Exemple #1
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.
   const char *mesh_file = "../../data/star.mesh";
   int order = 1;
   bool set_bc = true;
   bool static_cond = false;
   bool hybridization = false;
   bool visualization = 1;
   bool use_petsc = true;
   const char *petscrc_file = "";
   bool use_nonoverlapping = false;

   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(&set_bc, "-bc", "--impose-bc", "-no-bc", "--dont-impose-bc",
                  "Impose or not essential boundary conditions.");
   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(&hybridization, "-hb", "--hybridization", "-no-hb",
                  "--no-hybridization", "Enable hybridization.");
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
   args.AddOption(&use_petsc, "-usepetsc", "--usepetsc", "-no-petsc",
                  "--no-petsc",
                  "Use or not PETSc to solve the linear system.");
   args.AddOption(&petscrc_file, "-petscopts", "--petscopts",
                  "PetscOptions file to use.");
   args.AddOption(&use_nonoverlapping, "-nonoverlapping", "--nonoverlapping",
                  "-no-nonoverlapping", "--no-nonoverlapping",
                  "Use or not the block diagonal PETSc's matrix format "
                  "for non-overlapping domain decomposition.");
   args.Parse();
   if (!args.Good())
   {
      if (myid == 0)
      {
         args.PrintUsage(cout);
      }
      MPI_Finalize();
      return 1;
   }
   if (myid == 0)
   {
      args.PrintOptions(cout);
   }
   // 2b. We initialize PETSc
   if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }
   kappa = freq * M_PI;

   // 3. Read the (serial) mesh from the given mesh file on all processors.  We
   //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
   //    and volume, as well as periodic meshes with the same code.
   Mesh *mesh = new Mesh(mesh_file, 1, 1);
   int dim = mesh->Dimension();
   int sdim = mesh->SpaceDimension();

   // 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 (this is needed in the ADS solver below).
   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 Raviart-Thomas finite elements of the specified order.
   FiniteElementCollection *fec = new RT_FECollection(order-1, 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;
   if (pmesh->bdr_attributes.Size())
   {
      Array<int> ess_bdr(pmesh->bdr_attributes.Max());
      ess_bdr = set_bc ? 1 : 0;
      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.
   VectorFunctionCoefficient f(sdim, f_exact);
   ParLinearForm *b = new ParLinearForm(fespace);
   b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
   b->Assemble();

   // 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 faces will be used
   //    when eliminating the non-homogeneous boundary condition to modify the
   //    r.h.s. vector b.
   ParGridFunction x(fespace);
   VectorFunctionCoefficient F(sdim, F_exact);
   x.ProjectCoefficient(F);

   // 10. Set up the parallel bilinear form corresponding to the H(div)
   //     diffusion operator grad alpha div + beta I, by adding the div-div and
   //     the mass domain integrators.
   Coefficient *alpha = new ConstantCoefficient(1.0);
   Coefficient *beta  = new ConstantCoefficient(1.0);
   ParBilinearForm *a = new ParBilinearForm(fespace);
   a->AddDomainIntegrator(new DivDivIntegrator(*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,
   //     hybridization, etc.
   FiniteElementCollection *hfec = NULL;
   ParFiniteElementSpace *hfes = NULL;
   if (static_cond)
   {
      a->EnableStaticCondensation();
   }
   else if (hybridization)
   {
      hfec = new DG_Interface_FECollection(order-1, dim);
      hfes = new ParFiniteElementSpace(pmesh, hfec);
      a->EnableHybridization(hfes, new NormalTraceJumpIntegrator(),
                             ess_tdof_list);
   }
   a->Assemble();

   Vector B, X;
   CGSolver *pcg = new CGSolver(MPI_COMM_WORLD);
   pcg->SetRelTol(1e-12);
   pcg->SetMaxIter(500);
   pcg->SetPrintLevel(1);

   if (!use_petsc)
   {
      HypreParMatrix A;
      a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);

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

      // 12. Define and apply a parallel PCG solver for A X = B with the 2D AMS or
      //     the 3D ADS preconditioners from hypre. If using hybridization, the
      //     system is preconditioned with hypre's BoomerAMG.
      HypreSolver *prec = NULL;
      pcg->SetOperator(A);
      if (hybridization) { prec = new HypreBoomerAMG(A); }
      else
      {
         ParFiniteElementSpace *prec_fespace =
            (a->StaticCondensationIsEnabled() ? a->SCParFESpace() : fespace);
         if (dim == 2)   { prec = new HypreAMS(A, prec_fespace); }
         else            { prec = new HypreADS(A, prec_fespace); }
      }
      pcg->SetPreconditioner(*prec);
      pcg->Mult(B, X);
      delete prec;
   }
   else
   {
      PetscParMatrix A;
      PetscPreconditioner *prec = NULL;
      a->SetOperatorType(use_nonoverlapping ?
                         Operator::PETSC_MATIS : Operator::PETSC_MATAIJ);
      a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);

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

      pcg->SetOperator(A);
      if (use_nonoverlapping)
      {
         ParFiniteElementSpace *prec_fespace =
            (a->StaticCondensationIsEnabled() ? a->SCParFESpace() : fespace);

         // Auxiliary class for BDDC customization
         PetscBDDCSolverParams opts;
         // Inform the solver about the finite element space
         opts.SetSpace(prec_fespace);
         // Inform the solver about essential dofs
         opts.SetEssBdrDofs(&ess_tdof_list);
         // Create a BDDC solver with parameters
         prec = new PetscBDDCSolver(A, opts);
      }
      else
      {
         // Create an empty preconditioner that can be customized at runtime.
         prec = new PetscPreconditioner(A, "solver_");
      }
      pcg->SetPreconditioner(*prec);
      pcg->Mult(B, X);
      delete prec;
   }
   delete pcg;

   // 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(F);
      if (myid == 0)
      {
         cout << "\n|| F_h - F ||_{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;
   }

   // 17. Free the used memory.
   delete hfes;
   delete hfec;
   delete a;
   delete alpha;
   delete beta;
   delete b;
   delete fespace;
   delete fec;
   delete pmesh;

   // We finalize PETSc
   if (use_petsc) { MFEMFinalizePetsc(); }

   MPI_Finalize();

   return 0;
}
Exemple #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;
}
Exemple #3
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.
   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;
}
Exemple #4
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);
}