MFEM v2.0
ex4p.cpp
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00001 //                                MFEM Example 4
00002 //
00003 // Compile with: make ex4
00004 //
00005 // Sample runs:  mpirun -np 4 ex4p ../data/square-disc.mesh
00006 //               mpirun -np 4 ex4p ../data/star.mesh
00007 //               mpirun -np 4 ex4p ../data/beam-tet.mesh
00008 //               mpirun -np 4 ex4p ../data/beam-hex.mesh
00009 //               mpirun -np 4 ex4p ../data/escher.mesh
00010 //               mpirun -np 4 ex4p ../data/fichera.mesh
00011 //               mpirun -np 4 ex4p ../data/fichera-q2.vtk
00012 //               mpirun -np 4 ex4p ../data/fichera-q3.mesh
00013 //               mpirun -np 4 ex4p ../data/square-disc-nurbs.mesh
00014 //               mpirun -np 4 ex4p ../data/beam-hex-nurbs.mesh
00015 //
00016 // Description:  This example code solves a simple 2D/3D H(div) diffusion
00017 //               problem corresponding to the second order definite equation
00018 //               -grad(alpha div F) + beta F = f with boundary condition F dot n
00019 //               = <given normal field>. Here, we use a given exact solution F
00020 //               and compute the corresponding r.h.s. f.  We discretize with
00021 //               Raviart-Thomas finite elements.
00022 //
00023 //               The example demonstrates the use of H(div) finite element
00024 //               spaces with the grad-div and H(div) vector finite element mass
00025 //               bilinear form, as well as the computation of discretization
00026 //               error when the exact solution is known.
00027 //
00028 //               We recommend viewing examples 1-3 before viewing this example.
00029
00030 #include <fstream>
00031 #include "mfem.hpp"
00032
00033 // Exact solution, F, and r.h.s., f. See below for implementation.
00034 void F_exact(const Vector &, Vector &);
00035 void f_exact(const Vector &, Vector &);
00036
00037 int main (int argc, char *argv[])
00038 {
00039    int num_procs, myid;
00040
00041    // 1. Initialize MPI
00042    MPI_Init(&argc, &argv);
00043    MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
00044    MPI_Comm_rank(MPI_COMM_WORLD, &myid);
00045
00046    Mesh *mesh;
00047
00048    if (argc == 1)
00049    {
00050       cout << "\nUsage: mpirun -np <np> ex4p <mesh_file>\n" << endl;
00051       MPI_Finalize();
00052       return 1;
00053    }
00054
00055    // 2. Read the (serial) mesh from the given mesh file on all processors.
00056    //    In this 2D/3D example, we can handle triangular, quadrilateral,
00057    //    tetrahedral or hexahedral meshes with the same code.
00058    ifstream imesh(argv[1]);
00059    if (!imesh)
00060    {
00061       if (myid == 0)
00062          cerr << "\nCan not open mesh file: " << argv[1] << '\n' << endl;
00063       MPI_Finalize();
00064       return 2;
00065    }
00066    mesh = new Mesh(imesh, 1, 1);
00067    imesh.close();
00068
00069    const int dim = mesh->Dimension();
00070
00071    // 3. Refine the serial mesh on all processors to increase the resolution. In
00072    //    this example we do 'ref_levels' of uniform refinement. We choose
00073    //    'ref_levels' to be the largest number that gives a final mesh with no
00074    //    more than 1,000 elements.
00075    {
00076       int ref_levels =
00077          (int)floor(log(1000./mesh->GetNE())/log(2.)/dim);
00078       for (int l = 0; l < ref_levels; l++)
00079          mesh->UniformRefinement();
00080    }
00081
00082    // 4. Define a parallel mesh by a partitioning of the serial mesh. Refine
00083    //    this mesh further in parallel to increase the resolution. Once the
00084    //    parallel mesh is defined, the serial mesh can be deleted. Tetrahedral
00085    //    meshes need to be reoriented before we can define high-order Nedelec
00086    //    spaces on them (this is needed in the ADS solver below).
00087    ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
00088    delete mesh;
00089    {
00090       int par_ref_levels = 2;
00091       for (int l = 0; l < par_ref_levels; l++)
00092          pmesh->UniformRefinement();
00093    }
00094    pmesh->ReorientTetMesh();
00095
00096    // 5. Define a parallel finite element space on the parallel mesh. Here we
00097    //    use the lowest order Raviart-Thomas finite elements, but we can easily
00098    //    swich to higher-order spaces by changing the value of p.
00099    int p = 1;
00100    FiniteElementCollection *fec = new RT_FECollection(p-1, pmesh -> Dimension());
00101    ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
00102    int size = fespace->GlobalTrueVSize();
00103    if (myid == 0)
00104       cout << "Number of unknowns: " << size << endl;
00105
00106    // 6. Set up the parallel linear form b(.) which corresponds to the
00107    //    right-hand side of the FEM linear system, which in this case is
00108    //    (f,phi_i) where f is given by the function f_exact and phi_i are the
00109    //    basis functions in the finite element fespace.
00110    VectorFunctionCoefficient f(dim, f_exact);
00111    ParLinearForm *b = new ParLinearForm(fespace);
00113    b->Assemble();
00114
00115    // 7. Define the solution vector x as a parallel finite element grid function
00116    //    corresponding to fespace. Initialize x by projecting the exact
00117    //    solution. Note that only values from the boundary faces will be used
00118    //    when eliminating the non-homogeneous boundary condition to modify the
00119    //    r.h.s. vector b.
00120    ParGridFunction x(fespace);
00121    VectorFunctionCoefficient F(dim, F_exact);
00122    x.ProjectCoefficient(F);
00123
00124    // 8. Set up the parallel bilinear form corresponding to the H(div) diffusion
00125    //    operator grad alpha div + beta I, by adding the div-div and the
00126    //    mass domain integrators and finally imposing non-homogeneous Dirichlet
00127    //    boundary conditions. The boundary conditions are implemented by
00128    //    marking all the boundary attributes from the mesh as essential
00129    //    (Dirichlet). After serial and parallel assembly we extract the
00130    //    parallel matrix A.
00131    Coefficient *alpha = new ConstantCoefficient(1.0);
00132    Coefficient *beta  = new ConstantCoefficient(1.0);
00133    ParBilinearForm *a = new ParBilinearForm(fespace);
00136    a->Assemble();
00137    {
00138       Array<int> ess_bdr(pmesh->bdr_attributes.Max());
00139       ess_bdr = 1;
00140       Array<int> ess_dofs;
00141       fespace->GetEssentialVDofs(ess_bdr, ess_dofs);
00142       a->EliminateEssentialBCFromDofs(ess_dofs, x, *b);
00143    }
00144    a->Finalize();
00145
00146    // 9. Define the parallel (hypre) matrix and vectors representing a(.,.),
00147    //    b(.) and the finite element approximation.
00148    HypreParMatrix *A = a->ParallelAssemble();
00149    HypreParVector *B = b->ParallelAssemble();
00150    HypreParVector *X = x.ParallelAverage();
00151    *X = 0.0;
00152
00153    delete a;
00154    delete alpha;
00155    delete beta;
00156    delete b;
00157
00158    // 10. Define and apply a parallel PCG solver for AX=B with the 2D AMS or the
00159    //     3D ADS preconditioners from hypre.
00160    HypreSolver *prec;
00161    if (dim == 2)
00162       prec = new HypreAMS(*A, fespace);
00163    else
00164       prec = new HypreADS(*A, fespace);
00165    HyprePCG *pcg = new HyprePCG(*A);
00166    pcg->SetTol(1e-10);
00167    pcg->SetMaxIter(500);
00168    pcg->SetPrintLevel(2);
00169    pcg->SetPreconditioner(*prec);
00170    pcg->Mult(*B, *X);
00171
00172    // 11. Extract the parallel grid function corresponding to the finite element
00173    //     approximation X. This is the local solution on each processor.
00174    x = *X;
00175
00176    // 12. Compute and print the L^2 norm of the error.
00177    {
00178       double err = x.ComputeL2Error(F);
00179       if (myid == 0)
00180          cout << "\n|| F_h - F ||_{L^2} = " << err << '\n' << endl;
00181    }
00182
00183    // 13. Save the refined mesh and the solution in parallel. This output can
00184    //     be viewed later using GLVis: "glvis -np <np> -m mesh -g sol".
00185    {
00186       ostringstream mesh_name, sol_name;
00187       mesh_name << "mesh." << setfill('0') << setw(6) << myid;
00188       sol_name << "sol." << setfill('0') << setw(6) << myid;
00189
00190       ofstream mesh_ofs(mesh_name.str().c_str());
00191       mesh_ofs.precision(8);
00192       pmesh->Print(mesh_ofs);
00193
00194       ofstream sol_ofs(sol_name.str().c_str());
00195       sol_ofs.precision(8);
00196       x.Save(sol_ofs);
00197    }
00198
00199    // 14. (Optional) Send the solution by socket to a GLVis server.
00200    char vishost[] = "localhost";
00201    int  visport   = 19916;
00202    osockstream sol_sock(visport, vishost);
00203    sol_sock << "parallel " << num_procs << " " << myid << "\n";
00204    sol_sock << "solution\n";
00205    sol_sock.precision(8);
00206    pmesh->Print(sol_sock);
00207    x.Save(sol_sock);
00208    sol_sock.send();
00209
00210    // 15. Free the used memory.
00211    delete pcg;
00212    delete prec;
00213    delete X;
00214    delete B;
00215    delete A;
00216    delete fespace;
00217    delete fec;
00218    delete pmesh;
00219
00220    MPI_Finalize();
00221
00222    return 0;
00223 }
00224
00225
00226 // The exact solution
00227 void F_exact(const Vector &p, Vector &F)
00228 {
00229    double x,y,z;
00230
00231    int dim = p.Size();
00232
00233    x = p(0);
00234    y = p(1);
00235    if(dim == 3)
00236       z = p(2);
00237
00238    F(0) = cos(M_PI*x)*sin(M_PI*y);
00239    F(1) = cos(M_PI*y)*sin(M_PI*x);
00240    if(dim == 3)
00241       F(2) = 0.0;
00242 }
00243
00244 // The right hand side
00245 void f_exact(const Vector &p, Vector &f)
00246 {
00247    double x,y,z;
00248
00249    int dim = p.Size();
00250
00251    x = p(0);
00252    y = p(1);
00253    if(dim == 3)
00254       z = p(2);
00255
00256    double temp = 1 + 2*M_PI*M_PI;
00257
00258    f(0) = temp*cos(M_PI*x)*sin(M_PI*y);
00259    f(1) = temp*cos(M_PI*y)*sin(M_PI*x);
00260    if(dim == 3)
00261       f(2) = 0;
00262 }