Esempio n. 1
0
File: ex3p.cpp Progetto: YPCC/mfem
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);

   // 2. Parse command-line options.
   const char *mesh_file = "../data/beam-tet.mesh";
   int order = 1;
   bool visualization = 1;

   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(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
   args.Parse();
   if (!args.Good())
   {
      if (myid == 0)
         args.PrintUsage(cout);
      MPI_Finalize();
      return 1;
   }
   if (myid == 0)
      args.PrintOptions(cout);

   // 3. 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;
   ifstream imesh(mesh_file);
   if (!imesh)
   {
      if (myid == 0)
         cerr << "\nCan not open mesh file: " << mesh_file << '\n' << endl;
      MPI_Finalize();
      return 2;
   }
   mesh = new Mesh(imesh, 1, 1);
   imesh.close();
   int dim = mesh->Dimension();
   if (dim != 3)
   {
      if (myid == 0)
         cerr << "\nThis example requires a 3D mesh\n" << endl;
      MPI_Finalize();
      return 3;
   }

   // 4. 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();
   }

   // 5. 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. Tetrahedral
   //    meshes need to be reoriented before we can define high-order Nedelec
   //    spaces on them.
   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();
   }
   pmesh->ReorientTetMesh();

   // 6. Define a parallel finite element space on the parallel mesh. Here we
   //    use the lowest order Nedelec finite elements, but we can easily switch
   //    to higher-order spaces by changing the value of p.
   FiniteElementCollection *fec = new ND_FECollection(order, dim);
   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
   int size = fespace->GlobalTrueVSize();
   if (myid == 0)
      cout << "Number of unknowns: " << size << endl;

   // 7. 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(3, f_exact);
   ParLinearForm *b = new ParLinearForm(fespace);
   b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
   b->Assemble();

   // 8. 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(3, E_exact);
   x.ProjectCoefficient(E);

   // 9. 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 and finally imposing non-homogeneous Dirichlet
   //    boundary conditions. The boundary conditions are implemented by
   //    marking all the boundary attributes from the mesh as essential
   //    (Dirichlet). After serial and parallel assembly we extract the
   //    parallel matrix A.
   Coefficient *muinv = new ConstantCoefficient(1.0);
   Coefficient *sigma = new ConstantCoefficient(1.0);
   ParBilinearForm *a = new ParBilinearForm(fespace);
   a->AddDomainIntegrator(new CurlCurlIntegrator(*muinv));
   a->AddDomainIntegrator(new VectorFEMassIntegrator(*sigma));
   a->Assemble();
   Array<int> ess_bdr(pmesh->bdr_attributes.Max());
   ess_bdr = 1;
   a->EliminateEssentialBC(ess_bdr, x, *b);
   a->Finalize();

   // 10. Define the parallel (hypre) matrix and vectors representing a(.,.),
   //     b(.) and the finite element approximation.
   HypreParMatrix *A = a->ParallelAssemble();
   HypreParVector *B = b->ParallelAssemble();
   HypreParVector *X = x.ParallelAverage();
   *X = 0.0;

   delete a;
   delete sigma;
   delete muinv;
   delete b;

   // 11. Define and apply a parallel PCG solver for AX=B with the AMS
   //     preconditioner from hypre.
   HypreSolver *ams = new HypreAMS(*A, fespace);
   HyprePCG *pcg = new HyprePCG(*A);
   pcg->SetTol(1e-12);
   pcg->SetMaxIter(500);
   pcg->SetPrintLevel(2);
   pcg->SetPreconditioner(*ams);
   pcg->Mult(*B, *X);

   // 12. Extract the parallel grid function corresponding to the finite element
   //     approximation X. This is the local solution on each processor.
   x = *X;

   // 13. 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;
   }

   // 14. 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);
   }

   // 15. 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;
   }

   // 16. Free the used memory.
   delete pcg;
   delete ams;
   delete X;
   delete B;
   delete A;
   delete fespace;
   delete fec;
   delete pmesh;

   MPI_Finalize();

   return 0;
}
Esempio n. 2
0
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);

   // 2. Parse command-line options.
   int elem_type = 1;
   int ref_levels = 2;
   int amr = 0;
   int order = 2;
   bool always_snap = false;
   bool visualization = 1;

   OptionsParser args(argc, argv);
   args.AddOption(&elem_type, "-e", "--elem",
                  "Type of elements to use: 0 - triangles, 1 - quads.");
   args.AddOption(&order, "-o", "--order",
                  "Finite element order (polynomial degree).");
   args.AddOption(&ref_levels, "-r", "--refine",
                  "Number of times to refine the mesh uniformly.");
   args.AddOption(&amr, "-amr", "--refine-locally",
                  "Additional local (non-conforming) refinement:"
                  " 1 = refine around north pole, 2 = refine randomly.");
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
   args.AddOption(&always_snap, "-snap", "--always-snap", "-no-snap",
                  "--snap-at-the-end",
                  "If true, snap nodes to the sphere initially and after each refinement "
                  "otherwise, snap only after the last refinement");
   args.Parse();
   if (!args.Good())
   {
      if (myid == 0)
      {
         args.PrintUsage(cout);
      }
      MPI_Finalize();
      return 1;
   }
   if (myid == 0)
   {
      args.PrintOptions(cout);
   }

   // 3. Generate an initial high-order (surface) mesh on the unit sphere. The
   //    Mesh object represents a 2D mesh in 3 spatial dimensions. We first add
   //    the elements and the vertices of the mesh, and then make it high-order
   //    by specifying a finite element space for its nodes.
   int Nvert = 8, Nelem = 6;
   if (elem_type == 0)
   {
      Nvert = 6;
      Nelem = 8;
   }
   Mesh *mesh = new Mesh(2, Nvert, Nelem, 0, 3);

   if (elem_type == 0) // inscribed octahedron
   {
      const double tri_v[6][3] =
      {
         { 1,  0,  0}, { 0,  1,  0}, {-1,  0,  0},
         { 0, -1,  0}, { 0,  0,  1}, { 0,  0, -1}
      };
      const int tri_e[8][3] =
      {
         {0, 1, 4}, {1, 2, 4}, {2, 3, 4}, {3, 0, 4},
         {1, 0, 5}, {2, 1, 5}, {3, 2, 5}, {0, 3, 5}
      };

      for (int j = 0; j < Nvert; j++)
      {
         mesh->AddVertex(tri_v[j]);
      }
      for (int j = 0; j < Nelem; j++)
      {
         int attribute = j + 1;
         mesh->AddTriangle(tri_e[j], attribute);
      }
      mesh->FinalizeTriMesh(1, 1, true);
   }
   else // inscribed cube
   {
      const double quad_v[8][3] =
      {
         {-1, -1, -1}, {+1, -1, -1}, {+1, +1, -1}, {-1, +1, -1},
         {-1, -1, +1}, {+1, -1, +1}, {+1, +1, +1}, {-1, +1, +1}
      };
      const int quad_e[6][4] =
      {
         {3, 2, 1, 0}, {0, 1, 5, 4}, {1, 2, 6, 5},
         {2, 3, 7, 6}, {3, 0, 4, 7}, {4, 5, 6, 7}
      };

      for (int j = 0; j < Nvert; j++)
      {
         mesh->AddVertex(quad_v[j]);
      }
      for (int j = 0; j < Nelem; j++)
      {
         int attribute = j + 1;
         mesh->AddQuad(quad_e[j], attribute);
      }
      mesh->FinalizeQuadMesh(1, 1, true);
   }

   // Set the space for the high-order mesh nodes.
   H1_FECollection fec(order, mesh->Dimension());
   FiniteElementSpace nodal_fes(mesh, &fec, mesh->SpaceDimension());
   mesh->SetNodalFESpace(&nodal_fes);

   // 4. Refine the mesh while snapping nodes to the sphere. Number of parallel
   //    refinements is fixed to 2.
   for (int l = 0; l <= ref_levels; l++)
   {
      if (l > 0) // for l == 0 just perform snapping
      {
         mesh->UniformRefinement();
      }

      // Snap the nodes of the refined mesh back to sphere surface.
      if (always_snap)
      {
         SnapNodes(*mesh);
      }
   }

   if (amr == 1)
   {
      for (int l = 0; l < 3; l++)
      {
         mesh->RefineAtVertex(Vertex(0, 0, 1));
      }
      SnapNodes(*mesh);
   }
   else if (amr == 2)
   {
      for (int l = 0; l < 2; l++)
      {
         mesh->RandomRefinement(0.5); // 50% probability
      }
      SnapNodes(*mesh);
   }

   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();

         // Snap the nodes of the refined mesh back to sphere surface.
         if (always_snap)
         {
            SnapNodes(*pmesh);
         }
      }
      if (!always_snap || par_ref_levels < 1)
      {
         SnapNodes(*pmesh);
      }
   }

   if (amr == 1)
   {
      for (int l = 0; l < 2; l++)
      {
         pmesh->RefineAtVertex(Vertex(0, 0, 1));
      }
      SnapNodes(*pmesh);
   }
   else if (amr == 2)
   {
      for (int l = 0; l < 2; l++)
      {
         pmesh->RandomRefinement(0.5); // 50% probability
      }
      SnapNodes(*pmesh);
   }

   // 5. Define a finite element space on the mesh. Here we use isoparametric
   //    finite elements -- the same as the mesh nodes.
   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, &fec);
   HYPRE_Int size = fespace->GlobalTrueVSize();
   if (myid == 0)
   {
      cout << "Number of unknowns: " << size << endl;
   }

   // 6. Set up the linear form b(.) which corresponds to the right-hand side of
   //    the FEM linear system, which in this case is (1,phi_i) where phi_i are
   //    the basis functions in the finite element fespace.
   ParLinearForm *b = new ParLinearForm(fespace);
   ConstantCoefficient one(1.0);
   FunctionCoefficient rhs_coef (analytic_rhs);
   FunctionCoefficient sol_coef (analytic_solution);
   b->AddDomainIntegrator(new DomainLFIntegrator(rhs_coef));
   b->Assemble();

   // 7. Define the solution vector x as a finite element grid function
   //    corresponding to fespace. Initialize x with initial guess of zero.
   ParGridFunction x(fespace);
   x = 0.0;

   // 8. Set up the bilinear form a(.,.) on the finite element space
   //    corresponding to the Laplacian operator -Delta, by adding the Diffusion
   //    and Mass domain integrators.
   ParBilinearForm *a = new ParBilinearForm(fespace);
   a->AddDomainIntegrator(new DiffusionIntegrator(one));
   a->AddDomainIntegrator(new MassIntegrator(one));

   // 9. Assemble the parallel linear system, applying any transformations
   //    such as: parallel assembly, applying conforming constraints, etc.
   a->Assemble();
   HypreParMatrix A;
   Vector B, X;
   Array<int> empty_tdof_list;
   a->FormLinearSystem(empty_tdof_list, x, *b, A, X, B);

   // 10. Define and apply a parallel PCG solver for AX=B with the BoomerAMG
   //     preconditioner from hypre. Extract the parallel grid function x
   //     corresponding to the finite element approximation X. This is the local
   //     solution on each processor.
   HypreSolver *amg = new HypreBoomerAMG(A);
   HyprePCG *pcg = new HyprePCG(A);
   pcg->SetTol(1e-12);
   pcg->SetMaxIter(200);
   pcg->SetPrintLevel(2);
   pcg->SetPreconditioner(*amg);
   pcg->Mult(B, X);
   a->RecoverFEMSolution(X, *b, x);

   delete a;
   delete b;

   // 11. Compute and print the L^2 norm of the error.
   double err = x.ComputeL2Error(sol_coef);
   if (myid == 0)
   {
      cout << "\nL2 norm of error: " << err << endl;
   }

   // 12. Save the refined mesh and the solution. This output can be viewed
   //     later using GLVis: "glvis -np <np> -m sphere_refined -g sol".
   {
      ostringstream mesh_name, sol_name;
      mesh_name << "sphere_refined." << 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);
   }

   // 13. 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;
   }

   // 14. Free the used memory.
   delete pcg;
   delete amg;
   delete fespace;
   delete pmesh;

   MPI_Finalize();

   return 0;
}
Esempio n. 3
0
void
TeslaSolver::Solve()
{
   if (myid_ == 0) { cout << "Running solver ... " << endl << flush; }

   // Initialize the magnetic vector potential with its boundary conditions
   *a_ = 0.0;

   // Apply surface currents if available
   if ( k_ )
   {
      SurfCur_->ComputeSurfaceCurrent(*k_);
      *a_ = *k_;
   }

   // Apply uniform B boundary condition on remaining surfaces
   a_->ProjectBdrCoefficientTangent(*aBCCoef_, non_k_bdr_);

   // Initialize the RHS vector
   HypreParVector *RHS = new HypreParVector(HCurlFESpace_);
   *RHS = 0.0;

   HypreParMatrix *MassHCurl = hCurlMass_->ParallelAssemble();

   // Initialize the volumetric current density
   if ( j_ )
   {
      j_->ProjectCoefficient(*jCoef_);

      HypreParVector *J    = j_->ParallelProject();
      HypreParVector *JD   = new HypreParVector(HCurlFESpace_);

      MassHCurl->Mult(*J,*JD);
      DivFreeProj_->Mult(*JD, *RHS);

      delete J;
      delete JD;
   }

   // Initialize the Magnetization
   HypreParVector *M = NULL;
   if ( m_ )
   {
      m_->ProjectCoefficient(*mCoef_);
      M = m_->ParallelProject();

      HypreParMatrix *MassHDiv = hDivMassMuInv_->ParallelAssemble();
      HypreParVector *MD   = new HypreParVector(HDivFESpace_);

      MassHDiv->Mult(*M,*MD);
      Curl_->MultTranspose(*MD,*RHS,mu0_,1.0);

      delete MassHDiv;
      delete MD;
   }

   // Apply Dirichlet BCs to matrix and right hand side
   HypreParMatrix *CurlMuInvCurl = curlMuInvCurl_->ParallelAssemble();
   HypreParVector *A             = a_->ParallelProject();

   // Apply the boundary conditions to the assembled matrix and vectors
   curlMuInvCurl_->ParallelEliminateEssentialBC(ess_bdr_,
                                                *CurlMuInvCurl,
                                                *A, *RHS);

   // Define and apply a parallel PCG solver for AX=B with the AMS
   // preconditioner from hypre.
   HypreAMS *ams = new HypreAMS(*CurlMuInvCurl, HCurlFESpace_);
   ams->SetSingularProblem();

   HyprePCG *pcg = new HyprePCG(*CurlMuInvCurl);
   pcg->SetTol(1e-12);
   pcg->SetMaxIter(500);
   pcg->SetPrintLevel(2);
   pcg->SetPreconditioner(*ams);
   pcg->Mult(*RHS, *A);

   delete ams;
   delete pcg;
   delete CurlMuInvCurl;
   delete RHS;

   // Extract the parallel grid function corresponding to the finite
   // element approximation Phi. This is the local solution on each
   // processor.
   *a_ = *A;

   // Compute the negative Gradient of the solution vector.  This is
   // the magnetic field corresponding to the scalar potential
   // represented by phi.
   HypreParVector *B = new HypreParVector(HDivFESpace_);
   Curl_->Mult(*A,*B);
   *b_ = *B;

   // Compute magnetic field (H) from B and M
   if (myid_ == 0) { cout << "Computing H ... " << flush; }

   HypreParMatrix *HDivHCurlMuInv = hDivHCurlMuInv_->ParallelAssemble();
   HypreParVector *BD = new HypreParVector(HCurlFESpace_);
   HypreParVector *H  = new HypreParVector(HCurlFESpace_);

   HDivHCurlMuInv->Mult(*B,*BD);

   if ( M )
   {
      HDivHCurlMuInv->Mult(*M,*BD,-1.0*mu0_,1.0);
   }

   HyprePCG * pcgM = new HyprePCG(*MassHCurl);
   pcgM->SetTol(1e-12);
   pcgM->SetMaxIter(500);
   pcgM->SetPrintLevel(0);
   HypreDiagScale *diagM = new HypreDiagScale;
   pcgM->SetPreconditioner(*diagM);
   pcgM->Mult(*BD,*H);

   *h_ = *H;

   if (myid_ == 0) { cout << "done." << flush; }

   delete diagM;
   delete pcgM;
   delete HDivHCurlMuInv;
   delete MassHCurl;
   delete A;
   delete B;
   delete BD;
   delete H;
   delete M;

   if (myid_ == 0) { cout << " Solver done. " << flush; }
}
Esempio n. 4
0
void
VoltaSolver::Solve()
{
   if (myid_ == 0) { cout << "Running solver ... " << endl << flush; }

   // Initialize the electric potential with its boundary conditions
   *phi_ = 0.0;

   if ( dbcs_->Size() > 0 )
   {
      if ( phiBCCoef_ )
      {
         // Apply gradient boundary condition
         phi_->ProjectBdrCoefficient(*phiBCCoef_, ess_bdr_);
      }
      else
      {
         // Apply piecewise constant boundary condition
         Array<int> dbc_bdr_attr(pmesh_->bdr_attributes.Max());
         for (int i=0; i<dbcs_->Size(); i++)
         {
            ConstantCoefficient voltage((*dbcv_)[i]);
            dbc_bdr_attr = 0;
            dbc_bdr_attr[(*dbcs_)[i]-1] = 1;
            phi_->ProjectBdrCoefficient(voltage, dbc_bdr_attr);
         }
      }
   }

   // Initialize the RHS vector
   HypreParVector *RHS = new HypreParVector(H1FESpace_);
   *RHS = 0.0;

   // Initialize the volumetric charge density
   if ( rho_ )
   {
      rho_->ProjectCoefficient(*rhoCoef_);

      HypreParMatrix *MassH1 = h1Mass_->ParallelAssemble();
      HypreParVector *Rho    = rho_->ParallelProject();

      MassH1->Mult(*Rho,*RHS);

      delete MassH1;
      delete Rho;
   }

   // Initialize the Polarization
   HypreParVector *P = NULL;
   if ( p_ )
   {
      p_->ProjectCoefficient(*pCoef_);
      P = p_->ParallelProject();

      HypreParMatrix *MassHCurl = hCurlMass_->ParallelAssemble();
      HypreParVector *PD        = new HypreParVector(HCurlFESpace_);

      MassHCurl->Mult(*P,*PD);
      Grad_->MultTranspose(*PD,*RHS,-1.0,1.0);

      delete MassHCurl;
      delete PD;

   }

   // Initialize the surface charge density
   if ( sigma_ )
   {
      *sigma_ = 0.0;

      Array<int> nbc_bdr_attr(pmesh_->bdr_attributes.Max());
      for (int i=0; i<nbcs_->Size(); i++)
      {
         ConstantCoefficient sigma_coef((*nbcv_)[i]);
         nbc_bdr_attr = 0;
         nbc_bdr_attr[(*nbcs_)[i]-1] = 1;
         sigma_->ProjectBdrCoefficient(sigma_coef, nbc_bdr_attr);
      }

      HypreParMatrix *MassS = h1SurfMass_->ParallelAssemble();
      HypreParVector *Sigma = sigma_->ParallelProject();

      MassS->Mult(*Sigma,*RHS,1.0,1.0);

      delete MassS;
      delete Sigma;
   }

   // Apply Dirichlet BCs to matrix and right hand side
   HypreParMatrix *DivEpsGrad = divEpsGrad_->ParallelAssemble();
   HypreParVector *Phi        = phi_->ParallelProject();

   // Apply the boundary conditions to the assembled matrix and vectors
   if ( dbcs_->Size() > 0 )
   {
      // According to the selected surfaces
      divEpsGrad_->ParallelEliminateEssentialBC(ess_bdr_,
                                                *DivEpsGrad,
                                                *Phi, *RHS);
   }
   else
   {
      // No surfaces were labeled as Dirichlet so eliminate one DoF
      Array<int> dof_list(0);
      if ( myid_ == 0 )
      {
         dof_list.SetSize(1);
         dof_list[0] = 0;
      }
      DivEpsGrad->EliminateRowsCols(dof_list, *Phi, *RHS);
   }

   // Define and apply a parallel PCG solver for AX=B with the AMG
   // preconditioner from hypre.
   HypreSolver *amg = new HypreBoomerAMG(*DivEpsGrad);
   HyprePCG *pcg = new HyprePCG(*DivEpsGrad);
   pcg->SetTol(1e-12);
   pcg->SetMaxIter(500);
   pcg->SetPrintLevel(2);
   pcg->SetPreconditioner(*amg);
   pcg->Mult(*RHS, *Phi);

   delete amg;
   delete pcg;
   delete DivEpsGrad;
   delete RHS;

   // Extract the parallel grid function corresponding to the finite
   // element approximation Phi. This is the local solution on each
   // processor.
   *phi_ = *Phi;

   // Compute the negative Gradient of the solution vector.  This is
   // the magnetic field corresponding to the scalar potential
   // represented by phi.
   HypreParVector *E = new HypreParVector(HCurlFESpace_);
   Grad_->Mult(*Phi,*E,-1.0);
   *e_ = *E;

   delete Phi;

   // Compute electric displacement (D) from E and P
   if (myid_ == 0) { cout << "Computing D ... " << flush; }

   HypreParMatrix *HCurlHDivEps = hCurlHDivEps_->ParallelAssemble();
   HypreParVector *ED = new HypreParVector(HDivFESpace_);
   HypreParVector *D  = new HypreParVector(HDivFESpace_);

   HCurlHDivEps->Mult(*E,*ED);

   if ( P )
   {
      HypreParMatrix *HCurlHDiv = hCurlHDiv_->ParallelAssemble();
      HCurlHDiv->Mult(*P,*ED,-1.0,1.0);
      delete HCurlHDiv;
   }

   HypreParMatrix * MassHDiv = hDivMass_->ParallelAssemble();

   HyprePCG * pcgM = new HyprePCG(*MassHDiv);
   pcgM->SetTol(1e-12);
   pcgM->SetMaxIter(500);
   pcgM->SetPrintLevel(0);
   HypreDiagScale *diagM = new HypreDiagScale;
   pcgM->SetPreconditioner(*diagM);
   pcgM->Mult(*ED,*D);

   *d_ = *D;

   if (myid_ == 0) { cout << "done." << flush; }

   delete diagM;
   delete pcgM;
   delete HCurlHDivEps;
   delete MassHDiv;
   delete E;
   delete ED;
   delete D;
   delete P;

   if (myid_ == 0) { cout << " Solver done. " << flush; }
}
Esempio n. 5
0
double L2ZZErrorEstimator(BilinearFormIntegrator &flux_integrator,
                          const ParGridFunction &x,
                          ParFiniteElementSpace &smooth_flux_fes,
                          ParFiniteElementSpace &flux_fes,
                          Vector &errors,
                          int norm_p, double solver_tol, int solver_max_it)
{
   // Compute fluxes in discontinuous space
   GridFunction flux(&flux_fes);
   flux = 0.0;

   ParFiniteElementSpace *xfes = x.ParFESpace();
   Array<int> xdofs, fdofs;
   Vector el_x, el_f;

   for (int i = 0; i < xfes->GetNE(); i++)
   {
      xfes->GetElementVDofs(i, xdofs);
      x.GetSubVector(xdofs, el_x);

      ElementTransformation *Transf = xfes->GetElementTransformation(i);
      flux_integrator.ComputeElementFlux(*xfes->GetFE(i), *Transf, el_x,
                                         *flux_fes.GetFE(i), el_f, false);

      flux_fes.GetElementVDofs(i, fdofs);
      flux.AddElementVector(fdofs, el_f);
   }

   // Assemble the linear system for L2 projection into the "smooth" space
   ParBilinearForm *a = new ParBilinearForm(&smooth_flux_fes);
   ParLinearForm *b = new ParLinearForm(&smooth_flux_fes);
   VectorGridFunctionCoefficient f(&flux);

   if (xfes->GetNE())
   {
      if (smooth_flux_fes.GetFE(0)->GetRangeType() == FiniteElement::SCALAR)
      {
         VectorMassIntegrator *vmass = new VectorMassIntegrator;
         vmass->SetVDim(smooth_flux_fes.GetVDim());
         a->AddDomainIntegrator(vmass);
         b->AddDomainIntegrator(new VectorDomainLFIntegrator(f));
      }
      else
      {
         a->AddDomainIntegrator(new VectorFEMassIntegrator);
         b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
      }
   }

   b->Assemble();
   a->Assemble();
   a->Finalize();

   // The destination of the projected discontinuous flux
   ParGridFunction smooth_flux(&smooth_flux_fes);
   smooth_flux = 0.0;

   HypreParMatrix* A = a->ParallelAssemble();
   HypreParVector* B = b->ParallelAssemble();
   HypreParVector* X = smooth_flux.ParallelProject();

   delete a;
   delete b;

   // Define and apply a parallel PCG solver for AX=B with the BoomerAMG
   // preconditioner from hypre.
   HypreBoomerAMG *amg = new HypreBoomerAMG(*A);
   amg->SetPrintLevel(0);
   HyprePCG *pcg = new HyprePCG(*A);
   pcg->SetTol(solver_tol);
   pcg->SetMaxIter(solver_max_it);
   pcg->SetPrintLevel(0);
   pcg->SetPreconditioner(*amg);
   pcg->Mult(*B, *X);

   // Extract the parallel grid function corresponding to the finite element
   // approximation X. This is the local solution on each processor.
   smooth_flux = *X;

   delete A;
   delete B;
   delete X;
   delete amg;
   delete pcg;

   // Proceed through the elements one by one, and find the Lp norm differences
   // between the flux as computed per element and the flux projected onto the
   // smooth_flux_fes space.
   double total_error = 0.0;
   errors.SetSize(xfes->GetNE());
   for (int i = 0; i < xfes->GetNE(); i++)
   {
      errors(i) = ComputeElementLpDistance(norm_p, i, smooth_flux, flux);
      total_error += pow(errors(i), norm_p);
   }

   double glob_error;
   MPI_Allreduce(&total_error, &glob_error, 1, MPI_DOUBLE, MPI_SUM,
                 xfes->GetComm());

   return pow(glob_error, 1.0/norm_p);
}