mfem/examples/ex3p.cpp

//                       MFEM Example 3 - Parallel Version
//
// Compile with: make ex3p
//
// Sample runs:  mpirun -np 4 ex3p -m ../data/star.mesh
//               mpirun -np 4 ex3p -m ../data/square-disc.mesh -o 2
//               mpirun -np 4 ex3p -m ../data/beam-tet.mesh
//               mpirun -np 4 ex3p -m ../data/beam-tet.mesh -nc -o 2
//               mpirun -np 4 ex3p -m ../data/beam-hex.mesh
//               mpirun -np 4 ex3p -m ../data/beam-hex.mesh -o 2 -pa
//               mpirun -np 4 ex3p -m ../data/escher.mesh
//               mpirun -np 4 ex3p -m ../data/escher.mesh -o 2
//               mpirun -np 4 ex3p -m ../data/fichera.mesh
//               mpirun -np 4 ex3p -m ../data/fichera-q2.vtk
//               mpirun -np 4 ex3p -m ../data/fichera-q3.mesh
//               mpirun -np 4 ex3p -m ../data/square-disc-nurbs.mesh
//               mpirun -np 4 ex3p -m ../data/beam-hex-nurbs.mesh
//               mpirun -np 4 ex3p -m ../data/amr-quad.mesh -o 2
//               mpirun -np 4 ex3p -m ../data/amr-hex.mesh
//               mpirun -np 4 ex3p -m ../data/ref-prism.mesh -o 1
//               mpirun -np 4 ex3p -m ../data/octahedron.mesh -o 1
//               mpirun -np 4 ex3p -m ../data/star-surf.mesh -o 2
//               mpirun -np 4 ex3p -m ../data/mobius-strip.mesh -o 2 -f 0.1
//               mpirun -np 4 ex3p -m ../data/klein-bottle.mesh -o 2 -f 0.1
//
// Device sample runs:
//               mpirun -np 4 ex3p -m ../data/star.mesh -pa -d cuda
//               mpirun -np 4 ex3p -m ../data/star.mesh -no-pa -d cuda
//               mpirun -np 4 ex3p -m ../data/star.mesh -pa -d raja-cuda
//               mpirun -np 4 ex3p -m ../data/star.mesh -pa -d raja-omp
//               mpirun -np 4 ex3p -m ../data/beam-hex.mesh -pa -d cuda
//
// Description:  This example code solves a simple electromagnetic diffusion
//               problem corresponding to the second order definite Maxwell
//               equation curl curl E + E = f with boundary condition
//               E x n = <given tangential field>. Here, we use a given exact
//               solution E and compute the corresponding r.h.s. f.
//               We discretize with Nedelec finite elements in 2D or 3D.
//
//               The example demonstrates the use of H(curl) finite element
//               spaces with the curl-curl and the (vector finite element) mass
//               bilinear form, as well as the computation of discretization
//               error when the exact solution is known. Static condensation is
//               also illustrated.
//
//               We recommend viewing examples 1-2 before viewing this example.

#include "mfem.hpp"
#include <fstream>
#include <iostream>

using namespace std;
using namespace mfem;

// Exact solution, E, and r.h.s., f. See below for implementation.
void E_exact(const Vector &, Vector &);
void f_exact(const Vector &, Vector &);
real_t freq = 1.0, kappa;
int dim;

class Curl4dPrec : public Solver
{

private:
   HypreParMatrix *A;
   ParFiniteElementSpace *fespace;

   HypreParMatrix *idMat;
   HypreParMatrix *H1VecLaplaceMat;
   HypreBoomerAMG *amgVecH1;


   HypreParMatrix *gradMat;
   HypreParMatrix *H1LaplaceMat;
   HypreBoomerAMG *amgH1;

   HypreSmoother * smoother;
   CGSolver *pcgGrad;
   CGSolver *pcgH1Vec;

   Vector *f;
   Vector *fGrad, *uGrad;
   Vector *fH1Vec, *uH1Vec;

   bool exactSolves;

public:
   Curl4dPrec(HypreParMatrix *AUser, ParFiniteElementSpace *fespaceUser,
              const Array<int> &essBnd, int orderKernel=1, bool exactSolvesUser=false)
   {
      A = AUser;
      fespace = fespaceUser;
      ParMesh *pmesh = fespace->GetParMesh();
      int dim = pmesh->Dimension();

      exactSolves = exactSolvesUser;

      int orderIm=1;  //vecH1  --> H(curl)
      int orderKer=orderKernel; //grad V --> H(curl)

      smoother = new HypreSmoother(*A, 16, 3);

      //    //for the pure dirichlet case
      //    Array<int> essBnd(pmesh->bdr_attributes.Max()); essBnd = 1;

      Array<int> HCurl_essDof(fespace->GetVSize()); HCurl_essDof = 0;
      fespace->GetEssentialVDofs(essBnd, HCurl_essDof);

      //setup the H1 FESpace
      FiniteElementCollection* fecH1;
      if (orderKer==1) { fecH1 = new LinearFECollection; }
      else { fecH1 = new QuadraticFECollection; }

      ParFiniteElementSpace *H1FESpace = new ParFiniteElementSpace(pmesh, fecH1);
      Array<int> H1_essDof(H1FESpace->GetVSize()); H1_essDof = 0;
      H1FESpace->GetEssentialVDofs(essBnd, H1_essDof);

      //setup the discrete gradient
      ParDiscreteLinearOperator *disGrad = new ParDiscreteLinearOperator(H1FESpace,
                                                                         fespace);
      disGrad->AddDomainInterpolator(new GradientInterpolator);
      disGrad->Assemble();
      disGrad->Finalize();
      SparseMatrix* smat = &(disGrad->SpMat());
      smat->EliminateCols(H1_essDof);
      for (int dof=0; dof<HCurl_essDof.Size(); dof++) if (HCurl_essDof[dof]<0) { smat->EliminateRow(dof); }
      gradMat = disGrad->ParallelAssemble();
      delete disGrad;

      //setup the H1 preconditioner
      ParBilinearForm* H1Varf = new ParBilinearForm(H1FESpace);
      H1Varf->AddDomainIntegrator(new DiffusionIntegrator);
      H1Varf->AddDomainIntegrator(new MassIntegrator);
      H1Varf->Assemble();
      H1Varf->Finalize();

      SparseMatrix &matH1(H1Varf->SpMat());
      for (int dof=0; dof<H1_essDof.Size(); dof++) if (H1_essDof[dof]<0) { matH1.EliminateRowCol(dof); }
      H1LaplaceMat = H1Varf->ParallelAssemble();
      delete H1Varf;
      amgH1 = new HypreBoomerAMG(*H1LaplaceMat);


      //setup the H1 injection
      FiniteElementCollection* fecH1Vec;
      if (orderIm==1) { fecH1Vec = new LinearFECollection; }
      else { fecH1Vec = new QuadraticFECollection; }
      ParFiniteElementSpace *H1VecFESpace = new ParFiniteElementSpace(pmesh, fecH1Vec,
                                                                      dim, Ordering::byVDIM);
      Array<int> H1Vec_essDof(H1VecFESpace->GetVSize()); H1Vec_essDof = 0;
      H1VecFESpace->GetEssentialVDofs(essBnd, H1Vec_essDof);

      //setup the discrete gradient
      ParDiscreteLinearOperator *disInterpol = new ParDiscreteLinearOperator(
         H1VecFESpace, fespace);
      disInterpol->AddDomainInterpolator(new IdentityInterpolator);
      disInterpol->Assemble();
      disInterpol->Finalize();
      SparseMatrix* smatID = &(disInterpol->SpMat());
      smatID->EliminateCols(H1Vec_essDof);
      for (int dof=0; dof<HCurl_essDof.Size(); dof++) if (HCurl_essDof[dof]<0) { smatID->EliminateRow(dof); }
      idMat = disInterpol->ParallelAssemble();
      delete disInterpol;

      //setup the H1-vec preconditioner
      ParBilinearForm* H1VecVarf = new ParBilinearForm(H1VecFESpace);
      H1VecVarf->AddDomainIntegrator(new VectorDiffusionIntegrator);
      H1VecVarf->AddDomainIntegrator(new VectorMassIntegrator);
      H1VecVarf->Assemble();
      H1VecVarf->Finalize();

      SparseMatrix &matH1Vec(H1VecVarf->SpMat());
      for (int dof=0; dof<H1Vec_essDof.Size(); dof++) if (H1Vec_essDof[dof]<0) { matH1Vec.EliminateRowCol(dof); }
      H1VecLaplaceMat = H1VecVarf->ParallelAssemble();
      delete H1VecVarf;
      amgVecH1 = new HypreBoomerAMG(*H1VecLaplaceMat);
      amgVecH1->SetSystemsOptions(dim);


      f = new Vector(fespace->GetTrueVSize());

      fGrad = new Vector(H1FESpace->GetTrueVSize());
      uGrad = new Vector(H1FESpace->GetTrueVSize());

      fH1Vec = new Vector(H1VecFESpace->GetTrueVSize());
      uH1Vec = new Vector(H1VecFESpace->GetTrueVSize());;


      amgH1->Mult(*fGrad, *uGrad);
      amgVecH1->Mult(*fH1Vec, *uH1Vec);

      pcgGrad = new CGSolver(MPI_COMM_WORLD);
      pcgGrad->SetOperator(*H1LaplaceMat);
      pcgGrad->SetPreconditioner(*amgH1);
      pcgGrad->SetRelTol(1e-16);
      pcgGrad->SetMaxIter(100000000);
      pcgGrad->SetPrintLevel(-2);

      pcgH1Vec = new CGSolver(MPI_COMM_WORLD);
      pcgH1Vec->SetOperator(*H1VecLaplaceMat);
      pcgH1Vec->SetPreconditioner(*amgVecH1);
      pcgH1Vec->SetRelTol(1e-16);
      pcgH1Vec->SetMaxIter(100000000);
      pcgH1Vec->SetPrintLevel(-2);

   }

   void setExactSolve(bool exSol)
   {
      exactSolves = exSol;
   }

   virtual void Mult(const Vector &x, Vector &y) const
   {
      smoother->Mult(x,y);

      idMat->MultTranspose(x,*fH1Vec);
      *uH1Vec = 0.0;
      if (exactSolves) { pcgH1Vec->Mult(*fH1Vec, *uH1Vec); }
      else { amgVecH1->Mult(*fH1Vec, *uH1Vec); }
      idMat->Mult(1.0, *uH1Vec, 1.0, y);

      gradMat->MultTranspose(x,*fGrad);
      *uGrad = 0.0;
      if (exactSolves) { pcgGrad->Mult(*fGrad, *uGrad); }
      else { amgH1->Mult(*fGrad, *uGrad); }
      gradMat->Mult(1.0, *uGrad, 1.0, y);

   }

   virtual void SetOperator(const Operator &op) {};

};

int main(int argc, char *argv[])
{
   // 1. Initialize MPI and HYPRE.
   Mpi::Init(argc, argv);
   int num_procs = Mpi::WorldSize();
   int myid = Mpi::WorldRank();
   Hypre::Init();

   // 2. Parse command-line options.
   const char *mesh_file = "../data/beam-tet.mesh";
   int order = 1;
   bool static_cond = false;
   bool pa = false;
   bool nc = false;
   const char *device_config = "cpu";
   bool visualization = true;
#ifdef MFEM_USE_AMGX
   bool useAmgX = false;
#endif

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
                  "Mesh file to use.");
   args.AddOption(&order, "-o", "--order",
                  "Finite element order (polynomial degree).");
   args.AddOption(&freq, "-f", "--frequency", "Set the frequency for the exact"
                  " solution.");
   args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
                  "--no-static-condensation", "Enable static condensation.");
   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                  "--no-partial-assembly", "Enable Partial Assembly.");
   args.AddOption(&nc, "-nc", "--non-conforming", "-c",
                  "--conforming",
                  "Mark the mesh as nonconforming before partitioning.");
   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.");
#ifdef MFEM_USE_AMGX
   args.AddOption(&useAmgX, "-amgx", "--useAmgX", "-no-amgx",
                  "--no-useAmgX",
                  "Enable or disable AmgX in MatrixFreeAMS.");
#endif

   args.Parse();
   if (!args.Good())
   {
      if (myid == 0)
      {
         args.PrintUsage(cout);
      }
      return 1;
   }
   if (myid == 0)
   {
      args.PrintOptions(cout);
   }
   kappa = freq * M_PI;

   // 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.
   Mesh *mesh = new Mesh(mesh_file, 1, 1);
   dim = mesh->Dimension();
   int sdim = mesh->SpaceDimension();
   if (nc)
   {
      // Can set to false to use conformal refinement for simplices.
      mesh->EnsureNCMesh(true);
   }

   // 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 1,000 elements.
   {
      int ref_levels = (int)floor(log(1000./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 parallel finite element space on the parallel mesh. Here we
   //    use the Nedelec finite elements of the specified order.
   FiniteElementCollection *fec;
   if (dim==4)
   {
      if (order==1) { fec = new ND1_4DFECollection; }
      else { fec = new ND2_4DFECollection; }
   }
   else { fec = new ND_FECollection(order, dim); }
   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
   HYPRE_BigInt size = fespace->GlobalTrueVSize();
   if (myid == 0)
   {
      cout << "Number of finite element unknowns: " << size << endl;
   }

   // 8. Determine the list of true (i.e. parallel conforming) essential
   //    boundary dofs. In this example, the boundary conditions are defined
   //    by marking all the boundary attributes from the mesh as essential
   //    (Dirichlet) and converting them to a list of true dofs.
   Array<int> ess_tdof_list;
   Array<int> ess_bdr;
   if (pmesh->bdr_attributes.Size())
   {
      ess_bdr.SetSize(pmesh->bdr_attributes.Max());
      ess_bdr = 1;
      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
   }

   // 9. Set up the parallel linear form b(.) which corresponds to the
   //    right-hand side of the FEM linear system, which in this case is
   //    (f,phi_i) where f is given by the function f_exact and phi_i are the
   //    basis functions in the finite element fespace.
   VectorFunctionCoefficient f(sdim, f_exact);
   ParLinearForm *b = new ParLinearForm(fespace);
   b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
   b->Assemble();

   // 10. Define the solution vector x as a parallel finite element grid function
   //     corresponding to fespace. Initialize x by projecting the exact
   //     solution. Note that only values from the boundary edges will be used
   //     when eliminating the non-homogeneous boundary condition to modify the
   //     r.h.s. vector b.
   ParGridFunction x(fespace);
   VectorFunctionCoefficient E(sdim, E_exact);
   x.ProjectCoefficient(E);

   // 11. Set up the parallel bilinear form corresponding to the EM diffusion
   //     operator curl muinv curl + sigma I, by adding the curl-curl and the
   //     mass domain integrators.
   Coefficient *muinv = new ConstantCoefficient(1.0);
   Coefficient *sigma = new ConstantCoefficient(1.0);
   ParBilinearForm *a = new ParBilinearForm(fespace);
   if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
   a->AddDomainIntegrator(new CurlCurlIntegrator(*muinv));
   a->AddDomainIntegrator(new VectorFEMassIntegrator(*sigma));

   // 12. Assemble the parallel bilinear form and the corresponding linear
   //     system, applying any necessary transformations such as: parallel
   //     assembly, eliminating boundary conditions, applying conforming
   //     constraints for non-conforming AMR, static condensation, etc.
   if (static_cond) { a->EnableStaticCondensation(); }
   a->Assemble();

   OperatorPtr A;
   Vector B, X;
   a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);

   // 13. Solve the system AX=B using PCG with an AMS preconditioner.
   if (pa)
   {
#ifdef MFEM_USE_AMGX
      MatrixFreeAMS ams(*a, *A, *fespace, muinv, sigma, NULL, ess_bdr, useAmgX);
#else
      MatrixFreeAMS ams(*a, *A, *fespace, muinv, sigma, NULL, ess_bdr);
#endif
      CGSolver cg(MPI_COMM_WORLD);
      cg.SetRelTol(1e-12);
      cg.SetMaxIter(1000);
      cg.SetPrintLevel(1);
      cg.SetOperator(*A);
      cg.SetPreconditioner(ams);
      cg.Mult(B, X);
   }
   else
   {
      if (myid == 0)
      {
         cout << "Size of linear system: "
              << A.As<HypreParMatrix>()->GetGlobalNumRows() << endl;
      }

      ParFiniteElementSpace *prec_fespace =
         (a->StaticCondensationIsEnabled() ? a->SCParFESpace() : fespace);
      Solver *prec;
      HypreAMS ams(*A.As<HypreParMatrix>(), prec_fespace);
      if (dim <= 3)
      {
         prec = new HypreAMS(*A.As<HypreParMatrix>(), prec_fespace);
      }
      else if (dim == 4)
      {
         prec = new Curl4dPrec(A.As<HypreParMatrix>(), fespace, ess_bdr, order, false);
      }
      IterativeSolver *pcg = new CGSolver(MPI_COMM_WORLD);
      pcg->SetOperator(*A.As<HypreParMatrix>());
      pcg->SetTol(1e-12);
      pcg->SetMaxIter(500);
      pcg->SetPrintLevel(2);
      pcg->SetPreconditioner(*prec);
      pcg->Mult(B, X);

      delete pcg;
      delete prec;
   }

   // 13. Recover the parallel grid function corresponding to X. This is the
   // 14. Recover the parallel grid function corresponding to X. This is the
   //     local finite element solution on each processor.
   a->RecoverFEMSolution(X, *b, x);

   // 15. Compute and print the L^2 norm of the error.
   {
      real_t error = x.ComputeL2Error(E);
      if (myid == 0)
      {
         cout << "\n|| E_h - E ||_{L^2} = " << error << '\n' << endl;
      }
   }

   // 16. 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, sol_name;
      mesh_name << "mesh." << setfill('0') << setw(6) << myid;
      sol_name << "sol." << setfill('0') << setw(6) << myid;

      ofstream mesh_ofs(mesh_name.str().c_str());
      mesh_ofs.precision(8);
      pmesh->Print(mesh_ofs);

      ofstream sol_ofs(sol_name.str().c_str());
      sol_ofs.precision(8);
      x.Save(sol_ofs);
   }

   // 17. Send the solution by socket to a GLVis server.
   if (visualization)
   {
      char vishost[] = "localhost";
      int  visport   = 19916;
      socketstream sol_sock(vishost, visport);
      sol_sock << "parallel " << num_procs << " " << myid << "\n";
      sol_sock.precision(8);
      sol_sock << "solution\n" << *pmesh << x << flush;
   }

   // 18. Free the used memory.
   delete a;
   delete sigma;
   delete muinv;
   delete b;
   delete fespace;
   delete fec;
   delete pmesh;

   return 0;
}


void E_exact(const Vector &x, Vector &E)
{
   if (dim==4)
   {
      E(0) =  sin(M_PI*x(0))*cos(M_PI*x(1))*cos(M_PI*x(2))*cos(M_PI*x(3));
      E(1) = -cos(M_PI*x(0))*sin(M_PI*x(1))*cos(M_PI*x(2))*cos(M_PI*x(3));
      E(2) =  cos(M_PI*x(0))*cos(M_PI*x(1))*sin(M_PI*x(2))*cos(M_PI*x(3));
      E(3) = -cos(M_PI*x(0))*cos(M_PI*x(1))*cos(M_PI*x(2))*sin(M_PI*x(3));
   }
   else 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; }
   }
}

void f_exact(const Vector &x, Vector &f)
{
   //f_exact = E +  DivSkew P( curl E ), where P is the 4d permutation operator
   if (dim==4)
   {
      f(0) =  (1.0+4.0*M_PI*M_PI)*sin(M_PI*x(0))*cos(M_PI*x(1))*cos(M_PI*x(2))*cos(
                 M_PI*x(3));
      f(1) = -(1.0+4.0*M_PI*M_PI)*cos(M_PI*x(0))*sin(M_PI*x(1))*cos(M_PI*x(2))*cos(
                M_PI*x(3));
      f(2) =  (1.0+4.0*M_PI*M_PI)*cos(M_PI*x(0))*cos(M_PI*x(1))*sin(M_PI*x(2))*cos(
                 M_PI*x(3));
      f(3) = -(1.0+4.0*M_PI*M_PI)*cos(M_PI*x(0))*cos(M_PI*x(1))*cos(M_PI*x(2))*sin(
                M_PI*x(3));
   }
   else 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; }
   }
}