-06
+   Pass :  3   Iteration : 127  ||B r|| = 3.87968e-06
+   Pass :  3   Iteration : 128  ||B r|| = 3.79069e-06
+   Pass :  3   Iteration : 129  ||B r|| = 3.41879e-06
+   Pass :  3   Iteration : 130  ||B r|| = 3.22843e-06
+   Pass :  3   Iteration : 131  ||B r|| = 3.12011e-06
+   Pass :  3   Iteration : 132  ||B r|| = 2.76084e-06
+   Pass :  3   Iteration : 133  ||B r|| = 2.75187e-06
+   Pass :  3   Iteration : 134  ||B r|| = 2.29895e-06
+   Pass :  3   Iteration : 135  ||B r|| = 2.2923e-06
+   Pass :  3   Iteration : 136  ||B r|| = 1.98924e-06
+   Pass :  3   Iteration : 137  ||B r|| = 1.87521e-06
+   Pass :  3   Iteration : 138  ||B r|| = 1.70821e-06
+   Pass :  3   Iteration : 139  ||B r|| = 1.56383e-06
+   Pass :  3   Iteration : 140  ||B r|| = 1.51755e-06
+   Pass :  3   Iteration : 141  ||B r|| = 1.27982e-06
+   Pass :  3   Iteration : 142  ||B r|| = 1.27704e-06
+   Pass :  3   Iteration : 143  ||B r|| = 1.09518e-06
+   Pass :  3   Iteration : 144  ||B r|| = 1.07475e-06
+   Pass :  3   Iteration : 145  ||B r|| = 9.62266e-07
+   Pass :  3   Iteration : 146  ||B r|| = 9.12639e-07
+   Pass :  3   Iteration : 147  ||B r|| = 8.86745e-07
+   Pass :  3   Iteration : 148  ||B r|| = 8.17791e-07
+   Pass :  3   Iteration : 149  ||B r|| = 8.08441e-07
+   Pass :  3   Iteration : 150  ||B r|| = 6.91736e-07
+Restarting...
+   Pass :  4   Iteration : 151  ||B r|| = 6.90683e-07
+   Pass :  4   Iteration : 152  ||B r|| = 6.40767e-07
+   Pass :  4   Iteration : 153  ||B r|| = 6.29071e-07
+   Pass :  4   Iteration : 154  ||B r|| = 6.04991e-07
+   Pass :  4   Iteration : 155  ||B r|| = 5.68926e-07
+   Pass :  4   Iteration : 156  ||B r|| = 5.56556e-07
+   Pass :  4   Iteration : 157  ||B r|| = 5.00241e-07
+   Pass :  4   Iteration : 158  ||B r|| = 4.97432e-07
+   Pass :  4   Iteration : 159  ||B r|| = 4.42326e-07
+   Pass :  4   Iteration : 160  ||B r|| = 4.40108e-07
+   Pass :  4   Iteration : 161  ||B r|| = 4.0534e-07
+   Pass :  4   Iteration : 162  ||B r|| = 3.87866e-07
+   Pass :  4   Iteration : 163  ||B r|| = 3.71339e-07
+   Pass :  4   Iteration : 164  ||B r|| = 3.3364e-07
+   Pass :  4   Iteration : 165  ||B r|| = 3.24578e-07
+   Pass :  4   Iteration : 166  ||B r|| = 2.76839e-07
+   Pass :  4   Iteration : 167  ||B r|| = 2.76614e-07
+   Pass :  4   Iteration : 168  ||B r|| = 2.41385e-07
+   Pass :  4   Iteration : 169  ||B r|| = 2.37068e-07
+   Pass :  4   Iteration : 170  ||B r|| = 2.12812e-07
+   Pass :  4   Iteration : 171  ||B r|| = 1.98566e-07
+   Pass :  4   Iteration : 172  ||B r|| = 1.89446e-07
+   Pass :  4   Iteration : 173  ||B r|| = 1.62576e-07
+   Pass :  4   Iteration : 174  ||B r|| = 1.61144e-07
+   Pass :  4   Iteration : 175  ||B r|| = 1.287e-07
+   Pass :  4   Iteration : 176  ||B r|| = 1.2827e-07
+   Pass :  4   Iteration : 177  ||B r|| = 1.05376e-07
+   Pass :  4   Iteration : 178  ||B r|| = 9.95608e-08
+   Pass :  4   Iteration : 179  ||B r|| = 8.81795e-08
+   Pass :  4   Iteration : 180  ||B r|| = 7.61168e-08
+   Pass :  4   Iteration : 181  ||B r|| = 7.39937e-08
+   Pass :  4   Iteration : 182  ||B r|| = 5.83628e-08
+   Pass :  4   Iteration : 183  ||B r|| = 5.83626e-08
+   Pass :  4   Iteration : 184  ||B r|| = 4.72729e-08
+   Pass :  4   Iteration : 185  ||B r|| = 4.5707e-08
+   Pass :  4   Iteration : 186  ||B r|| = 3.99693e-08
+   Pass :  4   Iteration : 187  ||B r|| = 3.69314e-08
+   Pass :  4   Iteration : 188  ||B r|| = 3.53794e-08
+   Pass :  4   Iteration : 189  ||B r|| = 3.13631e-08
+   Pass :  4   Iteration : 190  ||B r|| = 3.12954e-08
+   Pass :  4   Iteration : 191  ||B r|| = 2.56091e-08
+   Pass :  4   Iteration : 192  ||B r|| = 2.54565e-08
+   Pass :  4   Iteration : 193  ||B r|| = 2.11121e-08
+GMRES+GS converged in 193 iterations with a residual norm of 2.11121e-08.
+solver took 31.9329s.
+|| q_h - q_ex || / || q_ex || = 8.25658e-07
+|| t_h - t_ex || / || t_ex || = 8.18053e-07

examples/regress_test/p2_o3_nlc_hdg2_umfpack.txt

@@ -0,0 +1,69 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --nonlinear
+   --nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 2
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 3280
+dim(W) = 1600
+dim(V+W) = 4880
+***********************************************************
+Assembly took 0.179758s.
+Preconditioner took 0.218006s.
+   Pass :  1   Iteration :   0  ||B r|| = 1.87617
+   Pass :  1   Iteration :   1  ||B r|| = 1.87443
+   Pass :  1   Iteration :   2  ||B r|| = 0.18234
+   Pass :  1   Iteration :   3  ||B r|| = 0.171481
+   Pass :  1   Iteration :   4  ||B r|| = 0.0334939
+   Pass :  1   Iteration :   5  ||B r|| = 0.0332163
+   Pass :  1   Iteration :   6  ||B r|| = 0.00818877
+   Pass :  1   Iteration :   7  ||B r|| = 0.00386167
+   Pass :  1   Iteration :   8  ||B r|| = 0.00278074
+   Pass :  1   Iteration :   9  ||B r|| = 0.00137145
+   Pass :  1   Iteration :  10  ||B r|| = 0.00101062
+   Pass :  1   Iteration :  11  ||B r|| = 0.000506094
+   Pass :  1   Iteration :  12  ||B r|| = 0.000238678
+   Pass :  1   Iteration :  13  ||B r|| = 0.000229464
+   Pass :  1   Iteration :  14  ||B r|| = 9.10592e-05
+   Pass :  1   Iteration :  15  ||B r|| = 4.50432e-05
+   Pass :  1   Iteration :  16  ||B r|| = 4.4943e-05
+   Pass :  1   Iteration :  17  ||B r|| = 2.21569e-05
+   Pass :  1   Iteration :  18  ||B r|| = 1.19208e-05
+   Pass :  1   Iteration :  19  ||B r|| = 1.18368e-05
+   Pass :  1   Iteration :  20  ||B r|| = 4.87269e-06
+   Pass :  1   Iteration :  21  ||B r|| = 2.14408e-06
+   Pass :  1   Iteration :  22  ||B r|| = 1.99757e-06
+   Pass :  1   Iteration :  23  ||B r|| = 9.51239e-07
+GMRES+UMFPack converged in 23 iterations with a residual norm of 9.51239e-07.
+solver took 2.99466s.
+|| q_h - q_ex || / || q_ex || = 6.03707e-07
+|| t_h - t_ex || / || t_ex || = 1.08497e-07

examples/regress_test/p2_o3_nlc_hdg3.txt

@@ -0,0 +1,244 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --nonlinear
+   --no-nonlinear-flux
+   --no-nonlinear-pot
+   --nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 3
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 3280
+dim(W) = 1600
+dim(V+W) = 4880
+***********************************************************
+Assembly took 0.197656s.
+Preconditioner took 0.227817s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.0220032
+   Pass :  1   Iteration :   1  ||B r|| = 0.0220032
+   Pass :  1   Iteration :   2  ||B r|| = 0.0208317
+   Pass :  1   Iteration :   3  ||B r|| = 0.0206802
+   Pass :  1   Iteration :   4  ||B r|| = 0.0196435
+   Pass :  1   Iteration :   5  ||B r|| = 0.0193751
+   Pass :  1   Iteration :   6  ||B r|| = 0.0193644
+   Pass :  1   Iteration :   7  ||B r|| = 0.0192222
+   Pass :  1   Iteration :   8  ||B r|| = 0.0191298
+   Pass :  1   Iteration :   9  ||B r|| = 0.0184188
+   Pass :  1   Iteration :  10  ||B r|| = 0.0182278
+   Pass :  1   Iteration :  11  ||B r|| = 0.0156396
+   Pass :  1   Iteration :  12  ||B r|| = 0.0155674
+   Pass :  1   Iteration :  13  ||B r|| = 0.0143963
+   Pass :  1   Iteration :  14  ||B r|| = 0.0143443
+   Pass :  1   Iteration :  15  ||B r|| = 0.0135627
+   Pass :  1   Iteration :  16  ||B r|| = 0.0135558
+   Pass :  1   Iteration :  17  ||B r|| = 0.0130116
+   Pass :  1   Iteration :  18  ||B r|| = 0.0125869
+   Pass :  1   Iteration :  19  ||B r|| = 0.0122169
+   Pass :  1   Iteration :  20  ||B r|| = 0.0109293
+   Pass :  1   Iteration :  21  ||B r|| = 0.0109181
+   Pass :  1   Iteration :  22  ||B r|| = 0.0097437
+   Pass :  1   Iteration :  23  ||B r|| = 0.00973885
+   Pass :  1   Iteration :  24  ||B r|| = 0.0085645
+   Pass :  1   Iteration :  25  ||B r|| = 0.00844063
+   Pass :  1   Iteration :  26  ||B r|| = 0.00769784
+   Pass :  1   Iteration :  27  ||B r|| = 0.00724603
+   Pass :  1   Iteration :  28  ||B r|| = 0.00696129
+   Pass :  1   Iteration :  29  ||B r|| = 0.00611181
+   Pass :  1   Iteration :  30  ||B r|| = 0.00609183
+   Pass :  1   Iteration :  31  ||B r|| = 0.00522302
+   Pass :  1   Iteration :  32  ||B r|| = 0.00521279
+   Pass :  1   Iteration :  33  ||B r|| = 0.00431424
+   Pass :  1   Iteration :  34  ||B r|| = 0.00413969
+   Pass :  1   Iteration :  35  ||B r|| = 0.0034955
+   Pass :  1   Iteration :  36  ||B r|| = 0.00304203
+   Pass :  1   Iteration :  37  ||B r|| = 0.00289708
+   Pass :  1   Iteration :  38  ||B r|| = 0.00219349
+   Pass :  1   Iteration :  39  ||B r|| = 0.00219047
+   Pass :  1   Iteration :  40  ||B r|| = 0.00163612
+   Pass :  1   Iteration :  41  ||B r|| = 0.00158611
+   Pass :  1   Iteration :  42  ||B r|| = 0.00126672
+   Pass :  1   Iteration :  43  ||B r|| = 0.00105371
+   Pass :  1   Iteration :  44  ||B r|| = 0.00100063
+   Pass :  1   Iteration :  45  ||B r|| = 0.000802595
+   Pass :  1   Iteration :  46  ||B r|| = 0.000801298
+   Pass :  1   Iteration :  47  ||B r|| = 0.000705846
+   Pass :  1   Iteration :  48  ||B r|| = 0.000696003
+   Pass :  1   Iteration :  49  ||B r|| = 0.000646771
+   Pass :  1   Iteration :  50  ||B r|| = 0.000627259
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 0.000621921
+   Pass :  2   Iteration :  52  ||B r|| = 0.000588136
+   Pass :  2   Iteration :  53  ||B r|| = 0.00058774
+   Pass :  2   Iteration :  54  ||B r|| = 0.000558169
+   Pass :  2   Iteration :  55  ||B r|| = 0.000543694
+   Pass :  2   Iteration :  56  ||B r|| = 0.000510469
+   Pass :  2   Iteration :  57  ||B r|| = 0.000470842
+   Pass :  2   Iteration :  58  ||B r|| = 0.000455589
+   Pass :  2   Iteration :  59  ||B r|| = 0.000397025
+   Pass :  2   Iteration :  60  ||B r|| = 0.000396534
+   Pass :  2   Iteration :  61  ||B r|| = 0.000352046
+   Pass :  2   Iteration :  62  ||B r|| = 0.00034964
+   Pass :  2   Iteration :  63  ||B r|| = 0.000316881
+   Pass :  2   Iteration :  64  ||B r|| = 0.000302877
+   Pass :  2   Iteration :  65  ||B r|| = 0.000290048
+   Pass :  2   Iteration :  66  ||B r|| = 0.000259631
+   Pass :  2   Iteration :  67  ||B r|| = 0.000252283
+   Pass :  2   Iteration :  68  ||B r|| = 0.000218729
+   Pass :  2   Iteration :  69  ||B r|| = 0.000218642
+   Pass :  2   Iteration :  70  ||B r|| = 0.000185129
+   Pass :  2   Iteration :  71  ||B r|| = 0.000183245
+   Pass :  2   Iteration :  72  ||B r|| = 0.000159439
+   Pass :  2   Iteration :  73  ||B r|| = 0.000139797
+   Pass :  2   Iteration :  74  ||B r|| = 0.000127418
+   Pass :  2   Iteration :  75  ||B r|| = 9.6403e-05
+   Pass :  2   Iteration :  76  ||B r|| = 9.62446e-05
+   Pass :  2   Iteration :  77  ||B r|| = 7.53468e-05
+   Pass :  2   Iteration :  78  ||B r|| = 7.34374e-05
+   Pass :  2   Iteration :  79  ||B r|| = 6.266e-05
+   Pass :  2   Iteration :  80  ||B r|| = 5.79039e-05
+   Pass :  2   Iteration :  81  ||B r|| = 5.2419e-05
+   Pass :  2   Iteration :  82  ||B r|| = 4.25861e-05
+   Pass :  2   Iteration :  83  ||B r|| = 4.1704e-05
+   Pass :  2   Iteration :  84  ||B r|| = 3.50184e-05
+   Pass :  2   Iteration :  85  ||B r|| = 3.47823e-05
+   Pass :  2   Iteration :  86  ||B r|| = 3.12451e-05
+   Pass :  2   Iteration :  87  ||B r|| = 2.95721e-05
+   Pass :  2   Iteration :  88  ||B r|| = 2.772e-05
+   Pass :  2   Iteration :  89  ||B r|| = 2.59836e-05
+   Pass :  2   Iteration :  90  ||B r|| = 2.4862e-05
+   Pass :  2   Iteration :  91  ||B r|| = 2.21712e-05
+   Pass :  2   Iteration :  92  ||B r|| = 2.20746e-05
+   Pass :  2   Iteration :  93  ||B r|| = 1.9872e-05
+   Pass :  2   Iteration :  94  ||B r|| = 1.9629e-05
+   Pass :  2   Iteration :  95  ||B r|| = 1.85378e-05
+   Pass :  2   Iteration :  96  ||B r|| = 1.77359e-05
+   Pass :  2   Iteration :  97  ||B r|| = 1.74624e-05
+   Pass :  2   Iteration :  98  ||B r|| = 1.66693e-05
+   Pass :  2   Iteration :  99  ||B r|| = 1.6335e-05
+   Pass :  2   Iteration : 100  ||B r|| = 1.51151e-05
+Restarting...
+   Pass :  3   Iteration : 101  ||B r|| = 1.5114e-05
+   Pass :  3   Iteration : 102  ||B r|| = 1.47315e-05
+   Pass :  3   Iteration : 103  ||B r|| = 1.47308e-05
+   Pass :  3   Iteration : 104  ||B r|| = 1.46118e-05
+   Pass :  3   Iteration : 105  ||B r|| = 1.41889e-05
+   Pass :  3   Iteration : 106  ||B r|| = 1.41359e-05
+   Pass :  3   Iteration : 107  ||B r|| = 1.34724e-05
+   Pass :  3   Iteration : 108  ||B r|| = 1.34435e-05
+   Pass :  3   Iteration : 109  ||B r|| = 1.27207e-05
+   Pass :  3   Iteration : 110  ||B r|| = 1.27061e-05
+   Pass :  3   Iteration : 111  ||B r|| = 1.20548e-05
+   Pass :  3   Iteration : 112  ||B r|| = 1.19735e-05
+   Pass :  3   Iteration : 113  ||B r|| = 1.16861e-05
+   Pass :  3   Iteration : 114  ||B r|| = 1.11145e-05
+   Pass :  3   Iteration : 115  ||B r|| = 1.10079e-05
+   Pass :  3   Iteration : 116  ||B r|| = 9.81707e-06
+   Pass :  3   Iteration : 117  ||B r|| = 9.76933e-06
+   Pass :  3   Iteration : 118  ||B r|| = 8.47019e-06
+   Pass :  3   Iteration : 119  ||B r|| = 8.44251e-06
+   Pass :  3   Iteration : 120  ||B r|| = 7.46965e-06
+   Pass :  3   Iteration : 121  ||B r|| = 7.13566e-06
+   Pass :  3   Iteration : 122  ||B r|| = 6.76319e-06
+   Pass :  3   Iteration : 123  ||B r|| = 5.83805e-06
+   Pass :  3   Iteration : 124  ||B r|| = 5.77071e-06
+   Pass :  3   Iteration : 125  ||B r|| = 4.65252e-06
+   Pass :  3   Iteration : 126  ||B r|| = 4.64659e-06
+   Pass :  3   Iteration : 127  ||B r|| = 3.87968e-06
+   Pass :  3   Iteration : 128  ||B r|| = 3.79069e-06
+   Pass :  3   Iteration : 129  ||B r|| = 3.41879e-06
+   Pass :  3   Iteration : 130  ||B r|| = 3.22843e-06
+   Pass :  3   Iteration : 131  ||B r|| = 3.12011e-06
+   Pass :  3   Iteration : 132  ||B r|| = 2.76084e-06
+   Pass :  3   Iteration : 133  ||B r|| = 2.75187e-06
+   Pass :  3   Iteration : 134  ||B r|| = 2.29895e-06
+   Pass :  3   Iteration : 135  ||B r|| = 2.2923e-06
+   Pass :  3   Iteration : 136  ||B r|| = 1.98924e-06
+   Pass :  3   Iteration : 137  ||B r|| = 1.87521e-06
+   Pass :  3   Iteration : 138  ||B r|| = 1.70821e-06
+   Pass :  3   Iteration : 139  ||B r|| = 1.56383e-06
+   Pass :  3   Iteration : 140  ||B r|| = 1.51755e-06
+   Pass :  3   Iteration : 141  ||B r|| = 1.27982e-06
+   Pass :  3   Iteration : 142  ||B r|| = 1.27704e-06
+   Pass :  3   Iteration : 143  ||B r|| = 1.09518e-06
+   Pass :  3   Iteration : 144  ||B r|| = 1.07475e-06
+   Pass :  3   Iteration : 145  ||B r|| = 9.62266e-07
+   Pass :  3   Iteration : 146  ||B r|| = 9.12639e-07
+   Pass :  3   Iteration : 147  ||B r|| = 8.86745e-07
+   Pass :  3   Iteration : 148  ||B r|| = 8.17791e-07
+   Pass :  3   Iteration : 149  ||B r|| = 8.08441e-07
+   Pass :  3   Iteration : 150  ||B r|| = 6.91736e-07
+Restarting...
+   Pass :  4   Iteration : 151  ||B r|| = 6.90683e-07
+   Pass :  4   Iteration : 152  ||B r|| = 6.40767e-07
+   Pass :  4   Iteration : 153  ||B r|| = 6.29071e-07
+   Pass :  4   Iteration : 154  ||B r|| = 6.04991e-07
+   Pass :  4   Iteration : 155  ||B r|| = 5.68926e-07
+   Pass :  4   Iteration : 156  ||B r|| = 5.56556e-07
+   Pass :  4   Iteration : 157  ||B r|| = 5.00241e-07
+   Pass :  4   Iteration : 158  ||B r|| = 4.97432e-07
+   Pass :  4   Iteration : 159  ||B r|| = 4.42326e-07
+   Pass :  4   Iteration : 160  ||B r|| = 4.40108e-07
+   Pass :  4   Iteration : 161  ||B r|| = 4.0534e-07
+   Pass :  4   Iteration : 162  ||B r|| = 3.87866e-07
+   Pass :  4   Iteration : 163  ||B r|| = 3.71339e-07
+   Pass :  4   Iteration : 164  ||B r|| = 3.3364e-07
+   Pass :  4   Iteration : 165  ||B r|| = 3.24578e-07
+   Pass :  4   Iteration : 166  ||B r|| = 2.76839e-07
+   Pass :  4   Iteration : 167  ||B r|| = 2.76614e-07
+   Pass :  4   Iteration : 168  ||B r|| = 2.41385e-07
+   Pass :  4   Iteration : 169  ||B r|| = 2.37068e-07
+   Pass :  4   Iteration : 170  ||B r|| = 2.12812e-07
+   Pass :  4   Iteration : 171  ||B r|| = 1.98566e-07
+   Pass :  4   Iteration : 172  ||B r|| = 1.89446e-07
+   Pass :  4   Iteration : 173  ||B r|| = 1.62576e-07
+   Pass :  4   Iteration : 174  ||B r|| = 1.61144e-07
+   Pass :  4   Iteration : 175  ||B r|| = 1.287e-07
+   Pass :  4   Iteration : 176  ||B r|| = 1.2827e-07
+   Pass :  4   Iteration : 177  ||B r|| = 1.05376e-07
+   Pass :  4   Iteration : 178  ||B r|| = 9.95608e-08
+   Pass :  4   Iteration : 179  ||B r|| = 8.81795e-08
+   Pass :  4   Iteration : 180  ||B r|| = 7.61168e-08
+   Pass :  4   Iteration : 181  ||B r|| = 7.39937e-08
+   Pass :  4   Iteration : 182  ||B r|| = 5.83628e-08
+   Pass :  4   Iteration : 183  ||B r|| = 5.83626e-08
+   Pass :  4   Iteration : 184  ||B r|| = 4.72729e-08
+   Pass :  4   Iteration : 185  ||B r|| = 4.5707e-08
+   Pass :  4   Iteration : 186  ||B r|| = 3.99693e-08
+   Pass :  4   Iteration : 187  ||B r|| = 3.69314e-08
+   Pass :  4   Iteration : 188  ||B r|| = 3.53794e-08
+   Pass :  4   Iteration : 189  ||B r|| = 3.13631e-08
+   Pass :  4   Iteration : 190  ||B r|| = 3.12954e-08
+   Pass :  4   Iteration : 191  ||B r|| = 2.56091e-08
+   Pass :  4   Iteration : 192  ||B r|| = 2.54565e-08
+   Pass :  4   Iteration : 193  ||B r|| = 2.11121e-08
+GMRES+GS converged in 193 iterations with a residual norm of 2.11121e-08.
+solver took 34.7016s.
+|| q_h - q_ex || / || q_ex || = 8.25658e-07
+|| t_h - t_ex || / || t_ex || = 8.18053e-07

examples/regress_test/p2_o3_nlc_hdg3_umfpack.txt

@@ -0,0 +1,69 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --nonlinear
+   --nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 3
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 3280
+dim(W) = 1600
+dim(V+W) = 4880
+***********************************************************
+Assembly took 0.182177s.
+Preconditioner took 0.233785s.
+   Pass :  1   Iteration :   0  ||B r|| = 1.87617
+   Pass :  1   Iteration :   1  ||B r|| = 1.87443
+   Pass :  1   Iteration :   2  ||B r|| = 0.18234
+   Pass :  1   Iteration :   3  ||B r|| = 0.171481
+   Pass :  1   Iteration :   4  ||B r|| = 0.0334939
+   Pass :  1   Iteration :   5  ||B r|| = 0.0332163
+   Pass :  1   Iteration :   6  ||B r|| = 0.00818877
+   Pass :  1   Iteration :   7  ||B r|| = 0.00386167
+   Pass :  1   Iteration :   8  ||B r|| = 0.00278074
+   Pass :  1   Iteration :   9  ||B r|| = 0.00137145
+   Pass :  1   Iteration :  10  ||B r|| = 0.00101062
+   Pass :  1   Iteration :  11  ||B r|| = 0.000506094
+   Pass :  1   Iteration :  12  ||B r|| = 0.000238678
+   Pass :  1   Iteration :  13  ||B r|| = 0.000229464
+   Pass :  1   Iteration :  14  ||B r|| = 9.10592e-05
+   Pass :  1   Iteration :  15  ||B r|| = 4.50432e-05
+   Pass :  1   Iteration :  16  ||B r|| = 4.4943e-05
+   Pass :  1   Iteration :  17  ||B r|| = 2.21569e-05
+   Pass :  1   Iteration :  18  ||B r|| = 1.19208e-05
+   Pass :  1   Iteration :  19  ||B r|| = 1.18368e-05
+   Pass :  1   Iteration :  20  ||B r|| = 4.87269e-06
+   Pass :  1   Iteration :  21  ||B r|| = 2.14408e-06
+   Pass :  1   Iteration :  22  ||B r|| = 1.99757e-06
+   Pass :  1   Iteration :  23  ||B r|| = 9.51239e-07
+GMRES+UMFPack converged in 23 iterations with a residual norm of 9.51239e-07.
+solver took 2.97169s.
+|| q_h - q_ex || / || q_ex || = 6.03707e-07
+|| t_h - t_ex || / || t_ex || = 1.08497e-07

examples/regress_test/p2_o3_nlc_hdg4.txt

@@ -0,0 +1,251 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --nonlinear
+   --no-nonlinear-flux
+   --no-nonlinear-pot
+   --nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 4
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+
+
+MFEM Warning: Upwinded flux is implemented only component-wise.
+ ... in function: mfem::ComponentwiseUpwindFlux::ComponentwiseUpwindFlux(const mfem::FluxFunction&)
+ ... in file: fem/hyperbolic.cpp:904
+
+***********************************************************
+dim(V) = 3280
+dim(W) = 1600
+dim(V+W) = 4880
+***********************************************************
+Assembly took 0.179966s.
+Preconditioner took 0.213841s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.022029
+   Pass :  1   Iteration :   1  ||B r|| = 0.022029
+   Pass :  1   Iteration :   2  ||B r|| = 0.020856
+   Pass :  1   Iteration :   3  ||B r|| = 0.0206994
+   Pass :  1   Iteration :   4  ||B r|| = 0.019636
+   Pass :  1   Iteration :   5  ||B r|| = 0.0193498
+   Pass :  1   Iteration :   6  ||B r|| = 0.0193453
+   Pass :  1   Iteration :   7  ||B r|| = 0.0192139
+   Pass :  1   Iteration :   8  ||B r|| = 0.0191179
+   Pass :  1   Iteration :   9  ||B r|| = 0.0183001
+   Pass :  1   Iteration :  10  ||B r|| = 0.0181721
+   Pass :  1   Iteration :  11  ||B r|| = 0.0156068
+   Pass :  1   Iteration :  12  ||B r|| = 0.0155459
+   Pass :  1   Iteration :  13  ||B r|| = 0.014403
+   Pass :  1   Iteration :  14  ||B r|| = 0.0143588
+   Pass :  1   Iteration :  15  ||B r|| = 0.0135545
+   Pass :  1   Iteration :  16  ||B r|| = 0.0135382
+   Pass :  1   Iteration :  17  ||B r|| = 0.0130322
+   Pass :  1   Iteration :  18  ||B r|| = 0.0125354
+   Pass :  1   Iteration :  19  ||B r|| = 0.0122266
+   Pass :  1   Iteration :  20  ||B r|| = 0.0108615
+   Pass :  1   Iteration :  21  ||B r|| = 0.0108614
+   Pass :  1   Iteration :  22  ||B r|| = 0.00970565
+   Pass :  1   Iteration :  23  ||B r|| = 0.00970515
+   Pass :  1   Iteration :  24  ||B r|| = 0.00855939
+   Pass :  1   Iteration :  25  ||B r|| = 0.00836874
+   Pass :  1   Iteration :  26  ||B r|| = 0.00771871
+   Pass :  1   Iteration :  27  ||B r|| = 0.00717169
+   Pass :  1   Iteration :  28  ||B r|| = 0.00696769
+   Pass :  1   Iteration :  29  ||B r|| = 0.00606509
+   Pass :  1   Iteration :  30  ||B r|| = 0.00606296
+   Pass :  1   Iteration :  31  ||B r|| = 0.00520498
+   Pass :  1   Iteration :  32  ||B r|| = 0.00516713
+   Pass :  1   Iteration :  33  ||B r|| = 0.00430612
+   Pass :  1   Iteration :  34  ||B r|| = 0.0040375
+   Pass :  1   Iteration :  35  ||B r|| = 0.00352252
+   Pass :  1   Iteration :  36  ||B r|| = 0.00297273
+   Pass :  1   Iteration :  37  ||B r|| = 0.00288746
+   Pass :  1   Iteration :  38  ||B r|| = 0.00214078
+   Pass :  1   Iteration :  39  ||B r|| = 0.0021383
+   Pass :  1   Iteration :  40  ||B r|| = 0.00163763
+   Pass :  1   Iteration :  41  ||B r|| = 0.0015311
+   Pass :  1   Iteration :  42  ||B r|| = 0.00128619
+   Pass :  1   Iteration :  43  ||B r|| = 0.00101578
+   Pass :  1   Iteration :  44  ||B r|| = 0.000996947
+   Pass :  1   Iteration :  45  ||B r|| = 0.000803315
+   Pass :  1   Iteration :  46  ||B r|| = 0.000797521
+   Pass :  1   Iteration :  47  ||B r|| = 0.000714146
+   Pass :  1   Iteration :  48  ||B r|| = 0.000697919
+   Pass :  1   Iteration :  49  ||B r|| = 0.000655925
+   Pass :  1   Iteration :  50  ||B r|| = 0.000625559
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 0.000618872
+   Pass :  2   Iteration :  52  ||B r|| = 0.000586465
+   Pass :  2   Iteration :  53  ||B r|| = 0.000586052
+   Pass :  2   Iteration :  54  ||B r|| = 0.000557417
+   Pass :  2   Iteration :  55  ||B r|| = 0.000542206
+   Pass :  2   Iteration :  56  ||B r|| = 0.000509114
+   Pass :  2   Iteration :  57  ||B r|| = 0.000473098
+   Pass :  2   Iteration :  58  ||B r|| = 0.000455139
+   Pass :  2   Iteration :  59  ||B r|| = 0.000398013
+   Pass :  2   Iteration :  60  ||B r|| = 0.000397302
+   Pass :  2   Iteration :  61  ||B r|| = 0.000349938
+   Pass :  2   Iteration :  62  ||B r|| = 0.00034704
+   Pass :  2   Iteration :  63  ||B r|| = 0.000314769
+   Pass :  2   Iteration :  64  ||B r|| = 0.000300538
+   Pass :  2   Iteration :  65  ||B r|| = 0.000285898
+   Pass :  2   Iteration :  66  ||B r|| = 0.000255744
+   Pass :  2   Iteration :  67  ||B r|| = 0.000249283
+   Pass :  2   Iteration :  68  ||B r|| = 0.000215596
+   Pass :  2   Iteration :  69  ||B r|| = 0.00021549
+   Pass :  2   Iteration :  70  ||B r|| = 0.000182327
+   Pass :  2   Iteration :  71  ||B r|| = 0.000180289
+   Pass :  2   Iteration :  72  ||B r|| = 0.00015632
+   Pass :  2   Iteration :  73  ||B r|| = 0.000135838
+   Pass :  2   Iteration :  74  ||B r|| = 0.000123613
+   Pass :  2   Iteration :  75  ||B r|| = 9.43373e-05
+   Pass :  2   Iteration :  76  ||B r|| = 9.42765e-05
+   Pass :  2   Iteration :  77  ||B r|| = 7.18741e-05
+   Pass :  2   Iteration :  78  ||B r|| = 6.97432e-05
+   Pass :  2   Iteration :  79  ||B r|| = 6.07355e-05
+   Pass :  2   Iteration :  80  ||B r|| = 5.63377e-05
+   Pass :  2   Iteration :  81  ||B r|| = 5.12011e-05
+   Pass :  2   Iteration :  82  ||B r|| = 4.2137e-05
+   Pass :  2   Iteration :  83  ||B r|| = 4.16798e-05
+   Pass :  2   Iteration :  84  ||B r|| = 3.46174e-05
+   Pass :  2   Iteration :  85  ||B r|| = 3.42915e-05
+   Pass :  2   Iteration :  86  ||B r|| = 3.08496e-05
+   Pass :  2   Iteration :  87  ||B r|| = 2.91955e-05
+   Pass :  2   Iteration :  88  ||B r|| = 2.74831e-05
+   Pass :  2   Iteration :  89  ||B r|| = 2.55666e-05
+   Pass :  2   Iteration :  90  ||B r|| = 2.46958e-05
+   Pass :  2   Iteration :  91  ||B r|| = 2.20629e-05
+   Pass :  2   Iteration :  92  ||B r|| = 2.20393e-05
+   Pass :  2   Iteration :  93  ||B r|| = 1.98858e-05
+   Pass :  2   Iteration :  94  ||B r|| = 1.95265e-05
+   Pass :  2   Iteration :  95  ||B r|| = 1.8629e-05
+   Pass :  2   Iteration :  96  ||B r|| = 1.76896e-05
+   Pass :  2   Iteration :  97  ||B r|| = 1.7486e-05
+   Pass :  2   Iteration :  98  ||B r|| = 1.66895e-05
+   Pass :  2   Iteration :  99  ||B r|| = 1.64623e-05
+   Pass :  2   Iteration : 100  ||B r|| = 1.52206e-05
+Restarting...
+   Pass :  3   Iteration : 101  ||B r|| = 1.52205e-05
+   Pass :  3   Iteration : 102  ||B r|| = 1.48373e-05
+   Pass :  3   Iteration : 103  ||B r|| = 1.48339e-05
+   Pass :  3   Iteration : 104  ||B r|| = 1.47629e-05
+   Pass :  3   Iteration : 105  ||B r|| = 1.42381e-05
+   Pass :  3   Iteration : 106  ||B r|| = 1.41964e-05
+   Pass :  3   Iteration : 107  ||B r|| = 1.35097e-05
+   Pass :  3   Iteration : 108  ||B r|| = 1.34834e-05
+   Pass :  3   Iteration : 109  ||B r|| = 1.27974e-05
+   Pass :  3   Iteration : 110  ||B r|| = 1.27928e-05
+   Pass :  3   Iteration : 111  ||B r|| = 1.21922e-05
+   Pass :  3   Iteration : 112  ||B r|| = 1.20549e-05
+   Pass :  3   Iteration : 113  ||B r|| = 1.18268e-05
+   Pass :  3   Iteration : 114  ||B r|| = 1.11367e-05
+   Pass :  3   Iteration : 115  ||B r|| = 1.10641e-05
+   Pass :  3   Iteration : 116  ||B r|| = 9.70155e-06
+   Pass :  3   Iteration : 117  ||B r|| = 9.68918e-06
+   Pass :  3   Iteration : 118  ||B r|| = 8.41859e-06
+   Pass :  3   Iteration : 119  ||B r|| = 8.33612e-06
+   Pass :  3   Iteration : 120  ||B r|| = 7.46782e-06
+   Pass :  3   Iteration : 121  ||B r|| = 6.98112e-06
+   Pass :  3   Iteration : 122  ||B r|| = 6.77193e-06
+   Pass :  3   Iteration : 123  ||B r|| = 5.73383e-06
+   Pass :  3   Iteration : 124  ||B r|| = 5.71615e-06
+   Pass :  3   Iteration : 125  ||B r|| = 4.62728e-06
+   Pass :  3   Iteration : 126  ||B r|| = 4.58033e-06
+   Pass :  3   Iteration : 127  ||B r|| = 3.87684e-06
+   Pass :  3   Iteration : 128  ||B r|| = 3.70327e-06
+   Pass :  3   Iteration : 129  ||B r|| = 3.40779e-06
+   Pass :  3   Iteration : 130  ||B r|| = 3.11203e-06
+   Pass :  3   Iteration : 131  ||B r|| = 3.06127e-06
+   Pass :  3   Iteration : 132  ||B r|| = 2.66494e-06
+   Pass :  3   Iteration : 133  ||B r|| = 2.66492e-06
+   Pass :  3   Iteration : 134  ||B r|| = 2.27334e-06
+   Pass :  3   Iteration : 135  ||B r|| = 2.24097e-06
+   Pass :  3   Iteration : 136  ||B r|| = 1.99619e-06
+   Pass :  3   Iteration : 137  ||B r|| = 1.83387e-06
+   Pass :  3   Iteration : 138  ||B r|| = 1.72523e-06
+   Pass :  3   Iteration : 139  ||B r|| = 1.51783e-06
+   Pass :  3   Iteration : 140  ||B r|| = 1.50252e-06
+   Pass :  3   Iteration : 141  ||B r|| = 1.25423e-06
+   Pass :  3   Iteration : 142  ||B r|| = 1.25071e-06
+   Pass :  3   Iteration : 143  ||B r|| = 1.11636e-06
+   Pass :  3   Iteration : 144  ||B r|| = 1.07203e-06
+   Pass :  3   Iteration : 145  ||B r|| = 9.98103e-07
+   Pass :  3   Iteration : 146  ||B r|| = 9.16113e-07
+   Pass :  3   Iteration : 147  ||B r|| = 9.03641e-07
+   Pass :  3   Iteration : 148  ||B r|| = 8.1855e-07
+   Pass :  3   Iteration : 149  ||B r|| = 8.17341e-07
+   Pass :  3   Iteration : 150  ||B r|| = 7.08372e-07
+Restarting...
+   Pass :  4   Iteration : 151  ||B r|| = 6.99448e-07
+   Pass :  4   Iteration : 152  ||B r|| = 6.61008e-07
+   Pass :  4   Iteration : 153  ||B r|| = 6.39231e-07
+   Pass :  4   Iteration : 154  ||B r|| = 6.25043e-07
+   Pass :  4   Iteration : 155  ||B r|| = 5.80258e-07
+   Pass :  4   Iteration : 156  ||B r|| = 5.75183e-07
+   Pass :  4   Iteration : 157  ||B r|| = 5.15028e-07
+   Pass :  4   Iteration : 158  ||B r|| = 5.14995e-07
+   Pass :  4   Iteration : 159  ||B r|| = 4.5915e-07
+   Pass :  4   Iteration : 160  ||B r|| = 4.50864e-07
+   Pass :  4   Iteration : 161  ||B r|| = 4.2472e-07
+   Pass :  4   Iteration : 162  ||B r|| = 3.94848e-07
+   Pass :  4   Iteration : 163  ||B r|| = 3.85486e-07
+   Pass :  4   Iteration : 164  ||B r|| = 3.32015e-07
+   Pass :  4   Iteration : 165  ||B r|| = 3.30713e-07
+   Pass :  4   Iteration : 166  ||B r|| = 2.82884e-07
+   Pass :  4   Iteration : 167  ||B r|| = 2.81608e-07
+   Pass :  4   Iteration : 168  ||B r|| = 2.49132e-07
+   Pass :  4   Iteration : 169  ||B r|| = 2.38284e-07
+   Pass :  4   Iteration : 170  ||B r|| = 2.22343e-07
+   Pass :  4   Iteration : 171  ||B r|| = 1.98031e-07
+   Pass :  4   Iteration : 172  ||B r|| = 1.94992e-07
+   Pass :  4   Iteration : 173  ||B r|| = 1.59718e-07
+   Pass :  4   Iteration : 174  ||B r|| = 1.59438e-07
+   Pass :  4   Iteration : 175  ||B r|| = 1.29137e-07
+   Pass :  4   Iteration : 176  ||B r|| = 1.22967e-07
+   Pass :  4   Iteration : 177  ||B r|| = 1.09611e-07
+   Pass :  4   Iteration : 178  ||B r|| = 9.5634e-08
+   Pass :  4   Iteration : 179  ||B r|| = 9.23188e-08
+   Pass :  4   Iteration : 180  ||B r|| = 7.39099e-08
+   Pass :  4   Iteration : 181  ||B r|| = 7.38795e-08
+   Pass :  4   Iteration : 182  ||B r|| = 5.85346e-08
+   Pass :  4   Iteration : 183  ||B r|| = 5.75933e-08
+   Pass :  4   Iteration : 184  ||B r|| = 4.90044e-08
+   Pass :  4   Iteration : 185  ||B r|| = 4.51497e-08
+   Pass :  4   Iteration : 186  ||B r|| = 4.22566e-08
+   Pass :  4   Iteration : 187  ||B r|| = 3.67448e-08
+   Pass :  4   Iteration : 188  ||B r|| = 3.66463e-08
+   Pass :  4   Iteration : 189  ||B r|| = 3.09553e-08
+   Pass :  4   Iteration : 190  ||B r|| = 3.07377e-08
+   Pass :  4   Iteration : 191  ||B r|| = 2.61137e-08
+   Pass :  4   Iteration : 192  ||B r|| = 2.47554e-08
+   Pass :  4   Iteration : 193  ||B r|| = 2.24693e-08
+   Pass :  4   Iteration : 194  ||B r|| = 2.04221e-08
+GMRES+GS converged in 194 iterations with a residual norm of 2.04221e-08.
+solver took 34.7799s.
+|| q_h - q_ex || / || q_ex || = 8.71533e-07
+|| t_h - t_ex || / || t_ex || = 8.70766e-07

examples/regress_test/p2_o3_nlc_hdg4_umfpack.txt

@@ -0,0 +1,73 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --nonlinear
+   --nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 4
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+
+
+MFEM Warning: Upwinded flux is implemented only component-wise.
+ ... in function: mfem::ComponentwiseUpwindFlux::ComponentwiseUpwindFlux(const mfem::FluxFunction&)
+ ... in file: fem/hyperbolic.cpp:904
+
+***********************************************************
+dim(V) = 3280
+dim(W) = 1600
+dim(V+W) = 4880
+***********************************************************
+Assembly took 0.180007s.
+Preconditioner took 0.232488s.
+   Pass :  1   Iteration :   0  ||B r|| = 1.87609
+   Pass :  1   Iteration :   1  ||B r|| = 1.87432
+   Pass :  1   Iteration :   2  ||B r|| = 0.16601
+   Pass :  1   Iteration :   3  ||B r|| = 0.161362
+   Pass :  1   Iteration :   4  ||B r|| = 0.0301646
+   Pass :  1   Iteration :   5  ||B r|| = 0.0295347
+   Pass :  1   Iteration :   6  ||B r|| = 0.00663266
+   Pass :  1   Iteration :   7  ||B r|| = 0.0030216
+   Pass :  1   Iteration :   8  ||B r|| = 0.00220853
+   Pass :  1   Iteration :   9  ||B r|| = 0.00111606
+   Pass :  1   Iteration :  10  ||B r|| = 0.000831543
+   Pass :  1   Iteration :  11  ||B r|| = 0.000380993
+   Pass :  1   Iteration :  12  ||B r|| = 0.000181673
+   Pass :  1   Iteration :  13  ||B r|| = 0.000172683
+   Pass :  1   Iteration :  14  ||B r|| = 7.12328e-05
+   Pass :  1   Iteration :  15  ||B r|| = 3.4761e-05
+   Pass :  1   Iteration :  16  ||B r|| = 3.46875e-05
+   Pass :  1   Iteration :  17  ||B r|| = 1.67153e-05
+   Pass :  1   Iteration :  18  ||B r|| = 8.63663e-06
+   Pass :  1   Iteration :  19  ||B r|| = 8.62185e-06
+   Pass :  1   Iteration :  20  ||B r|| = 3.82383e-06
+   Pass :  1   Iteration :  21  ||B r|| = 1.51087e-06
+GMRES+UMFPack converged in 21 iterations with a residual norm of 1.51087e-06.
+solver took 2.8086s.
+|| q_h - q_ex || / || q_ex || = 1.32976e-06
+|| t_h - t_ex || / || t_ex || = 3.94381e-07

examples/regress_test/p2_o3_nlp.txt

@@ -0,0 +1,251 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-flux
+   --nonlinear-pot
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 3280
+dim(W) = 1600
+dim(V+W) = 4880
+***********************************************************
+Assembly took 0.222587s.
+Preconditioner took 0.0651669s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.022067
+   Pass :  1   Iteration :   1  ||B r|| = 0.022067
+   Pass :  1   Iteration :   2  ||B r|| = 0.0208806
+   Pass :  1   Iteration :   3  ||B r|| = 0.0207166
+   Pass :  1   Iteration :   4  ||B r|| = 0.0196263
+   Pass :  1   Iteration :   5  ||B r|| = 0.0193127
+   Pass :  1   Iteration :   6  ||B r|| = 0.0193121
+   Pass :  1   Iteration :   7  ||B r|| = 0.0191814
+   Pass :  1   Iteration :   8  ||B r|| = 0.0190947
+   Pass :  1   Iteration :   9  ||B r|| = 0.0181552
+   Pass :  1   Iteration :  10  ||B r|| = 0.0180903
+   Pass :  1   Iteration :  11  ||B r|| = 0.0155652
+   Pass :  1   Iteration :  12  ||B r|| = 0.0155258
+   Pass :  1   Iteration :  13  ||B r|| = 0.014398
+   Pass :  1   Iteration :  14  ||B r|| = 0.0143695
+   Pass :  1   Iteration :  15  ||B r|| = 0.0135542
+   Pass :  1   Iteration :  16  ||B r|| = 0.0135172
+   Pass :  1   Iteration :  17  ||B r|| = 0.013078
+   Pass :  1   Iteration :  18  ||B r|| = 0.0124796
+   Pass :  1   Iteration :  19  ||B r|| = 0.0122545
+   Pass :  1   Iteration :  20  ||B r|| = 0.0108222
+   Pass :  1   Iteration :  21  ||B r|| = 0.0108121
+   Pass :  1   Iteration :  22  ||B r|| = 0.00967796
+   Pass :  1   Iteration :  23  ||B r|| = 0.00965621
+   Pass :  1   Iteration :  24  ||B r|| = 0.00858242
+   Pass :  1   Iteration :  25  ||B r|| = 0.0082878
+   Pass :  1   Iteration :  26  ||B r|| = 0.00776935
+   Pass :  1   Iteration :  27  ||B r|| = 0.00707955
+   Pass :  1   Iteration :  28  ||B r|| = 0.00697587
+   Pass :  1   Iteration :  29  ||B r|| = 0.00602293
+   Pass :  1   Iteration :  30  ||B r|| = 0.00601624
+   Pass :  1   Iteration :  31  ||B r|| = 0.00520713
+   Pass :  1   Iteration :  32  ||B r|| = 0.00510208
+   Pass :  1   Iteration :  33  ||B r|| = 0.0043413
+   Pass :  1   Iteration :  34  ||B r|| = 0.0039158
+   Pass :  1   Iteration :  35  ||B r|| = 0.00357861
+   Pass :  1   Iteration :  36  ||B r|| = 0.00291643
+   Pass :  1   Iteration :  37  ||B r|| = 0.0028874
+   Pass :  1   Iteration :  38  ||B r|| = 0.00212203
+   Pass :  1   Iteration :  39  ||B r|| = 0.00209429
+   Pass :  1   Iteration :  40  ||B r|| = 0.00167641
+   Pass :  1   Iteration :  41  ||B r|| = 0.00148563
+   Pass :  1   Iteration :  42  ||B r|| = 0.00132712
+   Pass :  1   Iteration :  43  ||B r|| = 0.000994524
+   Pass :  1   Iteration :  44  ||B r|| = 0.000994216
+   Pass :  1   Iteration :  45  ||B r|| = 0.000816498
+   Pass :  1   Iteration :  46  ||B r|| = 0.000799419
+   Pass :  1   Iteration :  47  ||B r|| = 0.000732239
+   Pass :  1   Iteration :  48  ||B r|| = 0.000702926
+   Pass :  1   Iteration :  49  ||B r|| = 0.000674539
+   Pass :  1   Iteration :  50  ||B r|| = 0.000627216
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 0.00062193
+   Pass :  2   Iteration :  52  ||B r|| = 0.0005892
+   Pass :  2   Iteration :  53  ||B r|| = 0.000588011
+   Pass :  2   Iteration :  54  ||B r|| = 0.000561997
+   Pass :  2   Iteration :  55  ||B r|| = 0.000543751
+   Pass :  2   Iteration :  56  ||B r|| = 0.000513188
+   Pass :  2   Iteration :  57  ||B r|| = 0.000478002
+   Pass :  2   Iteration :  58  ||B r|| = 0.000465486
+   Pass :  2   Iteration :  59  ||B r|| = 0.000400445
+   Pass :  2   Iteration :  60  ||B r|| = 0.000400246
+   Pass :  2   Iteration :  61  ||B r|| = 0.000352688
+   Pass :  2   Iteration :  62  ||B r|| = 0.000346668
+   Pass :  2   Iteration :  63  ||B r|| = 0.00031797
+   Pass :  2   Iteration :  64  ||B r|| = 0.000298695
+   Pass :  2   Iteration :  65  ||B r|| = 0.000286142
+   Pass :  2   Iteration :  66  ||B r|| = 0.000252347
+   Pass :  2   Iteration :  67  ||B r|| = 0.000250182
+   Pass :  2   Iteration :  68  ||B r|| = 0.000214181
+   Pass :  2   Iteration :  69  ||B r|| = 0.0002141
+   Pass :  2   Iteration :  70  ||B r|| = 0.000182374
+   Pass :  2   Iteration :  71  ||B r|| = 0.000175328
+   Pass :  2   Iteration :  72  ||B r|| = 0.000156797
+   Pass :  2   Iteration :  73  ||B r|| = 0.000132149
+   Pass :  2   Iteration :  74  ||B r|| = 0.000125112
+   Pass :  2   Iteration :  75  ||B r|| = 9.32759e-05
+   Pass :  2   Iteration :  76  ||B r|| = 9.28174e-05
+   Pass :  2   Iteration :  77  ||B r|| = 7.07716e-05
+   Pass :  2   Iteration :  78  ||B r|| = 6.67241e-05
+   Pass :  2   Iteration :  79  ||B r|| = 5.9584e-05
+   Pass :  2   Iteration :  80  ||B r|| = 5.37448e-05
+   Pass :  2   Iteration :  81  ||B r|| = 5.12479e-05
+   Pass :  2   Iteration :  82  ||B r|| = 4.10174e-05
+   Pass :  2   Iteration :  83  ||B r|| = 4.10131e-05
+   Pass :  2   Iteration :  84  ||B r|| = 3.4515e-05
+   Pass :  2   Iteration :  85  ||B r|| = 3.34606e-05
+   Pass :  2   Iteration :  86  ||B r|| = 3.0915e-05
+   Pass :  2   Iteration :  87  ||B r|| = 2.83458e-05
+   Pass :  2   Iteration :  88  ||B r|| = 2.72626e-05
+   Pass :  2   Iteration :  89  ||B r|| = 2.47577e-05
+   Pass :  2   Iteration :  90  ||B r|| = 2.44277e-05
+   Pass :  2   Iteration :  91  ||B r|| = 2.16201e-05
+   Pass :  2   Iteration :  92  ||B r|| = 2.15866e-05
+   Pass :  2   Iteration :  93  ||B r|| = 1.97523e-05
+   Pass :  2   Iteration :  94  ||B r|| = 1.8927e-05
+   Pass :  2   Iteration :  95  ||B r|| = 1.85086e-05
+   Pass :  2   Iteration :  96  ||B r|| = 1.71252e-05
+   Pass :  2   Iteration :  97  ||B r|| = 1.70655e-05
+   Pass :  2   Iteration :  98  ||B r|| = 1.62333e-05
+   Pass :  2   Iteration :  99  ||B r|| = 1.61703e-05
+   Pass :  2   Iteration : 100  ||B r|| = 1.49155e-05
+Restarting...
+   Pass :  3   Iteration : 101  ||B r|| = 1.48969e-05
+   Pass :  3   Iteration : 102  ||B r|| = 1.46428e-05
+   Pass :  3   Iteration : 103  ||B r|| = 1.46181e-05
+   Pass :  3   Iteration : 104  ||B r|| = 1.46045e-05
+   Pass :  3   Iteration : 105  ||B r|| = 1.39796e-05
+   Pass :  3   Iteration : 106  ||B r|| = 1.39764e-05
+   Pass :  3   Iteration : 107  ||B r|| = 1.32178e-05
+   Pass :  3   Iteration : 108  ||B r|| = 1.32131e-05
+   Pass :  3   Iteration : 109  ||B r|| = 1.25714e-05
+   Pass :  3   Iteration : 110  ||B r|| = 1.25594e-05
+   Pass :  3   Iteration : 111  ||B r|| = 1.21126e-05
+   Pass :  3   Iteration : 112  ||B r|| = 1.18562e-05
+   Pass :  3   Iteration : 113  ||B r|| = 1.17378e-05
+   Pass :  3   Iteration : 114  ||B r|| = 1.0941e-05
+   Pass :  3   Iteration : 115  ||B r|| = 1.09339e-05
+   Pass :  3   Iteration : 116  ||B r|| = 9.54335e-06
+   Pass :  3   Iteration : 117  ||B r|| = 9.51161e-06
+   Pass :  3   Iteration : 118  ||B r|| = 8.35379e-06
+   Pass :  3   Iteration : 119  ||B r|| = 8.04087e-06
+   Pass :  3   Iteration : 120  ||B r|| = 7.51408e-06
+   Pass :  3   Iteration : 121  ||B r|| = 6.80584e-06
+   Pass :  3   Iteration : 122  ||B r|| = 6.75339e-06
+   Pass :  3   Iteration : 123  ||B r|| = 5.66556e-06
+   Pass :  3   Iteration : 124  ||B r|| = 5.65505e-06
+   Pass :  3   Iteration : 125  ||B r|| = 4.72256e-06
+   Pass :  3   Iteration : 126  ||B r|| = 4.4958e-06
+   Pass :  3   Iteration : 127  ||B r|| = 3.98298e-06
+   Pass :  3   Iteration : 128  ||B r|| = 3.60389e-06
+   Pass :  3   Iteration : 129  ||B r|| = 3.48606e-06
+   Pass :  3   Iteration : 130  ||B r|| = 3.02899e-06
+   Pass :  3   Iteration : 131  ||B r|| = 3.02877e-06
+   Pass :  3   Iteration : 132  ||B r|| = 2.61592e-06
+   Pass :  3   Iteration : 133  ||B r|| = 2.58403e-06
+   Pass :  3   Iteration : 134  ||B r|| = 2.35026e-06
+   Pass :  3   Iteration : 135  ||B r|| = 2.2251e-06
+   Pass :  3   Iteration : 136  ||B r|| = 2.08811e-06
+   Pass :  3   Iteration : 137  ||B r|| = 1.80365e-06
+   Pass :  3   Iteration : 138  ||B r|| = 1.77968e-06
+   Pass :  3   Iteration : 139  ||B r|| = 1.47939e-06
+   Pass :  3   Iteration : 140  ||B r|| = 1.47722e-06
+   Pass :  3   Iteration : 141  ||B r|| = 1.25568e-06
+   Pass :  3   Iteration : 142  ||B r|| = 1.20881e-06
+   Pass :  3   Iteration : 143  ||B r|| = 1.14307e-06
+   Pass :  3   Iteration : 144  ||B r|| = 1.04547e-06
+   Pass :  3   Iteration : 145  ||B r|| = 1.02875e-06
+   Pass :  3   Iteration : 146  ||B r|| = 9.14727e-07
+   Pass :  3   Iteration : 147  ||B r|| = 9.14676e-07
+   Pass :  3   Iteration : 148  ||B r|| = 8.15389e-07
+   Pass :  3   Iteration : 149  ||B r|| = 7.99485e-07
+   Pass :  3   Iteration : 150  ||B r|| = 7.26065e-07
+Restarting...
+   Pass :  4   Iteration : 151  ||B r|| = 6.99694e-07
+   Pass :  4   Iteration : 152  ||B r|| = 6.84535e-07
+   Pass :  4   Iteration : 153  ||B r|| = 6.45898e-07
+   Pass :  4   Iteration : 154  ||B r|| = 6.43768e-07
+   Pass :  4   Iteration : 155  ||B r|| = 5.83403e-07
+   Pass :  4   Iteration : 156  ||B r|| = 5.8321e-07
+   Pass :  4   Iteration : 157  ||B r|| = 5.24621e-07
+   Pass :  4   Iteration : 158  ||B r|| = 5.19743e-07
+   Pass :  4   Iteration : 159  ||B r|| = 4.7987e-07
+   Pass :  4   Iteration : 160  ||B r|| = 4.51871e-07
+   Pass :  4   Iteration : 161  ||B r|| = 4.41169e-07
+   Pass :  4   Iteration : 162  ||B r|| = 3.9456e-07
+   Pass :  4   Iteration : 163  ||B r|| = 3.93689e-07
+   Pass :  4   Iteration : 164  ||B r|| = 3.34259e-07
+   Pass :  4   Iteration : 165  ||B r|| = 3.28851e-07
+   Pass :  4   Iteration : 166  ||B r|| = 2.90374e-07
+   Pass :  4   Iteration : 167  ||B r|| = 2.77779e-07
+   Pass :  4   Iteration : 168  ||B r|| = 2.62914e-07
+   Pass :  4   Iteration : 169  ||B r|| = 2.36644e-07
+   Pass :  4   Iteration : 170  ||B r|| = 2.32757e-07
+   Pass :  4   Iteration : 171  ||B r|| = 1.99214e-07
+   Pass :  4   Iteration : 172  ||B r|| = 1.98993e-07
+   Pass :  4   Iteration : 173  ||B r|| = 1.63031e-07
+   Pass :  4   Iteration : 174  ||B r|| = 1.56437e-07
+   Pass :  4   Iteration : 175  ||B r|| = 1.35415e-07
+   Pass :  4   Iteration : 176  ||B r|| = 1.17884e-07
+   Pass :  4   Iteration : 177  ||B r|| = 1.14297e-07
+   Pass :  4   Iteration : 178  ||B r|| = 9.45492e-08
+   Pass :  4   Iteration : 179  ||B r|| = 9.45387e-08
+   Pass :  4   Iteration : 180  ||B r|| = 7.49812e-08
+   Pass :  4   Iteration : 181  ||B r|| = 7.2875e-08
+   Pass :  4   Iteration : 182  ||B r|| = 6.20294e-08
+   Pass :  4   Iteration : 183  ||B r|| = 5.70125e-08
+   Pass :  4   Iteration : 184  ||B r|| = 5.34086e-08
+   Pass :  4   Iteration : 185  ||B r|| = 4.71283e-08
+   Pass :  4   Iteration : 186  ||B r|| = 4.69364e-08
+   Pass :  4   Iteration : 187  ||B r|| = 4.02849e-08
+   Pass :  4   Iteration : 188  ||B r|| = 3.9792e-08
+   Pass :  4   Iteration : 189  ||B r|| = 3.52261e-08
+   Pass :  4   Iteration : 190  ||B r|| = 3.36232e-08
+   Pass :  4   Iteration : 191  ||B r|| = 3.07331e-08
+   Pass :  4   Iteration : 192  ||B r|| = 2.82049e-08
+   Pass :  4   Iteration : 193  ||B r|| = 2.78326e-08
+   Pass :  4   Iteration : 194  ||B r|| = 2.53142e-08
+   Pass :  4   Iteration : 195  ||B r|| = 2.52644e-08
+   Pass :  4   Iteration : 196  ||B r|| = 2.37377e-08
+   Pass :  4   Iteration : 197  ||B r|| = 2.31322e-08
+   Pass :  4   Iteration : 198  ||B r|| = 2.26843e-08
+   Pass :  4   Iteration : 199  ||B r|| = 2.21043e-08
+   Pass :  4   Iteration : 200  ||B r|| = 2.16948e-08
+GMRES+GS converged in 200 iterations with a residual norm of 2.16948e-08.
+solver took 10.2713s.
+|| q_h - q_ex || / || q_ex || = 1.09996e-06
+|| t_h - t_ex || / || t_ex || = 1.10664e-06

examples/regress_test/p2_o3_nlp_umfpack.txt

@@ -0,0 +1,59 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-flux
+   --nonlinear-pot
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 3280
+dim(W) = 1600
+dim(V+W) = 4880
+***********************************************************
+Assembly took 0.22423s.
+Preconditioner took 0.0832514s.
+   Pass :  1   Iteration :   0  ||B r|| = 1.8759
+   Pass :  1   Iteration :   1  ||B r|| = 1.87404
+   Pass :  1   Iteration :   2  ||B r|| = 0.10605
+   Pass :  1   Iteration :   3  ||B r|| = 0.0890947
+   Pass :  1   Iteration :   4  ||B r|| = 0.00999938
+   Pass :  1   Iteration :   5  ||B r|| = 0.00420422
+   Pass :  1   Iteration :   6  ||B r|| = 0.00113566
+   Pass :  1   Iteration :   7  ||B r|| = 0.00016919
+   Pass :  1   Iteration :   8  ||B r|| = 8.64586e-05
+   Pass :  1   Iteration :   9  ||B r|| = 5.74549e-06
+   Pass :  1   Iteration :  10  ||B r|| = 5.21245e-06
+   Pass :  1   Iteration :  11  ||B r|| = 2.97692e-07
+GMRES+UMFPack converged in 11 iterations with a residual norm of 2.97692e-07.
+solver took 0.474743s.
+|| q_h - q_ex || / || q_ex || = 4.12091e-07
+|| t_h - t_ex || / || t_ex || = 1.10557e-07

examples/regress_test/p2_o3_nlu.txt

@@ -0,0 +1,251 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --no-nonlinear
+   --nonlinear-flux
+   --no-nonlinear-pot
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 3280
+dim(W) = 1600
+dim(V+W) = 4880
+***********************************************************
+Assembly took 0.243693s.
+Preconditioner took 0.162164s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.022067
+   Pass :  1   Iteration :   1  ||B r|| = 0.022067
+   Pass :  1   Iteration :   2  ||B r|| = 0.0208806
+   Pass :  1   Iteration :   3  ||B r|| = 0.0207166
+   Pass :  1   Iteration :   4  ||B r|| = 0.0196263
+   Pass :  1   Iteration :   5  ||B r|| = 0.0193127
+   Pass :  1   Iteration :   6  ||B r|| = 0.0193121
+   Pass :  1   Iteration :   7  ||B r|| = 0.0191814
+   Pass :  1   Iteration :   8  ||B r|| = 0.0190947
+   Pass :  1   Iteration :   9  ||B r|| = 0.0181552
+   Pass :  1   Iteration :  10  ||B r|| = 0.0180903
+   Pass :  1   Iteration :  11  ||B r|| = 0.0155652
+   Pass :  1   Iteration :  12  ||B r|| = 0.0155258
+   Pass :  1   Iteration :  13  ||B r|| = 0.014398
+   Pass :  1   Iteration :  14  ||B r|| = 0.0143695
+   Pass :  1   Iteration :  15  ||B r|| = 0.0135542
+   Pass :  1   Iteration :  16  ||B r|| = 0.0135172
+   Pass :  1   Iteration :  17  ||B r|| = 0.013078
+   Pass :  1   Iteration :  18  ||B r|| = 0.0124796
+   Pass :  1   Iteration :  19  ||B r|| = 0.0122545
+   Pass :  1   Iteration :  20  ||B r|| = 0.0108222
+   Pass :  1   Iteration :  21  ||B r|| = 0.0108121
+   Pass :  1   Iteration :  22  ||B r|| = 0.00967796
+   Pass :  1   Iteration :  23  ||B r|| = 0.00965621
+   Pass :  1   Iteration :  24  ||B r|| = 0.00858242
+   Pass :  1   Iteration :  25  ||B r|| = 0.0082878
+   Pass :  1   Iteration :  26  ||B r|| = 0.00776935
+   Pass :  1   Iteration :  27  ||B r|| = 0.00707955
+   Pass :  1   Iteration :  28  ||B r|| = 0.00697587
+   Pass :  1   Iteration :  29  ||B r|| = 0.00602293
+   Pass :  1   Iteration :  30  ||B r|| = 0.00601624
+   Pass :  1   Iteration :  31  ||B r|| = 0.00520713
+   Pass :  1   Iteration :  32  ||B r|| = 0.00510208
+   Pass :  1   Iteration :  33  ||B r|| = 0.0043413
+   Pass :  1   Iteration :  34  ||B r|| = 0.0039158
+   Pass :  1   Iteration :  35  ||B r|| = 0.00357861
+   Pass :  1   Iteration :  36  ||B r|| = 0.00291643
+   Pass :  1   Iteration :  37  ||B r|| = 0.0028874
+   Pass :  1   Iteration :  38  ||B r|| = 0.00212203
+   Pass :  1   Iteration :  39  ||B r|| = 0.00209429
+   Pass :  1   Iteration :  40  ||B r|| = 0.00167641
+   Pass :  1   Iteration :  41  ||B r|| = 0.00148563
+   Pass :  1   Iteration :  42  ||B r|| = 0.00132712
+   Pass :  1   Iteration :  43  ||B r|| = 0.000994524
+   Pass :  1   Iteration :  44  ||B r|| = 0.000994216
+   Pass :  1   Iteration :  45  ||B r|| = 0.000816498
+   Pass :  1   Iteration :  46  ||B r|| = 0.000799419
+   Pass :  1   Iteration :  47  ||B r|| = 0.000732239
+   Pass :  1   Iteration :  48  ||B r|| = 0.000702926
+   Pass :  1   Iteration :  49  ||B r|| = 0.000674539
+   Pass :  1   Iteration :  50  ||B r|| = 0.000627216
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 0.00062193
+   Pass :  2   Iteration :  52  ||B r|| = 0.0005892
+   Pass :  2   Iteration :  53  ||B r|| = 0.000588011
+   Pass :  2   Iteration :  54  ||B r|| = 0.000561997
+   Pass :  2   Iteration :  55  ||B r|| = 0.000543751
+   Pass :  2   Iteration :  56  ||B r|| = 0.000513188
+   Pass :  2   Iteration :  57  ||B r|| = 0.000478002
+   Pass :  2   Iteration :  58  ||B r|| = 0.000465486
+   Pass :  2   Iteration :  59  ||B r|| = 0.000400445
+   Pass :  2   Iteration :  60  ||B r|| = 0.000400246
+   Pass :  2   Iteration :  61  ||B r|| = 0.000352688
+   Pass :  2   Iteration :  62  ||B r|| = 0.000346668
+   Pass :  2   Iteration :  63  ||B r|| = 0.00031797
+   Pass :  2   Iteration :  64  ||B r|| = 0.000298695
+   Pass :  2   Iteration :  65  ||B r|| = 0.000286142
+   Pass :  2   Iteration :  66  ||B r|| = 0.000252347
+   Pass :  2   Iteration :  67  ||B r|| = 0.000250182
+   Pass :  2   Iteration :  68  ||B r|| = 0.000214181
+   Pass :  2   Iteration :  69  ||B r|| = 0.0002141
+   Pass :  2   Iteration :  70  ||B r|| = 0.000182374
+   Pass :  2   Iteration :  71  ||B r|| = 0.000175328
+   Pass :  2   Iteration :  72  ||B r|| = 0.000156797
+   Pass :  2   Iteration :  73  ||B r|| = 0.000132149
+   Pass :  2   Iteration :  74  ||B r|| = 0.000125112
+   Pass :  2   Iteration :  75  ||B r|| = 9.32759e-05
+   Pass :  2   Iteration :  76  ||B r|| = 9.28174e-05
+   Pass :  2   Iteration :  77  ||B r|| = 7.07716e-05
+   Pass :  2   Iteration :  78  ||B r|| = 6.67241e-05
+   Pass :  2   Iteration :  79  ||B r|| = 5.9584e-05
+   Pass :  2   Iteration :  80  ||B r|| = 5.37448e-05
+   Pass :  2   Iteration :  81  ||B r|| = 5.12479e-05
+   Pass :  2   Iteration :  82  ||B r|| = 4.10174e-05
+   Pass :  2   Iteration :  83  ||B r|| = 4.10131e-05
+   Pass :  2   Iteration :  84  ||B r|| = 3.4515e-05
+   Pass :  2   Iteration :  85  ||B r|| = 3.34606e-05
+   Pass :  2   Iteration :  86  ||B r|| = 3.0915e-05
+   Pass :  2   Iteration :  87  ||B r|| = 2.83458e-05
+   Pass :  2   Iteration :  88  ||B r|| = 2.72626e-05
+   Pass :  2   Iteration :  89  ||B r|| = 2.47577e-05
+   Pass :  2   Iteration :  90  ||B r|| = 2.44277e-05
+   Pass :  2   Iteration :  91  ||B r|| = 2.16201e-05
+   Pass :  2   Iteration :  92  ||B r|| = 2.15866e-05
+   Pass :  2   Iteration :  93  ||B r|| = 1.97523e-05
+   Pass :  2   Iteration :  94  ||B r|| = 1.8927e-05
+   Pass :  2   Iteration :  95  ||B r|| = 1.85086e-05
+   Pass :  2   Iteration :  96  ||B r|| = 1.71252e-05
+   Pass :  2   Iteration :  97  ||B r|| = 1.70655e-05
+   Pass :  2   Iteration :  98  ||B r|| = 1.62333e-05
+   Pass :  2   Iteration :  99  ||B r|| = 1.61703e-05
+   Pass :  2   Iteration : 100  ||B r|| = 1.49155e-05
+Restarting...
+   Pass :  3   Iteration : 101  ||B r|| = 1.48969e-05
+   Pass :  3   Iteration : 102  ||B r|| = 1.46428e-05
+   Pass :  3   Iteration : 103  ||B r|| = 1.46181e-05
+   Pass :  3   Iteration : 104  ||B r|| = 1.46045e-05
+   Pass :  3   Iteration : 105  ||B r|| = 1.39796e-05
+   Pass :  3   Iteration : 106  ||B r|| = 1.39764e-05
+   Pass :  3   Iteration : 107  ||B r|| = 1.32178e-05
+   Pass :  3   Iteration : 108  ||B r|| = 1.32131e-05
+   Pass :  3   Iteration : 109  ||B r|| = 1.25714e-05
+   Pass :  3   Iteration : 110  ||B r|| = 1.25594e-05
+   Pass :  3   Iteration : 111  ||B r|| = 1.21126e-05
+   Pass :  3   Iteration : 112  ||B r|| = 1.18562e-05
+   Pass :  3   Iteration : 113  ||B r|| = 1.17378e-05
+   Pass :  3   Iteration : 114  ||B r|| = 1.0941e-05
+   Pass :  3   Iteration : 115  ||B r|| = 1.09339e-05
+   Pass :  3   Iteration : 116  ||B r|| = 9.54335e-06
+   Pass :  3   Iteration : 117  ||B r|| = 9.51161e-06
+   Pass :  3   Iteration : 118  ||B r|| = 8.35379e-06
+   Pass :  3   Iteration : 119  ||B r|| = 8.04087e-06
+   Pass :  3   Iteration : 120  ||B r|| = 7.51408e-06
+   Pass :  3   Iteration : 121  ||B r|| = 6.80584e-06
+   Pass :  3   Iteration : 122  ||B r|| = 6.75339e-06
+   Pass :  3   Iteration : 123  ||B r|| = 5.66556e-06
+   Pass :  3   Iteration : 124  ||B r|| = 5.65505e-06
+   Pass :  3   Iteration : 125  ||B r|| = 4.72256e-06
+   Pass :  3   Iteration : 126  ||B r|| = 4.4958e-06
+   Pass :  3   Iteration : 127  ||B r|| = 3.98298e-06
+   Pass :  3   Iteration : 128  ||B r|| = 3.60389e-06
+   Pass :  3   Iteration : 129  ||B r|| = 3.48606e-06
+   Pass :  3   Iteration : 130  ||B r|| = 3.02899e-06
+   Pass :  3   Iteration : 131  ||B r|| = 3.02877e-06
+   Pass :  3   Iteration : 132  ||B r|| = 2.61592e-06
+   Pass :  3   Iteration : 133  ||B r|| = 2.58403e-06
+   Pass :  3   Iteration : 134  ||B r|| = 2.35026e-06
+   Pass :  3   Iteration : 135  ||B r|| = 2.2251e-06
+   Pass :  3   Iteration : 136  ||B r|| = 2.08811e-06
+   Pass :  3   Iteration : 137  ||B r|| = 1.80365e-06
+   Pass :  3   Iteration : 138  ||B r|| = 1.77968e-06
+   Pass :  3   Iteration : 139  ||B r|| = 1.47939e-06
+   Pass :  3   Iteration : 140  ||B r|| = 1.47722e-06
+   Pass :  3   Iteration : 141  ||B r|| = 1.25568e-06
+   Pass :  3   Iteration : 142  ||B r|| = 1.20881e-06
+   Pass :  3   Iteration : 143  ||B r|| = 1.14307e-06
+   Pass :  3   Iteration : 144  ||B r|| = 1.04547e-06
+   Pass :  3   Iteration : 145  ||B r|| = 1.02875e-06
+   Pass :  3   Iteration : 146  ||B r|| = 9.14727e-07
+   Pass :  3   Iteration : 147  ||B r|| = 9.14676e-07
+   Pass :  3   Iteration : 148  ||B r|| = 8.15389e-07
+   Pass :  3   Iteration : 149  ||B r|| = 7.99485e-07
+   Pass :  3   Iteration : 150  ||B r|| = 7.26065e-07
+Restarting...
+   Pass :  4   Iteration : 151  ||B r|| = 6.99694e-07
+   Pass :  4   Iteration : 152  ||B r|| = 6.84535e-07
+   Pass :  4   Iteration : 153  ||B r|| = 6.45898e-07
+   Pass :  4   Iteration : 154  ||B r|| = 6.43768e-07
+   Pass :  4   Iteration : 155  ||B r|| = 5.83403e-07
+   Pass :  4   Iteration : 156  ||B r|| = 5.8321e-07
+   Pass :  4   Iteration : 157  ||B r|| = 5.24621e-07
+   Pass :  4   Iteration : 158  ||B r|| = 5.19743e-07
+   Pass :  4   Iteration : 159  ||B r|| = 4.7987e-07
+   Pass :  4   Iteration : 160  ||B r|| = 4.51871e-07
+   Pass :  4   Iteration : 161  ||B r|| = 4.41169e-07
+   Pass :  4   Iteration : 162  ||B r|| = 3.9456e-07
+   Pass :  4   Iteration : 163  ||B r|| = 3.93689e-07
+   Pass :  4   Iteration : 164  ||B r|| = 3.34259e-07
+   Pass :  4   Iteration : 165  ||B r|| = 3.28851e-07
+   Pass :  4   Iteration : 166  ||B r|| = 2.90374e-07
+   Pass :  4   Iteration : 167  ||B r|| = 2.77779e-07
+   Pass :  4   Iteration : 168  ||B r|| = 2.62914e-07
+   Pass :  4   Iteration : 169  ||B r|| = 2.36644e-07
+   Pass :  4   Iteration : 170  ||B r|| = 2.32757e-07
+   Pass :  4   Iteration : 171  ||B r|| = 1.99214e-07
+   Pass :  4   Iteration : 172  ||B r|| = 1.98993e-07
+   Pass :  4   Iteration : 173  ||B r|| = 1.63031e-07
+   Pass :  4   Iteration : 174  ||B r|| = 1.56437e-07
+   Pass :  4   Iteration : 175  ||B r|| = 1.35415e-07
+   Pass :  4   Iteration : 176  ||B r|| = 1.17884e-07
+   Pass :  4   Iteration : 177  ||B r|| = 1.14297e-07
+   Pass :  4   Iteration : 178  ||B r|| = 9.45492e-08
+   Pass :  4   Iteration : 179  ||B r|| = 9.45387e-08
+   Pass :  4   Iteration : 180  ||B r|| = 7.49812e-08
+   Pass :  4   Iteration : 181  ||B r|| = 7.2875e-08
+   Pass :  4   Iteration : 182  ||B r|| = 6.20294e-08
+   Pass :  4   Iteration : 183  ||B r|| = 5.70125e-08
+   Pass :  4   Iteration : 184  ||B r|| = 5.34086e-08
+   Pass :  4   Iteration : 185  ||B r|| = 4.71283e-08
+   Pass :  4   Iteration : 186  ||B r|| = 4.69364e-08
+   Pass :  4   Iteration : 187  ||B r|| = 4.02849e-08
+   Pass :  4   Iteration : 188  ||B r|| = 3.9792e-08
+   Pass :  4   Iteration : 189  ||B r|| = 3.52261e-08
+   Pass :  4   Iteration : 190  ||B r|| = 3.36232e-08
+   Pass :  4   Iteration : 191  ||B r|| = 3.07331e-08
+   Pass :  4   Iteration : 192  ||B r|| = 2.82049e-08
+   Pass :  4   Iteration : 193  ||B r|| = 2.78326e-08
+   Pass :  4   Iteration : 194  ||B r|| = 2.53142e-08
+   Pass :  4   Iteration : 195  ||B r|| = 2.52644e-08
+   Pass :  4   Iteration : 196  ||B r|| = 2.37377e-08
+   Pass :  4   Iteration : 197  ||B r|| = 2.31322e-08
+   Pass :  4   Iteration : 198  ||B r|| = 2.26843e-08
+   Pass :  4   Iteration : 199  ||B r|| = 2.21043e-08
+   Pass :  4   Iteration : 200  ||B r|| = 2.16948e-08
+GMRES+GS converged in 200 iterations with a residual norm of 2.16948e-08.
+solver took 27.535s.
+|| q_h - q_ex || / || q_ex || = 1.09996e-06
+|| t_h - t_ex || / || t_ex || = 1.10664e-06

examples/regress_test/p2_o3_nlu_umfpack.txt

@@ -0,0 +1,59 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --no-hybridization
+   --no-nonlinear
+   --nonlinear-flux
+   --no-nonlinear-pot
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 3280
+dim(W) = 1600
+dim(V+W) = 4880
+***********************************************************
+Assembly took 0.244139s.
+Preconditioner took 0.163206s.
+   Pass :  1   Iteration :   0  ||B r|| = 1.8759
+   Pass :  1   Iteration :   1  ||B r|| = 1.87404
+   Pass :  1   Iteration :   2  ||B r|| = 0.10605
+   Pass :  1   Iteration :   3  ||B r|| = 0.0890947
+   Pass :  1   Iteration :   4  ||B r|| = 0.00999938
+   Pass :  1   Iteration :   5  ||B r|| = 0.00420422
+   Pass :  1   Iteration :   6  ||B r|| = 0.00113566
+   Pass :  1   Iteration :   7  ||B r|| = 0.00016919
+   Pass :  1   Iteration :   8  ||B r|| = 8.64586e-05
+   Pass :  1   Iteration :   9  ||B r|| = 5.74549e-06
+   Pass :  1   Iteration :  10  ||B r|| = 5.21245e-06
+   Pass :  1   Iteration :  11  ||B r|| = 2.97692e-07
+GMRES+UMFPack converged in 11 iterations with a residual norm of 2.97692e-07.
+solver took 1.72204s.
+|| q_h - q_ex || / || q_ex || = 4.12091e-07
+|| t_h - t_ex || / || t_ex || = 1.10557e-07

examples/regress_test/p2_o3_umfpack.txt

@@ -0,0 +1,62 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --bc-neumann
+   --no-reduction
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 3280
+dim(W) = 1600
+dim(V+W) = 4880
+***********************************************************
+Assembly took 0.255527s.
+Preconditioner took 0.0359602s.
+   Pass :  1   Iteration :   0  ||B r|| = 1.82811
+   Pass :  1   Iteration :   1  ||B r|| = 1.74851
+   Pass :  1   Iteration :   2  ||B r|| = 0.26157
+   Pass :  1   Iteration :   3  ||B r|| = 0.260109
+   Pass :  1   Iteration :   4  ||B r|| = 0.0414097
+   Pass :  1   Iteration :   5  ||B r|| = 0.0225871
+   Pass :  1   Iteration :   6  ||B r|| = 0.00541294
+   Pass :  1   Iteration :   7  ||B r|| = 0.00246937
+   Pass :  1   Iteration :   8  ||B r|| = 0.000801299
+   Pass :  1   Iteration :   9  ||B r|| = 0.000242776
+   Pass :  1   Iteration :  10  ||B r|| = 0.000185039
+   Pass :  1   Iteration :  11  ||B r|| = 4.57219e-05
+   Pass :  1   Iteration :  12  ||B r|| = 4.53027e-05
+   Pass :  1   Iteration :  13  ||B r|| = 1.82442e-05
+   Pass :  1   Iteration :  14  ||B r|| = 6.44667e-06
+   Pass :  1   Iteration :  15  ||B r|| = 6.07208e-06
+   Pass :  1   Iteration :  16  ||B r|| = 2.0149e-06
+   Pass :  1   Iteration :  17  ||B r|| = 1.32354e-06
+GMRES+UMFPack converged in 17 iterations with a residual norm of 1.32354e-06.
+solver took 0.065152s.
+|| q_h - q_ex || / || q_ex || = 2.40858e-06
+|| t_h - t_ex || / || t_ex || = 6.44073e-07

examples/regress_test/p3_o1_dg_hb.txt

@@ -0,0 +1,50 @@
+Options used:
+   --mesh 
+   --ncells-x 20
+   --ncells-y 20
+   --size-x 1
+   --size-y 1
+   --order 1
+   --discontinuous
+   --centered
+   --problem 3
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1e-07
+   --velocity 1
+   --stab_diff 0.5
+   --hybridization
+   --no-nonlinear
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00169381s.
+***********************************************************
+dim(V) = 3200
+dim(W) = 1600
+dim(M) = 1680
+dim(V+W+M) = 6480
+***********************************************************
+Assembly took 0.0176451s.
+Preconditioner took 9.001e-06s.
+   Pass :  1   Iteration :   0  ||B r|| = 11.6753
+   Pass :  1   Iteration :   1  ||B r|| = 5.74672
+   Pass :  1   Iteration :   2  ||B r|| = 3.19801
+   Pass :  1   Iteration :   3  ||B r|| = 0.750678
+   Pass :  1   Iteration :   4  ||B r|| = 0.089894
+   Pass :  1   Iteration :   5  ||B r|| = 0.0104578
+   Pass :  1   Iteration :   6  ||B r|| = 0.00347189
+   Pass :  1   Iteration :   7  ||B r|| = 0.000197833
+   Pass :  1   Iteration :   8  ||B r|| = 3.56619e-05
+   Pass :  1   Iteration :   9  ||B r|| = 3.18273e-06
+GMRES+GS converged in 9 iterations with a residual norm of 3.18273e-06.
+solver took 0.00198556s.
+|| q_h - q_ex || / || q_ex || = 0.351557
+|| t_h - t_ex || / || t_ex || = 0.052059

examples/regress_test/p3_o1_dg_hb_nl.txt

@@ -0,0 +1,215 @@
+Options used:
+   --mesh 
+   --ncells-x 20
+   --ncells-y 20
+   --size-x 1
+   --size-y 1
+   --order 1
+   --discontinuous
+   --no-broken-RT
+   --centered
+   --problem 3
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1e-07
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-flux
+   --no-nonlinear-pot
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.017069s.
+***********************************************************
+dim(V) = 3200
+dim(W) = 1600
+dim(M) = 1680
+dim(V+W+M) = 6480
+***********************************************************
+Assembly took 0.00895548s.
+Preconditioner took 5.5463e-05s.
+LBFGS iteration 0 : ||r|| = 0.0176863
+LBFGS iteration 1 : ||r|| = 0.0177559, ||r||/||r_0|| = 1.00393
+LBFGS iteration 2 : ||r|| = 0.0181656, ||r||/||r_0|| = 1.0271
+LBFGS iteration 3 : ||r|| = 0.0183349, ||r||/||r_0|| = 1.03667
+LBFGS iteration 4 : ||r|| = 0.0616206, ||r||/||r_0|| = 3.48409
+LBFGS iteration 5 : ||r|| = 0.0408661, ||r||/||r_0|| = 2.31061
+LBFGS iteration 6 : ||r|| = 0.050128, ||r||/||r_0|| = 2.83429
+LBFGS iteration 7 : ||r|| = 0.0142123, ||r||/||r_0|| = 0.803579
+LBFGS iteration 8 : ||r|| = 0.0100388, ||r||/||r_0|| = 0.567604
+LBFGS iteration 9 : ||r|| = 0.0163692, ||r||/||r_0|| = 0.92553
+LBFGS iteration 10 : ||r|| = 0.0172847, ||r||/||r_0|| = 0.977292
+LBFGS iteration 11 : ||r|| = 0.0205551, ||r||/||r_0|| = 1.1622
+LBFGS iteration 12 : ||r|| = 0.0203594, ||r||/||r_0|| = 1.15114
+LBFGS iteration 13 : ||r|| = 0.0366231, ||r||/||r_0|| = 2.0707
+LBFGS iteration 14 : ||r|| = 0.0204175, ||r||/||r_0|| = 1.15443
+LBFGS iteration 15 : ||r|| = 0.0409078, ||r||/||r_0|| = 2.31297
+LBFGS iteration 16 : ||r|| = 0.0130461, ||r||/||r_0|| = 0.73764
+LBFGS iteration 17 : ||r|| = 0.00566817, ||r||/||r_0|| = 0.320484
+LBFGS iteration 18 : ||r|| = 0.00292798, ||r||/||r_0|| = 0.165551
+LBFGS iteration 19 : ||r|| = 0.00212401, ||r||/||r_0|| = 0.120093
+LBFGS iteration 20 : ||r|| = 0.00120763, ||r||/||r_0|| = 0.0682806
+LBFGS iteration 21 : ||r|| = 0.00137247, ||r||/||r_0|| = 0.077601
+LBFGS iteration 22 : ||r|| = 0.00122957, ||r||/||r_0|| = 0.0695212
+LBFGS iteration 23 : ||r|| = 0.00149969, ||r||/||r_0|| = 0.0847941
+LBFGS iteration 24 : ||r|| = 0.00153547, ||r||/||r_0|| = 0.0868168
+LBFGS iteration 25 : ||r|| = 0.00103896, ||r||/||r_0|| = 0.0587441
+LBFGS iteration 26 : ||r|| = 0.000837703, ||r||/||r_0|| = 0.0473646
+LBFGS iteration 27 : ||r|| = 0.000730943, ||r||/||r_0|| = 0.0413282
+LBFGS iteration 28 : ||r|| = 0.000540398, ||r||/||r_0|| = 0.0305547
+LBFGS iteration 29 : ||r|| = 0.000624913, ||r||/||r_0|| = 0.0353332
+LBFGS iteration 30 : ||r|| = 0.000512208, ||r||/||r_0|| = 0.0289608
+LBFGS iteration 31 : ||r|| = 0.000596801, ||r||/||r_0|| = 0.0337437
+LBFGS iteration 32 : ||r|| = 0.000445415, ||r||/||r_0|| = 0.0251842
+LBFGS iteration 33 : ||r|| = 0.000418279, ||r||/||r_0|| = 0.0236499
+LBFGS iteration 34 : ||r|| = 0.000259397, ||r||/||r_0|| = 0.0146666
+LBFGS iteration 35 : ||r|| = 0.000235846, ||r||/||r_0|| = 0.013335
+LBFGS iteration 36 : ||r|| = 0.000315463, ||r||/||r_0|| = 0.0178366
+LBFGS iteration 37 : ||r|| = 0.000577426, ||r||/||r_0|| = 0.0326482
+LBFGS iteration 38 : ||r|| = 0.000874589, ||r||/||r_0|| = 0.0494502
+LBFGS iteration 39 : ||r|| = 0.000545193, ||r||/||r_0|| = 0.0308258
+LBFGS iteration 40 : ||r|| = 0.000994735, ||r||/||r_0|| = 0.0562433
+LBFGS iteration 41 : ||r|| = 0.000481429, ||r||/||r_0|| = 0.0272205
+LBFGS iteration 42 : ||r|| = 0.0008811, ||r||/||r_0|| = 0.0498183
+LBFGS iteration 43 : ||r|| = 0.000218085, ||r||/||r_0|| = 0.0123307
+LBFGS iteration 44 : ||r|| = 0.000159511, ||r||/||r_0|| = 0.00901889
+LBFGS iteration 45 : ||r|| = 5.45211e-05, ||r||/||r_0|| = 0.00308268
+LBFGS iteration 46 : ||r|| = 5.78341e-05, ||r||/||r_0|| = 0.00327
+LBFGS iteration 47 : ||r|| = 5.92185e-05, ||r||/||r_0|| = 0.00334827
+LBFGS iteration 48 : ||r|| = 9.73784e-05, ||r||/||r_0|| = 0.00550587
+LBFGS iteration 49 : ||r|| = 0.000138427, ||r||/||r_0|| = 0.0078268
+LBFGS iteration 50 : ||r|| = 0.000116232, ||r||/||r_0|| = 0.00657186
+LBFGS iteration 51 : ||r|| = 0.000134195, ||r||/||r_0|| = 0.00758753
+LBFGS iteration 52 : ||r|| = 0.000113768, ||r||/||r_0|| = 0.00643256
+LBFGS iteration 53 : ||r|| = 8.95477e-05, ||r||/||r_0|| = 0.00506312
+LBFGS iteration 54 : ||r|| = 7.10941e-05, ||r||/||r_0|| = 0.00401973
+LBFGS iteration 55 : ||r|| = 7.83524e-05, ||r||/||r_0|| = 0.00443012
+LBFGS iteration 56 : ||r|| = 5.41869e-05, ||r||/||r_0|| = 0.00306378
+LBFGS iteration 57 : ||r|| = 6.54361e-05, ||r||/||r_0|| = 0.00369982
+LBFGS iteration 58 : ||r|| = 4.20196e-05, ||r||/||r_0|| = 0.00237583
+LBFGS iteration 59 : ||r|| = 2.4456e-05, ||r||/||r_0|| = 0.00138277
+LBFGS iteration 60 : ||r|| = 2.4681e-05, ||r||/||r_0|| = 0.00139549
+LBFGS iteration 61 : ||r|| = 4.49901e-05, ||r||/||r_0|| = 0.00254379
+LBFGS iteration 62 : ||r|| = 5.0166e-05, ||r||/||r_0|| = 0.00283644
+LBFGS iteration 63 : ||r|| = 3.02193e-05, ||r||/||r_0|| = 0.00170863
+LBFGS iteration 64 : ||r|| = 2.50938e-05, ||r||/||r_0|| = 0.00141883
+LBFGS iteration 65 : ||r|| = 2.14888e-05, ||r||/||r_0|| = 0.001215
+LBFGS iteration 66 : ||r|| = 2.76062e-05, ||r||/||r_0|| = 0.00156088
+LBFGS iteration 67 : ||r|| = 2.19443e-05, ||r||/||r_0|| = 0.00124075
+LBFGS iteration 68 : ||r|| = 2.73122e-05, ||r||/||r_0|| = 0.00154426
+LBFGS iteration 69 : ||r|| = 3.70152e-05, ||r||/||r_0|| = 0.00209287
+LBFGS iteration 70 : ||r|| = 3.10424e-05, ||r||/||r_0|| = 0.00175517
+LBFGS iteration 71 : ||r|| = 2.7278e-05, ||r||/||r_0|| = 0.00154233
+LBFGS iteration 72 : ||r|| = 3.92654e-05, ||r||/||r_0|| = 0.00222011
+LBFGS iteration 73 : ||r|| = 3.61658e-05, ||r||/||r_0|| = 0.00204485
+LBFGS iteration 74 : ||r|| = 2.52977e-05, ||r||/||r_0|| = 0.00143036
+LBFGS iteration 75 : ||r|| = 3.42292e-05, ||r||/||r_0|| = 0.00193535
+LBFGS iteration 76 : ||r|| = 3.64372e-05, ||r||/||r_0|| = 0.00206019
+LBFGS iteration 77 : ||r|| = 2.52401e-05, ||r||/||r_0|| = 0.0014271
+LBFGS iteration 78 : ||r|| = 3.78801e-05, ||r||/||r_0|| = 0.00214178
+LBFGS iteration 79 : ||r|| = 3.92759e-05, ||r||/||r_0|| = 0.0022207
+LBFGS iteration 80 : ||r|| = 3.18735e-05, ||r||/||r_0|| = 0.00180216
+LBFGS iteration 81 : ||r|| = 2.96258e-05, ||r||/||r_0|| = 0.00167507
+LBFGS iteration 82 : ||r|| = 4.26882e-05, ||r||/||r_0|| = 0.00241363
+LBFGS iteration 83 : ||r|| = 1.99283e-05, ||r||/||r_0|| = 0.00112677
+LBFGS iteration 84 : ||r|| = 1.83222e-05, ||r||/||r_0|| = 0.00103596
+LBFGS iteration 85 : ||r|| = 3.91629e-06, ||r||/||r_0|| = 0.000221431
+LBFGS iteration 86 : ||r|| = 2.77235e-06, ||r||/||r_0|| = 0.000156752
+LBFGS iteration 87 : ||r|| = 5.46098e-06, ||r||/||r_0|| = 0.000308769
+LBFGS iteration 88 : ||r|| = 7.45354e-06, ||r||/||r_0|| = 0.000421431
+LBFGS iteration 89 : ||r|| = 1.14572e-05, ||r||/||r_0|| = 0.000647801
+LBFGS iteration 90 : ||r|| = 8.43631e-06, ||r||/||r_0|| = 0.000476998
+LBFGS iteration 91 : ||r|| = 1.34693e-05, ||r||/||r_0|| = 0.000761566
+LBFGS iteration 92 : ||r|| = 1.36538e-05, ||r||/||r_0|| = 0.000772001
+LBFGS iteration 93 : ||r|| = 3.37147e-05, ||r||/||r_0|| = 0.00190626
+LBFGS iteration 94 : ||r|| = 1.68047e-05, ||r||/||r_0|| = 0.000950156
+LBFGS iteration 95 : ||r|| = 2.22129e-05, ||r||/||r_0|| = 0.00125594
+LBFGS iteration 96 : ||r|| = 3.12312e-06, ||r||/||r_0|| = 0.000176585
+LBFGS iteration 97 : ||r|| = 1.84773e-06, ||r||/||r_0|| = 0.000104473
+LBFGS iteration 98 : ||r|| = 3.01648e-06, ||r||/||r_0|| = 0.000170555
+LBFGS iteration 99 : ||r|| = 3.98302e-06, ||r||/||r_0|| = 0.000225204
+LBFGS iteration 100 : ||r|| = 4.0937e-06, ||r||/||r_0|| = 0.000231462
+LBFGS iteration 101 : ||r|| = 7.75263e-06, ||r||/||r_0|| = 0.000438342
+LBFGS iteration 102 : ||r|| = 5.17157e-06, ||r||/||r_0|| = 0.000292406
+LBFGS iteration 103 : ||r|| = 1.01397e-05, ||r||/||r_0|| = 0.000573307
+LBFGS iteration 104 : ||r|| = 3.91549e-06, ||r||/||r_0|| = 0.000221386
+LBFGS iteration 105 : ||r|| = 4.51086e-06, ||r||/||r_0|| = 0.000255049
+LBFGS iteration 106 : ||r|| = 1.3212e-06, ||r||/||r_0|| = 7.47022e-05
+LBFGS iteration 107 : ||r|| = 8.97781e-07, ||r||/||r_0|| = 5.07614e-05
+LBFGS iteration 108 : ||r|| = 1.15254e-06, ||r||/||r_0|| = 6.51658e-05
+LBFGS iteration 109 : ||r|| = 1.7572e-06, ||r||/||r_0|| = 9.93539e-05
+LBFGS iteration 110 : ||r|| = 1.48689e-06, ||r||/||r_0|| = 8.40701e-05
+LBFGS iteration 111 : ||r|| = 2.91207e-06, ||r||/||r_0|| = 0.000164651
+LBFGS iteration 112 : ||r|| = 8.57e-07, ||r||/||r_0|| = 4.84557e-05
+LBFGS iteration 113 : ||r|| = 1.10774e-06, ||r||/||r_0|| = 6.26327e-05
+LBFGS iteration 114 : ||r|| = 1.26595e-06, ||r||/||r_0|| = 7.15781e-05
+LBFGS iteration 115 : ||r|| = 1.15131e-06, ||r||/||r_0|| = 6.5096e-05
+LBFGS iteration 116 : ||r|| = 1.523e-06, ||r||/||r_0|| = 8.61119e-05
+LBFGS iteration 117 : ||r|| = 2.07575e-06, ||r||/||r_0|| = 0.000117365
+LBFGS iteration 118 : ||r|| = 2.07607e-06, ||r||/||r_0|| = 0.000117383
+LBFGS iteration 119 : ||r|| = 1.7568e-06, ||r||/||r_0|| = 9.93313e-05
+LBFGS iteration 120 : ||r|| = 2.65432e-06, ||r||/||r_0|| = 0.000150078
+LBFGS iteration 121 : ||r|| = 2.24973e-06, ||r||/||r_0|| = 0.000127202
+LBFGS iteration 122 : ||r|| = 2.9224e-06, ||r||/||r_0|| = 0.000165235
+LBFGS iteration 123 : ||r|| = 1.82461e-06, ||r||/||r_0|| = 0.000103165
+LBFGS iteration 124 : ||r|| = 2.33641e-06, ||r||/||r_0|| = 0.000132103
+LBFGS iteration 125 : ||r|| = 4.92589e-07, ||r||/||r_0|| = 2.78515e-05
+LBFGS iteration 126 : ||r|| = 2.40269e-07, ||r||/||r_0|| = 1.35851e-05
+LBFGS iteration 127 : ||r|| = 2.91841e-07, ||r||/||r_0|| = 1.6501e-05
+LBFGS iteration 128 : ||r|| = 1.07622e-06, ||r||/||r_0|| = 6.08505e-05
+LBFGS iteration 129 : ||r|| = 7.21656e-07, ||r||/||r_0|| = 4.08032e-05
+LBFGS iteration 130 : ||r|| = 4.82071e-07, ||r||/||r_0|| = 2.72568e-05
+LBFGS iteration 131 : ||r|| = 2.66587e-07, ||r||/||r_0|| = 1.50731e-05
+LBFGS iteration 132 : ||r|| = 2.39356e-07, ||r||/||r_0|| = 1.35334e-05
+LBFGS iteration 133 : ||r|| = 4.6404e-07, ||r||/||r_0|| = 2.62373e-05
+LBFGS iteration 134 : ||r|| = 5.73728e-07, ||r||/||r_0|| = 3.24391e-05
+LBFGS iteration 135 : ||r|| = 4.50134e-07, ||r||/||r_0|| = 2.5451e-05
+LBFGS iteration 136 : ||r|| = 9.87962e-07, ||r||/||r_0|| = 5.58604e-05
+LBFGS iteration 137 : ||r|| = 5.77943e-07, ||r||/||r_0|| = 3.26775e-05
+LBFGS iteration 138 : ||r|| = 7.49328e-07, ||r||/||r_0|| = 4.23678e-05
+LBFGS iteration 139 : ||r|| = 1.88762e-07, ||r||/||r_0|| = 1.06728e-05
+LBFGS iteration 140 : ||r|| = 1.27315e-07, ||r||/||r_0|| = 7.19853e-06
+LBFGS iteration 141 : ||r|| = 1.48767e-07, ||r||/||r_0|| = 8.41144e-06
+LBFGS iteration 142 : ||r|| = 2.69628e-07, ||r||/||r_0|| = 1.5245e-05
+LBFGS iteration 143 : ||r|| = 3.8879e-07, ||r||/||r_0|| = 2.19826e-05
+LBFGS iteration 144 : ||r|| = 6.33094e-07, ||r||/||r_0|| = 3.57958e-05
+LBFGS iteration 145 : ||r|| = 8.01578e-07, ||r||/||r_0|| = 4.5322e-05
+LBFGS iteration 146 : ||r|| = 1.46468e-06, ||r||/||r_0|| = 8.28143e-05
+LBFGS iteration 147 : ||r|| = 9.56041e-07, ||r||/||r_0|| = 5.40555e-05
+LBFGS iteration 148 : ||r|| = 2.80374e-06, ||r||/||r_0|| = 0.000158526
+LBFGS iteration 149 : ||r|| = 6.11482e-07, ||r||/||r_0|| = 3.45738e-05
+LBFGS iteration 150 : ||r|| = 6.66026e-08, ||r||/||r_0|| = 3.76578e-06
+LBFGS iteration 151 : ||r|| = 6.06604e-08, ||r||/||r_0|| = 3.4298e-06
+LBFGS iteration 152 : ||r|| = 7.07473e-08, ||r||/||r_0|| = 4.00012e-06
+LBFGS iteration 153 : ||r|| = 1.4772e-07, ||r||/||r_0|| = 8.35221e-06
+LBFGS iteration 154 : ||r|| = 8.89459e-08, ||r||/||r_0|| = 5.02909e-06
+LBFGS iteration 155 : ||r|| = 1.1204e-07, ||r||/||r_0|| = 6.33484e-06
+LBFGS iteration 156 : ||r|| = 3.03325e-08, ||r||/||r_0|| = 1.71503e-06
+LBFGS iteration 157 : ||r|| = 1.9289e-08, ||r||/||r_0|| = 1.09062e-06
+LBFGS iteration 158 : ||r|| = 1.94901e-08, ||r||/||r_0|| = 1.10199e-06
+LBFGS iteration 159 : ||r|| = 5.78168e-08, ||r||/||r_0|| = 3.26902e-06
+LBFGS iteration 160 : ||r|| = 3.07913e-08, ||r||/||r_0|| = 1.74097e-06
+LBFGS iteration 161 : ||r|| = 4.49479e-08, ||r||/||r_0|| = 2.5414e-06
+LBFGS iteration 162 : ||r|| = 3.70569e-08, ||r||/||r_0|| = 2.09524e-06
+LBFGS iteration 163 : ||r|| = 6.89008e-08, ||r||/||r_0|| = 3.89572e-06
+LBFGS iteration 164 : ||r|| = 3.16074e-08, ||r||/||r_0|| = 1.78711e-06
+LBFGS iteration 165 : ||r|| = 1.27752e-08, ||r||/||r_0|| = 7.22321e-07
+LBFGS/Newton+GMRES converged in 165 iterations with a residual norm of 1.27752e-08.
+solver took 14.0971s.
+|| q_h - q_ex || / || q_ex || = 0.351557
+|| t_h - t_ex || / || t_ex || = 0.052059

examples/regress_test/p3_o1_dg_hb_nl_newton.txt

@@ -0,0 +1,48 @@
+Options used:
+   --mesh 
+   --ncells-x 20
+   --ncells-y 20
+   --size-x 1
+   --size-y 1
+   --order 1
+   --discontinuous
+   --centered
+   --problem 3
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1e-07
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0207414s.
+***********************************************************
+dim(V) = 3200
+dim(W) = 1600
+dim(M) = 1680
+dim(V+W+M) = 6480
+***********************************************************
+Assembly took 0.00912456s.
+Preconditioner took 1.0539e-05s.
+Newton iteration  0 : ||r|| = 0.0176863
+Newton iteration  1 : ||r|| = 3.56271e-07, ||r||/||r_0|| = 2.01439e-05
+Newton iteration  2 : ||r|| = 3.50978e-10, ||r||/||r_0|| = 1.98447e-08
+Newton+GMRES+GS/Newton+GMRES converged in 2 iterations with a residual norm of 3.50978e-10.
+solver took 1.99737s.
+|| q_h - q_ex || / || q_ex || = 0.351557
+|| t_h - t_ex || / || t_ex || = 0.052059

examples/regress_test/p3_o1_dg_hb_upwind.txt

@@ -0,0 +1,47 @@
+Options used:
+   --mesh 
+   --ncells-x 20
+   --ncells-y 20
+   --size-x 1
+   --size-y 1
+   --order 1
+   --discontinuous
+   --upwinded
+   --problem 3
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1e-07
+   --velocity 1
+   --stab_diff 0.5
+   --hybridization
+   --no-nonlinear
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00165538s.
+***********************************************************
+dim(V) = 3200
+dim(W) = 1600
+dim(M) = 1680
+dim(V+W+M) = 6480
+***********************************************************
+Assembly took 0.0164776s.
+Preconditioner took 1.0172e-05s.
+   Pass :  1   Iteration :   0  ||B r|| = 13.4522
+   Pass :  1   Iteration :   1  ||B r|| = 6.65679
+   Pass :  1   Iteration :   2  ||B r|| = 2.41587
+   Pass :  1   Iteration :   3  ||B r|| = 0.323379
+   Pass :  1   Iteration :   4  ||B r|| = 0.00392814
+   Pass :  1   Iteration :   5  ||B r|| = 2.66137e-05
+   Pass :  1   Iteration :   6  ||B r|| = 1.65603e-08
+GMRES+GS converged in 6 iterations with a residual norm of 1.65603e-08.
+solver took 0.00177551s.
+|| q_h - q_ex || / || q_ex || = 0.329984
+|| t_h - t_ex || / || t_ex || = 0.0520583

examples/regress_test/p3_o1_dg_hb_upwind_nl.txt

@@ -0,0 +1,155 @@
+Options used:
+   --mesh 
+   --ncells-x 20
+   --ncells-y 20
+   --size-x 1
+   --size-y 1
+   --order 1
+   --discontinuous
+   --no-broken-RT
+   --upwinded
+   --problem 3
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1e-07
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-flux
+   --no-nonlinear-pot
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0127946s.
+***********************************************************
+dim(V) = 3200
+dim(W) = 1600
+dim(M) = 1680
+dim(V+W+M) = 6480
+***********************************************************
+Assembly took 0.0652081s.
+Preconditioner took 6.1726e-05s.
+LBFGS iteration 0 : ||r|| = 0.0183123
+LBFGS iteration 1 : ||r|| = 0.0183897, ||r||/||r_0|| = 1.00422
+LBFGS iteration 2 : ||r|| = 0.01822, ||r||/||r_0|| = 0.994957
+LBFGS iteration 3 : ||r|| = 0.0185995, ||r||/||r_0|| = 1.01568
+LBFGS iteration 4 : ||r|| = 0.0635017, ||r||/||r_0|| = 3.4677
+LBFGS iteration 5 : ||r|| = 0.041188, ||r||/||r_0|| = 2.2492
+LBFGS iteration 6 : ||r|| = 0.0445004, ||r||/||r_0|| = 2.43007
+LBFGS iteration 7 : ||r|| = 0.0132524, ||r||/||r_0|| = 0.723686
+LBFGS iteration 8 : ||r|| = 0.00970717, ||r||/||r_0|| = 0.530089
+LBFGS iteration 9 : ||r|| = 0.0175909, ||r||/||r_0|| = 0.960601
+LBFGS iteration 10 : ||r|| = 0.0170105, ||r||/||r_0|| = 0.928911
+LBFGS iteration 11 : ||r|| = 0.0224613, ||r||/||r_0|| = 1.22657
+LBFGS iteration 12 : ||r|| = 0.019769, ||r||/||r_0|| = 1.07955
+LBFGS iteration 13 : ||r|| = 0.034024, ||r||/||r_0|| = 1.85798
+LBFGS iteration 14 : ||r|| = 0.0133646, ||r||/||r_0|| = 0.729816
+LBFGS iteration 15 : ||r|| = 0.0197056, ||r||/||r_0|| = 1.07608
+LBFGS iteration 16 : ||r|| = 0.0103753, ||r||/||r_0|| = 0.566572
+LBFGS iteration 17 : ||r|| = 0.00753398, ||r||/||r_0|| = 0.411415
+LBFGS iteration 18 : ||r|| = 0.00495109, ||r||/||r_0|| = 0.270369
+LBFGS iteration 19 : ||r|| = 0.00263671, ||r||/||r_0|| = 0.143986
+LBFGS iteration 20 : ||r|| = 0.0018055, ||r||/||r_0|| = 0.0985947
+LBFGS iteration 21 : ||r|| = 0.0010424, ||r||/||r_0|| = 0.0569233
+LBFGS iteration 22 : ||r|| = 0.000845399, ||r||/||r_0|| = 0.0461655
+LBFGS iteration 23 : ||r|| = 0.0008781, ||r||/||r_0|| = 0.0479512
+LBFGS iteration 24 : ||r|| = 0.00201054, ||r||/||r_0|| = 0.109791
+LBFGS iteration 25 : ||r|| = 0.00360285, ||r||/||r_0|| = 0.196744
+LBFGS iteration 26 : ||r|| = 0.00105083, ||r||/||r_0|| = 0.0573838
+LBFGS iteration 27 : ||r|| = 0.000468076, ||r||/||r_0|| = 0.0255607
+LBFGS iteration 28 : ||r|| = 0.000388529, ||r||/||r_0|| = 0.0212168
+LBFGS iteration 29 : ||r|| = 0.000715295, ||r||/||r_0|| = 0.0390608
+LBFGS iteration 30 : ||r|| = 0.00100074, ||r||/||r_0|| = 0.0546484
+LBFGS iteration 31 : ||r|| = 0.00129052, ||r||/||r_0|| = 0.0704725
+LBFGS iteration 32 : ||r|| = 0.00120519, ||r||/||r_0|| = 0.0658131
+LBFGS iteration 33 : ||r|| = 0.00103999, ||r||/||r_0|| = 0.0567916
+LBFGS iteration 34 : ||r|| = 0.000844204, ||r||/||r_0|| = 0.0461003
+LBFGS iteration 35 : ||r|| = 0.000553374, ||r||/||r_0|| = 0.0302187
+LBFGS iteration 36 : ||r|| = 0.000334639, ||r||/||r_0|| = 0.018274
+LBFGS iteration 37 : ||r|| = 0.000323716, ||r||/||r_0|| = 0.0176775
+LBFGS iteration 38 : ||r|| = 0.000222974, ||r||/||r_0|| = 0.0121761
+LBFGS iteration 39 : ||r|| = 0.000117315, ||r||/||r_0|| = 0.00640633
+LBFGS iteration 40 : ||r|| = 4.5269e-05, ||r||/||r_0|| = 0.00247205
+LBFGS iteration 41 : ||r|| = 4.04003e-05, ||r||/||r_0|| = 0.00220618
+LBFGS iteration 42 : ||r|| = 3.79241e-05, ||r||/||r_0|| = 0.00207096
+LBFGS iteration 43 : ||r|| = 8.33788e-05, ||r||/||r_0|| = 0.00455315
+LBFGS iteration 44 : ||r|| = 0.000149064, ||r||/||r_0|| = 0.00814009
+LBFGS iteration 45 : ||r|| = 5.4113e-05, ||r||/||r_0|| = 0.002955
+LBFGS iteration 46 : ||r|| = 2.26301e-05, ||r||/||r_0|| = 0.00123578
+LBFGS iteration 47 : ||r|| = 2.05851e-05, ||r||/||r_0|| = 0.00112411
+LBFGS iteration 48 : ||r|| = 8.0932e-05, ||r||/||r_0|| = 0.00441954
+LBFGS iteration 49 : ||r|| = 3.19442e-05, ||r||/||r_0|| = 0.00174441
+LBFGS iteration 50 : ||r|| = 2.58603e-05, ||r||/||r_0|| = 0.00141218
+LBFGS iteration 51 : ||r|| = 2.80962e-05, ||r||/||r_0|| = 0.00153428
+LBFGS iteration 52 : ||r|| = 6.23129e-05, ||r||/||r_0|| = 0.00340278
+LBFGS iteration 53 : ||r|| = 1.09085e-05, ||r||/||r_0|| = 0.000595693
+LBFGS iteration 54 : ||r|| = 9.19398e-06, ||r||/||r_0|| = 0.000502065
+LBFGS iteration 55 : ||r|| = 1.29797e-05, ||r||/||r_0|| = 0.000708795
+LBFGS iteration 56 : ||r|| = 1.4571e-05, ||r||/||r_0|| = 0.000795694
+LBFGS iteration 57 : ||r|| = 1.82241e-05, ||r||/||r_0|| = 0.000995183
+LBFGS iteration 58 : ||r|| = 2.33195e-05, ||r||/||r_0|| = 0.00127343
+LBFGS iteration 59 : ||r|| = 2.34654e-05, ||r||/||r_0|| = 0.0012814
+LBFGS iteration 60 : ||r|| = 2.7346e-05, ||r||/||r_0|| = 0.00149331
+LBFGS iteration 61 : ||r|| = 2.43537e-05, ||r||/||r_0|| = 0.0013299
+LBFGS iteration 62 : ||r|| = 3.94601e-05, ||r||/||r_0|| = 0.00215484
+LBFGS iteration 63 : ||r|| = 3.01746e-05, ||r||/||r_0|| = 0.00164778
+LBFGS iteration 64 : ||r|| = 4.63432e-05, ||r||/||r_0|| = 0.00253071
+LBFGS iteration 65 : ||r|| = 2.49646e-05, ||r||/||r_0|| = 0.00136327
+LBFGS iteration 66 : ||r|| = 5.16036e-05, ||r||/||r_0|| = 0.00281797
+LBFGS iteration 67 : ||r|| = 4.13745e-06, ||r||/||r_0|| = 0.000225938
+LBFGS iteration 68 : ||r|| = 2.81975e-06, ||r||/||r_0|| = 0.000153981
+LBFGS iteration 69 : ||r|| = 2.11971e-06, ||r||/||r_0|| = 0.000115753
+LBFGS iteration 70 : ||r|| = 1.8112e-06, ||r||/||r_0|| = 9.89062e-05
+LBFGS iteration 71 : ||r|| = 1.91724e-06, ||r||/||r_0|| = 0.000104697
+LBFGS iteration 72 : ||r|| = 2.48608e-06, ||r||/||r_0|| = 0.00013576
+LBFGS iteration 73 : ||r|| = 2.18684e-06, ||r||/||r_0|| = 0.000119419
+LBFGS iteration 74 : ||r|| = 3.34982e-06, ||r||/||r_0|| = 0.000182927
+LBFGS iteration 75 : ||r|| = 2.64254e-06, ||r||/||r_0|| = 0.000144304
+LBFGS iteration 76 : ||r|| = 1.4576e-06, ||r||/||r_0|| = 7.95965e-05
+LBFGS iteration 77 : ||r|| = 1.39852e-06, ||r||/||r_0|| = 7.63704e-05
+LBFGS iteration 78 : ||r|| = 9.16242e-07, ||r||/||r_0|| = 5.00341e-05
+LBFGS iteration 79 : ||r|| = 5.6683e-07, ||r||/||r_0|| = 3.09534e-05
+LBFGS iteration 80 : ||r|| = 5.30738e-07, ||r||/||r_0|| = 2.89825e-05
+LBFGS iteration 81 : ||r|| = 7.69182e-07, ||r||/||r_0|| = 4.20035e-05
+LBFGS iteration 82 : ||r|| = 1.62178e-06, ||r||/||r_0|| = 8.85624e-05
+LBFGS iteration 83 : ||r|| = 4.96833e-07, ||r||/||r_0|| = 2.7131e-05
+LBFGS iteration 84 : ||r|| = 1.78659e-07, ||r||/||r_0|| = 9.75622e-06
+LBFGS iteration 85 : ||r|| = 1.41715e-07, ||r||/||r_0|| = 7.73878e-06
+LBFGS iteration 86 : ||r|| = 1.82314e-07, ||r||/||r_0|| = 9.9558e-06
+LBFGS iteration 87 : ||r|| = 2.91922e-07, ||r||/||r_0|| = 1.59412e-05
+LBFGS iteration 88 : ||r|| = 3.08653e-07, ||r||/||r_0|| = 1.68549e-05
+LBFGS iteration 89 : ||r|| = 3.84785e-07, ||r||/||r_0|| = 2.10123e-05
+LBFGS iteration 90 : ||r|| = 2.14826e-07, ||r||/||r_0|| = 1.17312e-05
+LBFGS iteration 91 : ||r|| = 2.00017e-07, ||r||/||r_0|| = 1.09225e-05
+LBFGS iteration 92 : ||r|| = 5.55699e-08, ||r||/||r_0|| = 3.03456e-06
+LBFGS iteration 93 : ||r|| = 5.17893e-08, ||r||/||r_0|| = 2.82811e-06
+LBFGS iteration 94 : ||r|| = 1.1665e-07, ||r||/||r_0|| = 6.37002e-06
+LBFGS iteration 95 : ||r|| = 6.49058e-08, ||r||/||r_0|| = 3.54437e-06
+LBFGS iteration 96 : ||r|| = 6.36792e-08, ||r||/||r_0|| = 3.47739e-06
+LBFGS iteration 97 : ||r|| = 6.60881e-08, ||r||/||r_0|| = 3.60894e-06
+LBFGS iteration 98 : ||r|| = 7.42024e-08, ||r||/||r_0|| = 4.05204e-06
+LBFGS iteration 99 : ||r|| = 4.32837e-08, ||r||/||r_0|| = 2.36364e-06
+LBFGS iteration 100 : ||r|| = 4.64962e-08, ||r||/||r_0|| = 2.53906e-06
+LBFGS iteration 101 : ||r|| = 4.5351e-08, ||r||/||r_0|| = 2.47653e-06
+LBFGS iteration 102 : ||r|| = 6.13974e-08, ||r||/||r_0|| = 3.35279e-06
+LBFGS iteration 103 : ||r|| = 3.12357e-08, ||r||/||r_0|| = 1.70572e-06
+LBFGS iteration 104 : ||r|| = 2.33291e-08, ||r||/||r_0|| = 1.27396e-06
+LBFGS iteration 105 : ||r|| = 1.53917e-08, ||r||/||r_0|| = 8.4051e-07
+LBFGS/Newton+GMRES converged in 105 iterations with a residual norm of 1.53917e-08.
+solver took 11.5328s.
+|| q_h - q_ex || / || q_ex || = 0.329984
+|| t_h - t_ex || / || t_ex || = 0.0520583