mfem/examples/ex3p_4d.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-hex.mesh
//               mpirun -np 4 ex3p -m ../data/escher.mesh
//               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/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
//
// 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>
#include "./spe10_coeff.cpp"

using namespace std;
using namespace mfem;


int* LoadIterations(int NRows, int NCol)
{
   ifstream in("iter_curl.txt");

   //initialize
   int *iters = new int[NCol*NRows];
   for (int col = 0; col < NCol; col++)
   {
      for (int row = 0; row < NRows; row++)
      {
         iters[row*NCol+col] = -1;
      }
   }

   if (!in)
   {
      cout << "Cannot open file.\n";
      return iters;
   }

   for (int row = 0; row < NRows; row++)
      for (int col = 0; col < NCol; col++)
      {
         if (in.eof())
         {
            in.close();
            return iters;
         }
         in >> iters[row*NCol+col];
      }


   in.close();

   return iters;
}

void putIterationsInArray(int iter, int row, int col, int NCol, int* iters)
{
   iters[row*NCol+col] = iter;
}

void WriteIterations(int *iters, int NRows, int NCol)
{
   ofstream out;
   out.open("iter_curl.txt",fstream::out);

   if (!out)
   {
      cout << "Cannot open file.\n";
      delete[] iters;

      return;
   }

   for (int row = 0; row < NRows; row++)
   {
      for (int col = 0; col < NCol; col++)
      {
         out << iters[row*NCol+col] << "\t";
      }
      out << endl;
   }
   out.close();

   delete[] iters;
}


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

double osziCoeff(const Vector &x)
{
   return 1.0001 + sin(100*x(0))*sin(200*x(1))*sin(300*x(2))*sin(400*x(3));
}

class Curl4dPrec : public Solver
{

private:
   HypreParMatrix *A;
   ParFiniteElementSpace *fespace;
   Coefficient *alpha_, *beta_, *neg_beta_;

   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()
   {
      delete pcgH1Vec;
      delete pcgGrad;

      delete   f, fGrad, uGrad, fH1Vec, uH1Vec;

      delete smoother;

      delete amgVecH1, H1VecLaplaceMat;
      delete idMat;
      delete amgH1, H1LaplaceMat;
      delete gradMat;
   }

   Curl4dPrec(HypreParMatrix *AUser, ParFiniteElementSpace *fespaceUser,
              Coefficient *alpha, Coefficient *beta, Coefficient *neg_beta,
              const Array<int> &essBnd, int orderKernel=1, bool exactSolvesUser=false)
   {
      A = AUser;
      fespace = fespaceUser;
      alpha_ = alpha;
      beta_ = beta;
      neg_beta_=neg_beta;

      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(*beta_));
      //    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(*alpha_));
      H1VecVarf->AddDomainIntegrator(new VectorMassIntegrator(*neg_beta_));
      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);

      delete H1FESpace; delete fecH1;
      delete H1VecFESpace; delete fecH1Vec;

   }

   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.
   int num_procs, myid;
   MPI_Init(&argc, &argv);
   MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
   MPI_Comm_rank(MPI_COMM_WORLD, &myid);

   bool verbose = (myid==0);

   // 2. Parse command-line options.
   const char *mesh_file = "../data/cube4d_96.MFEM";
   int order = 1;
   bool set_bc = true;
   bool static_cond = false;
   bool visualization = 1;
   int sequ_ref_levels = 0;
   int par_ref_levels = 0;
   double tol = 1e-6;
   double coeffWeight = 1.0;
   bool exactH1Solver = false;
   bool spe10Coeff = false;
   bool standardCG = true;

   int NExpo = 8;
   int weightStart = -NExpo;
   int weightEnd = NExpo;

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
                  "Mesh file to use.");
   args.AddOption(&sequ_ref_levels, "-sr", "--seqrefinement",
                  "Number of sequential refinement steps.");
   args.AddOption(&par_ref_levels, "-pr", "--parrefinement",
                  "Number of parallel refinement steps.");
   args.AddOption(&order, "-o", "--order",
                  "Polynomial order of the finite element space.");
   args.AddOption(&set_bc, "-bc", "--impose-bc", "-no-bc", "--dont-impose-bc",
                  "Impose or not essential boundary conditions.");
   args.AddOption(&tol, "-tol", "--tol",
                  "A parameter.");
   args.AddOption(&freq, "-f", "--frequency", "Set the frequency for the exact"
                  " solution.");
   args.AddOption(&coeffWeight, "-c", "--coeffMass",
                  "the weight for the mass term.");
   args.AddOption(&exactH1Solver, "-exH1Sol", "--exactH1Solver", "-H1prec",
                  "--H1preconditioner",
                  "Use exact H1 solvers for the preconditioner.");
   args.AddOption(&spe10Coeff, "-spe10", "--useSPE10Coeff", "-constCoeff",
                  "--constCoeff",
                  "Switch between the coefficients for the mass bilinear form.");
   args.AddOption(&standardCG, "-sCG", "--stdCG", "-rCG", "--resCG",
                  "Switch between standard PCG or recompute residuals in every step and use the residuals itself for the stopping criteria.");
   args.AddOption(&weightStart, "-ws", "--weightStart",
                  "the exponent for the starting weight (for the mass term).");
   args.AddOption(&weightEnd, "-we", "--weightEnd",
                  "the exponent for the weight at the end (for the mass term).");

   args.Parse();
   if (!args.Good())
   {
      args.PrintUsage(cout);
      return 1;
   }
   if (verbose) { args.PrintOptions(cout); }

   kappa = freq * M_PI;

   Mesh *mesh;
   ifstream imesh(mesh_file);
   if (!imesh)
   {
      cerr << "\nCan not open mesh file: " << mesh_file << '\n' << endl;
      return 2;
   }

   mesh = new Mesh(imesh, 1, 1);
   imesh.close();

   dim = mesh->Dimension();
   int sdim = mesh->SpaceDimension();


   if (dim !=4 || sdim != 4)
   {
      MPI_Finalize();
      return 0;
   }

   for (int i=0; i<sequ_ref_levels; i++) { mesh->UniformRefinement(); }
   if (verbose) { mesh->PrintCharacteristics(); }

   if (verbose) { cout << "now we partition the mesh..." << endl << endl; }

   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
   delete mesh;

   for (int i=0; i<par_ref_levels; i++) { pmesh->UniformRefinement(); }

   pmesh->ReorientTetMesh();

   pmesh->PrintInfo(std::cout);
   if (verbose) { cout << endl; }

   // 6. 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_Int size = fespace->GlobalTrueVSize();
   if (myid == 0)
   {
      cout << "Number of finite element unknowns: " << size << endl;
   }

   // 7. 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(pmesh->bdr_attributes.Max());
   ess_bdr = set_bc ? 1 : 0;
   if (pmesh->bdr_attributes.Size())
   {
      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
   }

   // 8. 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.


   // 9. 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);

   for (int expo=weightStart; expo<=weightEnd; expo++)
   {
      double weight = pow(10.0,expo);
      kappa = weight;

      VectorFunctionCoefficient f(sdim, f_exact);
      ParLinearForm *b = new ParLinearForm(fespace);
      b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
      b->Assemble();

      x.ProjectCoefficient(E);

      // 10. 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.
      //    std::string permFile = "spe_perm.dat";
      //    InversePermeabilityFunction::ReadPermeabilityFile(permFile, MPI_COMM_WORLD);

      Coefficient *alpha = new ConstantCoefficient(1.0);
      Coefficient *beta;
      //    if(spe10Coeff) beta = new FunctionCoefficient(InversePermeabilityFunction::Norm2Permeability);
      //    else
      beta = new ConstantCoefficient(weight);
      Coefficient *neg_beta = new ConstantCoefficient(-weight);

      ParBilinearForm *a = new ParBilinearForm(fespace);
      a->AddDomainIntegrator(new CurlCurlIntegrator(*alpha));
      a->AddDomainIntegrator(new VectorFEMassIntegrator(*beta));

      // 11. 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();

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

      if (myid == 0)
      {
         cout << "Size of linear system: " << A.GetGlobalNumRows() << endl;
      }

      // 12. Define and apply a parallel PCG solver for AX=B with the AMS
      //     preconditioner from hypre.
      ParFiniteElementSpace *prec_fespace =
         (a->StaticCondensationIsEnabled() ? a->SCParFESpace() : fespace);
      Solver *prec;
      if (dim<=3) { prec = new HypreAMS(A, prec_fespace); }
      else if (dim==4) { prec = new Curl4dPrec(&A, fespace, alpha, beta, neg_beta, ess_bdr, order, false); }
      IterativeSolver *pcg = new CGSolver(MPI_COMM_WORLD);
      pcg->SetOperator(A);
      pcg->SetRelTol(tol);
      pcg->SetMaxIter(5000);
      pcg->SetPrintLevel(1);
      pcg->SetPreconditioner(*prec);
      pcg->Mult(B, X);

      int iter = pcg->GetNumIterations();
      if (myid==0)
      {
         cout << "Weigth: " << weight << " " << iter << endl;

         int *iters = LoadIterations(10, 2*NExpo+1);
         putIterationsInArray(iter, sequ_ref_levels+par_ref_levels, expo+NExpo,
                              2*NExpo+1, iters);
         WriteIterations(iters, 10, 2*NExpo+1);
      }

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

      // 14. Compute and print the L^2 norm of the error.
      {
         double err = x.ComputeL2Error(E);
         if (myid == 0)
         {
            cout << "\n|| E_h - E ||_{L^2} = " << err << '\n' << endl;
         }
      }

      // 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, 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);
      //   }

      //   // 16. 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;
      //   }

      delete pcg;
      delete prec;
      delete a;
      delete alpha;
      delete beta;
      delete b;

   }

   // 17. Free the used memory.

   delete fespace;
   delete fec;
   delete pmesh;

   MPI_Finalize();

   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) =  (kappa+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) = -(kappa+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) =  (kappa+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) = -(kappa+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; }
   }
}