349 lines
11 KiB
C++
349 lines
11 KiB
C++
// MFEM Example 24 - Parallel Version
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//
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// Compile with: make ex24p
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//
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// Sample runs: mpirun -np 4 ex24p -m ../data/star.mesh
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// mpirun -np 4 ex24p -m ../data/square-disc.mesh -o 2
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// mpirun -np 4 ex24p -m ../data/beam-tet.mesh
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// mpirun -np 4 ex24p -m ../data/beam-hex.mesh -o 2 -pa
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// mpirun -np 4 ex24p -m ../data/escher.mesh
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// mpirun -np 4 ex24p -m ../data/escher.mesh -o 2
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// mpirun -np 4 ex24p -m ../data/fichera.mesh
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// mpirun -np 4 ex24p -m ../data/fichera-q2.vtk
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// mpirun -np 4 ex24p -m ../data/fichera-q3.mesh
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// mpirun -np 4 ex24p -m ../data/square-disc-nurbs.mesh
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// mpirun -np 4 ex24p -m ../data/beam-hex-nurbs.mesh
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// mpirun -np 4 ex24p -m ../data/amr-quad.mesh -o 2
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// mpirun -np 4 ex24p -m ../data/amr-hex.mesh
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//
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// Device sample runs:
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// mpirun -np 4 ex24p -m ../data/star.mesh -pa -d cuda
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// mpirun -np 4 ex24p -m ../data/star.mesh -pa -d raja-cuda
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// mpirun -np 4 ex24p -m ../data/star.mesh -pa -d raja-omp
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// mpirun -np 4 ex24p -m ../data/beam-hex.mesh -pa -d cuda
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//
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// Description: This example code illustrates usage of mixed finite element
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// spaces. Using two different approaches, we project a gradient
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// of a function in H^1 to H(curl). Other spaces and example
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// computations are to be added in the future.
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//
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// We recommend viewing examples 1 and 3 before viewing this
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// example.
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#include "mfem.hpp"
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#include <fstream>
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#include <iostream>
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using namespace std;
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using namespace mfem;
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double p_exact(const Vector &x);
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void gradp_exact(const Vector &, Vector &);
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int dim;
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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/beam-hex.mesh";
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int order = 1;
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bool static_cond = false;
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bool pa = false;
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const char *device_config = "cpu";
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bool visualization = 1;
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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(&static_cond, "-sc", "--static-condensation", "-no-sc",
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"--no-static-condensation", "Enable static condensation.");
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args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
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"--no-partial-assembly", "Enable Partial Assembly.");
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args.AddOption(&device_config, "-d", "--device",
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"Device configuration string, see Device::Configure().");
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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.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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// 3. Enable hardware devices such as GPUs, and programming models such as
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// CUDA, OCCA, RAJA and OpenMP based on command line options.
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Device device(device_config);
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if (myid == 0) { device.Print(); }
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// 4. 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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dim = mesh->Dimension();
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int sdim = mesh->SpaceDimension();
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// 5. Refine the serial mesh on all processors to increase the resolution. In
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// this example we do 'ref_levels' of uniform refinement. We choose
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// 'ref_levels' to be the largest number that gives a final mesh with no
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// more than 1,000 elements.
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{
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int ref_levels = (int)floor(log(1000./mesh->GetNE())/log(2.)/dim);
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for (int l = 0; l < ref_levels; l++)
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{
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mesh->UniformRefinement();
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}
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}
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// 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
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// this mesh further in parallel to increase the resolution. Once the
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// parallel mesh is defined, the serial mesh can be deleted. Tetrahedral
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// meshes need to be reoriented before we can define high-order Nedelec
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// spaces on them.
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ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
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delete mesh;
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{
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int par_ref_levels = 1;
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for (int l = 0; l < par_ref_levels; l++)
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{
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pmesh->UniformRefinement();
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}
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}
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pmesh->ReorientTetMesh();
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// 7. Define a parallel finite element space on the parallel mesh. Here we
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// use the Nedelec finite elements of the specified order.
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FiniteElementCollection *fec = new ND_FECollection(order, dim);
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FiniteElementCollection *H1fec = new H1_FECollection(order, dim);
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ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
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ParFiniteElementSpace *H1fespace = new ParFiniteElementSpace(pmesh, H1fec);
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HYPRE_Int size = fespace->GlobalTrueVSize();
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HYPRE_Int H1size = H1fespace->GlobalTrueVSize();
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if (myid == 0)
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{
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cout << "Number of Nedelec finite element unknowns: " << size << endl;
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cout << "Number of H1 finite element unknowns: " << H1size << endl;
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}
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// 8. Define the solution vector x as a parallel finite element grid function
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// corresponding to fespace. Initialize x by projecting the exact
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// solution. Note that only values from the boundary edges will be used
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// when eliminating the non-homogeneous boundary condition to modify the
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// r.h.s. vector b.
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ParGridFunction x(fespace);
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FunctionCoefficient p_coef(p_exact);
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ParGridFunction p(H1fespace);
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p.ProjectCoefficient(p_coef);
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p.SetTrueVector();
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p.SetFromTrueVector();
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VectorFunctionCoefficient gradp_coef(sdim, gradp_exact);
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// 9. Set up the parallel bilinear forms.
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Coefficient *muinv = new ConstantCoefficient(1.0);
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Coefficient *sigma = new ConstantCoefficient(1.0);
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ParBilinearForm *a = new ParBilinearForm(fespace);
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ParMixedBilinearForm *a_NDH1 = new ParMixedBilinearForm(H1fespace, fespace);
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if (pa)
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{
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a->SetAssemblyLevel(AssemblyLevel::PARTIAL);
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a_NDH1->SetAssemblyLevel(AssemblyLevel::PARTIAL);
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}
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// First approach: L2 projection
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a->AddDomainIntegrator(new VectorFEMassIntegrator(*sigma));
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a_NDH1->AddDomainIntegrator(new MixedVectorGradientIntegrator(*muinv));
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// 10. Assemble the parallel bilinear form and the corresponding linear
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// system, applying any necessary transformations such as: parallel
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// assembly, eliminating boundary conditions, applying conforming
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// constraints for non-conforming AMR, static condensation, etc.
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if (static_cond) { a->EnableStaticCondensation(); }
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a->Assemble();
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if (!pa) { a->Finalize(); }
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a_NDH1->Assemble();
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if (!pa) { a_NDH1->Finalize(); }
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Vector B(fespace->GetTrueVSize());
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Vector X(fespace->GetTrueVSize());
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if (pa)
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{
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ParLinearForm *b = new ParLinearForm(fespace); // used as a vector
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a_NDH1->Mult(p, *b); // process-local multiplication
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b->ParallelAssemble(B);
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delete b;
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}
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else
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{
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HypreParMatrix *NDH1 = a_NDH1->ParallelAssemble();
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Vector P(H1fespace->GetTrueVSize());
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p.GetTrueDofs(P);
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NDH1->Mult(P,B);
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delete NDH1;
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}
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// 11. Define and apply a parallel PCG solver for AX=B with Jacobi
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// preconditioner.
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if (pa)
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{
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Array<int> ess_tdof_list; // empty
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OperatorPtr A;
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a->FormSystemMatrix(ess_tdof_list, A);
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OperatorJacobiSmoother Jacobi(*a, ess_tdof_list);
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CGSolver cg(MPI_COMM_WORLD);
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cg.SetRelTol(1e-12);
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cg.SetMaxIter(1000);
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cg.SetPrintLevel(1);
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cg.SetOperator(*A);
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cg.SetPreconditioner(Jacobi);
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X = 0.0;
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cg.Mult(B, X);
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}
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else
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{
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HypreParMatrix *Amat = a->ParallelAssemble();
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HypreDiagScale Jacobi(*Amat);
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HyprePCG pcg(*Amat);
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pcg.SetTol(1e-12);
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pcg.SetMaxIter(1000);
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pcg.SetPrintLevel(2);
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pcg.SetPreconditioner(Jacobi);
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X = 0.0;
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pcg.Mult(B, X);
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delete Amat;
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}
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x.SetFromTrueDofs(X);
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// 12. Second approach: compute the same solution by applying
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// GradientInterpolator in H(curl).
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ParDiscreteLinearOperator grad(H1fespace, fespace);
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grad.AddDomainInterpolator(new GradientInterpolator());
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grad.Assemble();
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ParGridFunction gradp(fespace);
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grad.Mult(p, gradp);
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// 13. Compute the projection of the exact grad p.
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ParGridFunction exact_gradp(fespace);
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exact_gradp.ProjectCoefficient(gradp_coef);
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exact_gradp.SetTrueVector();
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exact_gradp.SetFromTrueVector();
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// 14. Compute and print the L^2 norm of the error.
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{
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double errSol = x.ComputeL2Error(gradp_coef);
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double errInterp = gradp.ComputeL2Error(gradp_coef);
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double errProj = exact_gradp.ComputeL2Error(gradp_coef);
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if (myid == 0)
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{
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cout << "\n Solution of (E_h,v) = (grad p_h,v) for E_h and v in "
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"H(curl): || E_h - grad p ||_{L^2} = " << errSol << '\n' << endl;
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cout << " Gradient interpolant E_h = grad p_h in H(curl): || E_h - "
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"grad p ||_{L^2} = " << errInterp << '\n' << endl;
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cout << " Projection E_h of exact grad p in H(curl): || E_h - grad p "
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"||_{L^2} = " << errProj << '\n' << endl;
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}
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}
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// 15. Save the refined mesh and the solution in parallel. This output can
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// be viewed later using GLVis: "glvis -np <np> -m mesh -g sol".
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{
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ostringstream mesh_name, sol_name;
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mesh_name << "mesh." << setfill('0') << setw(6) << myid;
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sol_name << "sol." << setfill('0') << setw(6) << myid;
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ofstream mesh_ofs(mesh_name.str().c_str());
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mesh_ofs.precision(8);
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pmesh->Print(mesh_ofs);
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ofstream sol_ofs(sol_name.str().c_str());
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sol_ofs.precision(8);
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x.Save(sol_ofs);
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}
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// 16. Send the solution by socket to a GLVis server.
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if (visualization)
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{
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char vishost[] = "localhost";
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int visport = 19916;
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socketstream sol_sock(vishost, visport);
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sol_sock << "parallel " << num_procs << " " << myid << "\n";
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sol_sock.precision(8);
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sol_sock << "solution\n" << *pmesh << x << flush;
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}
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// 17. Free the used memory.
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delete a;
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delete a_NDH1;
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delete sigma;
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delete muinv;
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delete fespace;
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delete H1fespace;
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delete fec;
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delete H1fec;
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delete pmesh;
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MPI_Finalize();
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return 0;
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}
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double p_exact(const Vector &x)
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{
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if (dim == 3)
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{
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return sin(x(0)) * sin(x(1)) * sin(x(2));
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}
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else if (dim == 2)
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{
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return sin(x(0)) * sin(x(1));
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}
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return 0.0;
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}
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void gradp_exact(const Vector &x, Vector &f)
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{
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if (dim == 3)
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{
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f(0) = cos(x(0)) * sin(x(1)) * sin(x(2));
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f(1) = sin(x(0)) * cos(x(1)) * sin(x(2));
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f(2) = sin(x(0)) * sin(x(1)) * cos(x(2));
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}
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else
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{
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f(0) = cos(x(0)) * sin(x(1));
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f(1) = sin(x(0)) * cos(x(1));
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if (x.Size() == 3) { f(2) = 0.0; }
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}
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}
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