# mfem/mfem

Switch branches/tags
Nothing to show
Fetching contributors…
Cannot retrieve contributors at this time
325 lines (294 sloc) 11.7 KB
 // MFEM Example 2 - Parallel Version // // Compile with: make ex2p // // Sample runs: mpirun -np 4 ex2p -m ../data/beam-tri.mesh // mpirun -np 4 ex2p -m ../data/beam-quad.mesh // mpirun -np 4 ex2p -m ../data/beam-tet.mesh // mpirun -np 4 ex2p -m ../data/beam-hex.mesh // mpirun -np 4 ex2p -m ../data/beam-tri.mesh -o 2 -sys // mpirun -np 4 ex2p -m ../data/beam-quad.mesh -o 3 -elast // mpirun -np 4 ex2p -m ../data/beam-quad.mesh -o 3 -sc // mpirun -np 4 ex2p -m ../data/beam-quad-nurbs.mesh // mpirun -np 4 ex2p -m ../data/beam-hex-nurbs.mesh // // Description: This example code solves a simple linear elasticity problem // describing a multi-material cantilever beam. // // Specifically, we approximate the weak form of -div(sigma(u))=0 // where sigma(u)=lambda*div(u)*I+mu*(grad*u+u*grad) is the stress // tensor corresponding to displacement field u, and lambda and mu // are the material Lame constants. The boundary conditions are // u=0 on the fixed part of the boundary with attribute 1, and // sigma(u).n=f on the remainder with f being a constant pull down // vector on boundary elements with attribute 2, and zero // otherwise. The geometry of the domain is assumed to be as // follows: // // +----------+----------+ // boundary --->| material | material |<--- boundary // attribute 1 | 1 | 2 | attribute 2 // (fixed) +----------+----------+ (pull down) // // The example demonstrates the use of high-order and NURBS vector // finite element spaces with the linear elasticity bilinear form, // meshes with curved elements, and the definition of piece-wise // constant and vector coefficient objects. Static condensation is // also illustrated. // // We recommend viewing Example 1 before viewing this example. #include "mfem.hpp" #include #include 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-tri.mesh"; int order = 1; bool static_cond = false; bool visualization = 1; bool amg_elast = 0; 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(&amg_elast, "-elast", "--amg-for-elasticity", "-sys", "--amg-for-systems", "Use the special AMG elasticity solver (GM/LN approaches), " "or standard AMG for systems (unknown approach)."); args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc", "--no-static-condensation", "Enable static condensation."); 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(); if (mesh->attributes.Max() < 2 || mesh->bdr_attributes.Max() < 2) { if (myid == 0) cerr << "\nInput mesh should have at least two materials and " << "two boundary attributes! (See schematic in ex2.cpp)\n" << endl; MPI_Finalize(); return 3; } // 4. Select the order of the finite element discretization space. For NURBS // meshes, we increase the order by degree elevation. if (mesh->NURBSext) { mesh->DegreeElevate(order, order); } // 5. 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(); } } // 6. 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. ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh); delete mesh; { int par_ref_levels = 1; for (int l = 0; l < par_ref_levels; l++) { pmesh->UniformRefinement(); } } // 7. Define a parallel finite element space on the parallel mesh. Here we // use vector finite elements, i.e. dim copies of a scalar finite element // space. We use the ordering by vector dimension (the last argument of // the FiniteElementSpace constructor) which is expected in the systems // version of BoomerAMG preconditioner. For NURBS meshes, we use the // (degree elevated) NURBS space associated with the mesh nodes. FiniteElementCollection *fec; ParFiniteElementSpace *fespace; const bool use_nodal_fespace = pmesh->NURBSext && !amg_elast; if (use_nodal_fespace) { fec = NULL; fespace = (ParFiniteElementSpace *)pmesh->GetNodes()->FESpace(); } else { fec = new H1_FECollection(order, dim); fespace = new ParFiniteElementSpace(pmesh, fec, dim, Ordering::byVDIM); } HYPRE_Int size = fespace->GlobalTrueVSize(); if (myid == 0) { cout << "Number of finite element unknowns: " << size << endl << "Assembling: " << flush; } // 8. Determine the list of true (i.e. parallel conforming) essential // boundary dofs. In this example, the boundary conditions are defined by // marking only boundary attribute 1 from the mesh as essential and // converting it to a list of true dofs. Array ess_tdof_list, ess_bdr(pmesh->bdr_attributes.Max()); ess_bdr = 0; ess_bdr[0] = 1; fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list); // 9. Set up the parallel linear form b(.) which corresponds to the // right-hand side of the FEM linear system. In this case, b_i equals the // boundary integral of f*phi_i where f represents a "pull down" force on // the Neumann part of the boundary and phi_i are the basis functions in // the finite element fespace. The force is defined by the object f, which // is a vector of Coefficient objects. The fact that f is non-zero on // boundary attribute 2 is indicated by the use of piece-wise constants // coefficient for its last component. VectorArrayCoefficient f(dim); for (int i = 0; i < dim-1; i++) { f.Set(i, new ConstantCoefficient(0.0)); } { Vector pull_force(pmesh->bdr_attributes.Max()); pull_force = 0.0; pull_force(1) = -1.0e-2; f.Set(dim-1, new PWConstCoefficient(pull_force)); } ParLinearForm *b = new ParLinearForm(fespace); b->AddBoundaryIntegrator(new VectorBoundaryLFIntegrator(f)); if (myid == 0) { cout << "r.h.s. ... " << flush; } b->Assemble(); // 10. Define the solution vector x as a parallel finite element grid // function corresponding to fespace. Initialize x with initial guess of // zero, which satisfies the boundary conditions. ParGridFunction x(fespace); x = 0.0; // 11. Set up the parallel bilinear form a(.,.) on the finite element space // corresponding to the linear elasticity integrator with piece-wise // constants coefficient lambda and mu. Vector lambda(pmesh->attributes.Max()); lambda = 1.0; lambda(0) = lambda(1)*50; PWConstCoefficient lambda_func(lambda); Vector mu(pmesh->attributes.Max()); mu = 1.0; mu(0) = mu(1)*50; PWConstCoefficient mu_func(mu); ParBilinearForm *a = new ParBilinearForm(fespace); a->AddDomainIntegrator(new ElasticityIntegrator(lambda_func, mu_func)); // 12. Assemble the parallel bilinear form and the corresponding linear // system, applying any necessary transformations such as: parallel // assembly, eliminating boundary conditions, applying conforming // constraints for non-conforming AMR, static condensation, etc. if (myid == 0) { cout << "matrix ... " << flush; } if (static_cond) { a->EnableStaticCondensation(); } a->Assemble(); HypreParMatrix A; Vector B, X; a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B); if (myid == 0) { cout << "done." << endl; cout << "Size of linear system: " << A.GetGlobalNumRows() << endl; } // 13. Define and apply a parallel PCG solver for A X = B with the BoomerAMG // preconditioner from hypre. HypreBoomerAMG *amg = new HypreBoomerAMG(A); if (amg_elast && !a->StaticCondensationIsEnabled()) { amg->SetElasticityOptions(fespace); } else { amg->SetSystemsOptions(dim); } HyprePCG *pcg = new HyprePCG(A); pcg->SetTol(1e-8); pcg->SetMaxIter(500); pcg->SetPrintLevel(2); pcg->SetPreconditioner(*amg); pcg->Mult(B, X); // 14. Recover the parallel grid function corresponding to X. This is the // local finite element solution on each processor. a->RecoverFEMSolution(X, *b, x); // 15. For non-NURBS meshes, make the mesh curved based on the finite element // space. This means that we define the mesh elements through a fespace // based transformation of the reference element. This allows us to save // the displaced mesh as a curved mesh when using high-order finite // element displacement field. We assume that the initial mesh (read from // the file) is not higher order curved mesh compared to the chosen FE // space. if (!use_nodal_fespace) { pmesh->SetNodalFESpace(fespace); } // 16. Save in parallel the displaced mesh and the inverted solution (which // gives the backward displacements to the original grid). This output // can be viewed later using GLVis: "glvis -np -m mesh -g sol". { GridFunction *nodes = pmesh->GetNodes(); *nodes += x; x *= -1; 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); } // 17. Send the above data by socket to a GLVis server. Use the "n" and "b" // keys in GLVis to visualize the displacements. 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; } // 18. Free the used memory. delete pcg; delete amg; delete a; delete b; if (fec) { delete fespace; delete fec; } delete pmesh; MPI_Finalize(); return 0; }