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
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);
}