323 lines
12 KiB
C++
323 lines
12 KiB
C++
// MFEM Example 6 - Parallel Version
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// PETSc Modification
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//
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// Compile with: make ex6p
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//
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// Sample runs:
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// mpirun -np 4 ex6p -m ../../data/amr-quad.mesh
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// mpirun -np 4 ex6p -m ../../data/amr-quad.mesh -nonoverlapping
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//
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// Description: This is a version of Example 1 with a simple adaptive mesh
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// refinement loop. The problem being solved is again the Laplace
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// equation -Delta u = 1 with homogeneous Dirichlet boundary
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// conditions. The problem is solved on a sequence of meshes which
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// are locally refined in a conforming (triangles, tetrahedrons)
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// or non-conforming (quadrilaterals, hexahedra) manner according
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// to a simple ZZ error estimator.
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//
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// The example demonstrates MFEM's capability to work with both
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// conforming and nonconforming refinements, in 2D and 3D, on
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// linear, curved and surface meshes. Interpolation of functions
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// from coarse to fine meshes, as well as persistent GLVis
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// visualization are also illustrated.
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//
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// PETSc assembly timings can be benchmarked if requested by
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// command line.
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//
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// We recommend viewing Example 1 before viewing this example.
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#include "mfem.hpp"
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#include <fstream>
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#include <iostream>
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#ifndef MFEM_USE_PETSC
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#error This example requires that MFEM is built with MFEM_USE_PETSC=YES
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#endif
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using namespace std;
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using namespace mfem;
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int main(int argc, char *argv[])
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{
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// 1. Initialize MPI.
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int num_procs, myid;
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MPI_Init(&argc, &argv);
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MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
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MPI_Comm_rank(MPI_COMM_WORLD, &myid);
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// 2. Parse command-line options.
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const char *mesh_file = "../../data/star.mesh";
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int order = 1;
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bool visualization = true;
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int max_dofs = 100000;
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bool use_petsc = true;
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const char *petscrc_file = "";
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bool use_nonoverlapping = false;
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OptionsParser args(argc, argv);
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args.AddOption(&mesh_file, "-m", "--mesh",
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"Mesh file to use.");
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args.AddOption(&order, "-o", "--order",
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"Finite element order (polynomial degree).");
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args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
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"--no-visualization",
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"Enable or disable GLVis visualization.");
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args.AddOption(&max_dofs, "-md", "--max_dofs",
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"Maximum number of dofs.");
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args.AddOption(&use_petsc, "-usepetsc", "--usepetsc", "-no-petsc",
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"--no-petsc",
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"Use or not PETSc to solve the linear system.");
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args.AddOption(&petscrc_file, "-petscopts", "--petscopts",
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"PetscOptions file to use.");
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args.AddOption(&use_nonoverlapping, "-nonoverlapping", "--nonoverlapping",
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"-no-nonoverlapping", "--no-nonoverlapping",
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"Use or not the block diagonal PETSc's matrix format "
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"for non-overlapping domain decomposition.");
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args.Parse();
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if (!args.Good())
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{
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if (myid == 0)
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{
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args.PrintUsage(cout);
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}
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MPI_Finalize();
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return 1;
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}
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if (myid == 0)
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{
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args.PrintOptions(cout);
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}
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// 2b. We initialize PETSc
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if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }
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// 3. Read the (serial) mesh from the given mesh file on all processors. We
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// can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
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// and volume meshes with the same code.
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Mesh *mesh = new Mesh(mesh_file, 1, 1);
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int dim = mesh->Dimension();
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int sdim = mesh->SpaceDimension();
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// 4. Refine the serial mesh on all processors to increase the resolution.
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// Also project a NURBS mesh to a piecewise-quadratic curved mesh. Make
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// sure that the mesh is non-conforming.
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if (mesh->NURBSext)
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{
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mesh->UniformRefinement();
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mesh->SetCurvature(2);
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}
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mesh->EnsureNCMesh();
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// 5. Define a parallel mesh by partitioning the serial mesh.
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// Once the parallel mesh is defined, the serial mesh can be deleted.
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ParMesh pmesh(MPI_COMM_WORLD, *mesh);
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delete mesh;
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MFEM_VERIFY(pmesh.bdr_attributes.Size() > 0,
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"Boundary attributes required in the mesh.");
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Array<int> ess_bdr(pmesh.bdr_attributes.Max());
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ess_bdr = 1;
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// 6. Define a finite element space on the mesh. The polynomial order is
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// one (linear) by default, but this can be changed on the command line.
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H1_FECollection fec(order, dim);
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ParFiniteElementSpace fespace(&pmesh, &fec);
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// 7. As in Example 1p, we set up bilinear and linear forms corresponding to
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// the Laplace problem -\Delta u = 1. We don't assemble the discrete
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// problem yet, this will be done in the main loop.
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ParBilinearForm a(&fespace);
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ParLinearForm b(&fespace);
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ConstantCoefficient one(1.0);
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BilinearFormIntegrator *integ = new DiffusionIntegrator(one);
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a.AddDomainIntegrator(integ);
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b.AddDomainIntegrator(new DomainLFIntegrator(one));
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// 8. The solution vector x and the associated finite element grid function
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// will be maintained over the AMR iterations. We initialize it to zero.
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ParGridFunction x(&fespace);
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x = 0;
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// 9. Connect to GLVis.
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char vishost[] = "localhost";
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int visport = 19916;
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socketstream sout;
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if (visualization)
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{
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sout.open(vishost, visport);
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if (!sout)
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{
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if (myid == 0)
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{
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cout << "Unable to connect to GLVis server at "
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<< vishost << ':' << visport << endl;
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cout << "GLVis visualization disabled.\n";
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}
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visualization = false;
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}
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sout.precision(8);
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}
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// 10. Set up an error estimator. Here we use the Zienkiewicz-Zhu estimator
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// with L2 projection in the smoothing step to better handle hanging
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// nodes and parallel partitioning. We need to supply a space for the
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// discontinuous flux (L2) and a space for the smoothed flux (H(div) is
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// used here).
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L2_FECollection flux_fec(order, dim);
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ParFiniteElementSpace flux_fes(&pmesh, &flux_fec, sdim);
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RT_FECollection smooth_flux_fec(order-1, dim);
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ParFiniteElementSpace smooth_flux_fes(&pmesh, &smooth_flux_fec);
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// Another possible option for the smoothed flux space:
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// H1_FECollection smooth_flux_fec(order, dim);
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// ParFiniteElementSpace smooth_flux_fes(&pmesh, &smooth_flux_fec, dim);
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L2ZienkiewiczZhuEstimator estimator(*integ, x, flux_fes, smooth_flux_fes);
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// 11. A refiner selects and refines elements based on a refinement strategy.
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// The strategy here is to refine elements with errors larger than a
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// fraction of the maximum element error. Other strategies are possible.
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// The refiner will call the given error estimator.
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ThresholdRefiner refiner(estimator);
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refiner.SetTotalErrorFraction(0.7);
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// 12. The main AMR loop. In each iteration we solve the problem on the
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// current mesh, visualize the solution, and refine the mesh.
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for (int it = 0; ; it++)
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{
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HYPRE_Int global_dofs = fespace.GlobalTrueVSize();
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if (myid == 0)
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{
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cout << "\nAMR iteration " << it << endl;
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cout << "Number of unknowns: " << global_dofs << endl;
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}
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// 13. Assemble the stiffness matrix and the right-hand side. Note that
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// MFEM doesn't care at this point that the mesh is nonconforming
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// and parallel. The FE space is considered 'cut' along hanging
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// edges/faces, and also across processor boundaries.
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a.Assemble();
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b.Assemble();
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// 14. Create the parallel linear system: eliminate boundary conditions,
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// constrain hanging nodes and nodes across processor boundaries.
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// The system will be solved for true (unconstrained/unique) DOFs only.
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Array<int> ess_tdof_list;
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fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
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double time;
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const int copy_interior = 1;
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if (use_petsc)
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{
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a.SetOperatorType(use_nonoverlapping ?
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Operator::PETSC_MATIS : Operator::PETSC_MATAIJ);
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PetscParMatrix pA;
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Vector pX,pB;
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MPI_Barrier(MPI_COMM_WORLD);
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time = -MPI_Wtime();
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a.FormLinearSystem(ess_tdof_list, x, b, pA, pX, pB, copy_interior);
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MPI_Barrier(MPI_COMM_WORLD);
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time += MPI_Wtime();
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if (myid == 0) { cout << "PETSc assembly timing : " << time << endl; }
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}
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a.Assemble();
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b.Assemble();
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a.SetOperatorType(Operator::Hypre_ParCSR);
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HypreParMatrix A;
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Vector B, X;
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MPI_Barrier(MPI_COMM_WORLD);
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time = -MPI_Wtime();
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a.FormLinearSystem(ess_tdof_list, x, b, A, X, B, copy_interior);
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MPI_Barrier(MPI_COMM_WORLD);
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time += MPI_Wtime();
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if (myid == 0) { cout << "HYPRE assembly timing : " << time << endl; }
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// 15. Define and apply a parallel PCG solver for AX=B with the BoomerAMG
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// preconditioner from hypre.
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HypreBoomerAMG amg;
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amg.SetPrintLevel(0);
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CGSolver pcg(A.GetComm());
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pcg.SetPreconditioner(amg);
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pcg.SetOperator(A);
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pcg.SetRelTol(1e-6);
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pcg.SetMaxIter(200);
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pcg.SetPrintLevel(3); // print the first and the last iterations only
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pcg.Mult(B, X);
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// 16. Extract the parallel grid function corresponding to the finite element
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// approximation X. This is the local solution on each processor.
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a.RecoverFEMSolution(X, b, x);
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// 17. Send the solution by socket to a GLVis server.
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if (visualization)
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{
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sout << "parallel " << num_procs << " " << myid << "\n";
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sout << "solution\n" << pmesh << x << flush;
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}
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if (global_dofs > max_dofs)
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{
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if (myid == 0)
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{
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cout << "Reached the maximum number of dofs. Stop." << endl;
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}
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// we need to call Update here to delete any internal PETSc object that
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// have been created by the ParBilinearForm; otherwise, these objects
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// will be destroyed at the end of the main scope, when PETSc has been
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// already finalized.
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a.Update();
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b.Update();
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break;
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}
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// 18. Call the refiner to modify the mesh. The refiner calls the error
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// estimator to obtain element errors, then it selects elements to be
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// refined and finally it modifies the mesh. The Stop() method can be
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// used to determine if a stopping criterion was met.
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refiner.Apply(pmesh);
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if (refiner.Stop())
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{
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if (myid == 0)
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{
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cout << "Stopping criterion satisfied. Stop." << endl;
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}
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a.Update();
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b.Update();
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break;
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}
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// 19. Update the finite element space (recalculate the number of DOFs,
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// etc.) and create a grid function update matrix. Apply the matrix
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// to any GridFunctions over the space. In this case, the update
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// matrix is an interpolation matrix so the updated GridFunction will
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// still represent the same function as before refinement.
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fespace.Update();
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x.Update();
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// 20. Load balance the mesh, and update the space and solution. Currently
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// available only for nonconforming meshes.
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if (pmesh.Nonconforming())
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{
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pmesh.Rebalance();
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// Update the space and the GridFunction. This time the update matrix
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// redistributes the GridFunction among the processors.
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fespace.Update();
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x.Update();
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}
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// 21. Inform also the bilinear and linear forms that the space has
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// changed.
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a.Update();
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b.Update();
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}
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// We finalize PETSc
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if (use_petsc) { MFEMFinalizePetsc(); }
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MPI_Finalize();
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return 0;
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}
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