ex13p.cpp

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//                       MFEM Example 13 - Parallel Version
//
// Compile with: make ex13p
//
// Sample runs:  mpirun -np 4 ex13p -m ../data/star.mesh
//               mpirun -np 4 ex13p -m ../data/square-disc.mesh -o 2
//               mpirun -np 4 ex13p -m ../data/beam-tet.mesh
//               mpirun -np 4 ex13p -m ../data/beam-hex.mesh
//               mpirun -np 4 ex13p -m ../data/escher.mesh
//               mpirun -np 4 ex13p -m ../data/fichera.mesh
//               mpirun -np 4 ex13p -m ../data/fichera-q2.vtk
//               mpirun -np 4 ex13p -m ../data/fichera-q3.mesh
//               mpirun -np 4 ex13p -m ../data/square-disc-nurbs.mesh
//               mpirun -np 4 ex13p -m ../data/beam-hex-nurbs.mesh
//               mpirun -np 4 ex13p -m ../data/amr-quad.mesh -o 2
//               mpirun -np 4 ex13p -m ../data/amr-hex.mesh
//               mpirun -np 4 ex13p -m ../data/mobius-strip.mesh -n 8 -o 2
//               mpirun -np 4 ex13p -m ../data/klein-bottle.mesh -n 10 -o 2
//
// Description:  This example code solves the Maxwell (electromagnetic)
//               eigenvalue problem curl curl E = lambda E with homogeneous
//               Dirichlet boundary conditions E x n = 0.
//
//               We compute a number of the lowest nonzero eigenmodes by
//               discretizing the curl curl operator using a Nedelec FE space of
//               the specified order in 2D or 3D.
//
//               The example highlights the use of the AME subspace eigenvalue
//               solver from HYPRE, which uses LOBPCG and AMS internally.
//               Reusing a single GLVis visualization window for multiple
//               eigenfunctions is also illustrated.
//
//               We recommend viewing examples 3 and 11 before viewing this
//               example.

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

using namespace std;
using namespace 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 ser_ref_levels = 2;
   int par_ref_levels = 1;
   int order = 1;
   int nev = 5;
   bool visualization = 1;

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
                  "Mesh file to use.");
   args.AddOption(&ser_ref_levels, "-rs", "--refine-serial",
                  "Number of times to refine the mesh uniformly in serial.");
   args.AddOption(&par_ref_levels, "-rp", "--refine-parallel",
                  "Number of times to refine the mesh uniformly in parallel.");
   args.AddOption(&order, "-o", "--order",
                  "Finite element order (polynomial degree) or -1 for"
                  " isoparametric space.");
   args.AddOption(&nev, "-n", "--num-eigs",
                  "Number of desired eigenmodes.");
   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 = new Mesh(mesh_file, 1, 1);
   int dim = mesh->Dimension();

   // 4. Refine the serial mesh on all processors to increase the resolution. In
   //    this example we do 'ref_levels' of uniform refinement (2 by default, or
   //    specified on the command line with -rs).
   for (int lev = 0; lev < ser_ref_levels; lev++)
   {
      mesh->UniformRefinement();
   }

   // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
   //    this mesh further in parallel to increase the resolution (1 time by
   //    default, or specified on the command line with -rp). Once the parallel
   //    mesh is defined, the serial mesh can be deleted.
   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
   delete mesh;
   for (int lev = 0; lev < par_ref_levels; lev++)
   {
      pmesh->UniformRefinement();
   }

   // 6. Define a parallel finite element space on the parallel mesh. Here we
   //    use the Nedelec finite elements of the specified order.
   FiniteElementCollection *fec = new ND_FECollection(order, dim);
   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
   HYPRE_Int size = fespace->GlobalTrueVSize();
   if (myid == 0)
   {
      cout << "Number of unknowns: " << size << endl;
   }

   // 7. Set up the parallel bilinear forms a(.,.) and m(.,.) on the finite
   //    element space. The first corresponds to the curl curl, while the second
   //    is a simple mass matrix needed on the right hand side of the
   //    generalized eigenvalue problem below. The boundary conditions are
   //    implemented by marking all the boundary attributes from the mesh as
   //    essential. The corresponding degrees of freedom are eliminated with
   //    special values on the diagonal to shift the Dirichlet eigenvalues out
   //    of the computational range. After serial and parallel assembly we
   //    extract the corresponding parallel matrices A and M.
   ConstantCoefficient one(1.0);
   Array<int> ess_bdr;
   if (pmesh->bdr_attributes.Size())
   {
      ess_bdr.SetSize(pmesh->bdr_attributes.Max());
      ess_bdr = 1;
   }

   ParBilinearForm *a = new ParBilinearForm(fespace);
   a->AddDomainIntegrator(new CurlCurlIntegrator(one));
   if (pmesh->bdr_attributes.Size() == 0)
   {
      // Add a mass term if the mesh has no boundary, e.g. periodic mesh or
      // closed surface.
      a->AddDomainIntegrator(new VectorFEMassIntegrator(one));
   }
   a->Assemble();
   a->EliminateEssentialBCDiag(ess_bdr, 1.0);
   a->Finalize();

   ParBilinearForm *m = new ParBilinearForm(fespace);
   m->AddDomainIntegrator(new VectorFEMassIntegrator(one));
   m->Assemble();
   // shift the eigenvalue corresponding to eliminated dofs to a large value
   m->EliminateEssentialBCDiag(ess_bdr, numeric_limits<double>::min());
   m->Finalize();

   HypreParMatrix *A = a->ParallelAssemble();
   HypreParMatrix *M = m->ParallelAssemble();

   delete a;
   delete m;

   // 8. Define and configure the AME eigensolver and the AMS preconditioner for
   //    A to be used within the solver. Set the matrices which define the
   //    generalized eigenproblem A x = lambda M x.
   HypreAMS *ams = new HypreAMS(*A,fespace);
   ams->SetPrintLevel(0);
   ams->SetSingularProblem();

   HypreAME *ame = new HypreAME(MPI_COMM_WORLD);
   ame->SetNumModes(nev);
   ame->SetPreconditioner(*ams);
   ame->SetMaxIter(100);
   ame->SetTol(1e-8);
   ame->SetPrintLevel(1);
   ame->SetMassMatrix(*M);
   ame->SetOperator(*A);

   // 9. Compute the eigenmodes and extract the array of eigenvalues. Define a
   //    parallel grid function to represent each of the eigenmodes returned by
   //    the solver.
   Array<double> eigenvalues;
   ame->Solve();
   ame->GetEigenvalues(eigenvalues);
   ParGridFunction x(fespace);

   // 10. Save the refined mesh and the modes in parallel. This output can be
   //     viewed later using GLVis: "glvis -np <np> -m mesh -g mode".
   {
      ostringstream mesh_name, mode_name;
      mesh_name << "mesh." << setfill('0') << setw(6) << myid;

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

      for (int i=0; i<nev; i++)
      {
         // convert eigenvector from HypreParVector to ParGridFunction
         x = ame->GetEigenvector(i);

         mode_name << "mode_" << setfill('0') << setw(2) << i << "."
                   << setfill('0') << setw(6) << myid;

         ofstream mode_ofs(mode_name.str().c_str());
         mode_ofs.precision(8);
         x.Save(mode_ofs);
         mode_name.str("");
      }
   }

   // 11. Send the solution by socket to a GLVis server.
   if (visualization)
   {
      char vishost[] = "localhost";
      int  visport   = 19916;
      socketstream mode_sock(vishost, visport);
      mode_sock.precision(8);

      for (int i=0; i<nev; i++)
      {
         if ( myid == 0 )
         {
            cout << "Eigenmode " << i+1 << '/' << nev
                 << ", Lambda = " << eigenvalues[i] << endl;
         }

         // convert eigenvector from HypreParVector to ParGridFunction
         x = ame->GetEigenvector(i);

         mode_sock << "parallel " << num_procs << " " << myid << "\n"
                   << "solution\n" << *pmesh << x << flush
                   << "window_title 'Eigenmode " << i+1 << '/' << nev
                   << ", Lambda = " << eigenvalues[i] << "'" << endl;

         char c;
         if (myid == 0)
         {
            cout << "press (q)uit or (c)ontinue --> " << flush;
            cin >> c;
         }
         MPI_Bcast(&c, 1, MPI_CHAR, 0, MPI_COMM_WORLD);

         if (c != 'c')
         {
            break;
         }
      }
      mode_sock.close();
   }

   // 12. Free the used memory.
   delete ame;
   delete ams;
   delete M;
   delete A;

   delete fespace;
   delete fec;
   delete pmesh;

   MPI_Finalize();

   return 0;
}