368 lines
14 KiB
C++
368 lines
14 KiB
C++
// MFEM Example 21
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//
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// Compile with: make ex21p
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//
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// Sample runs: mpirun -np 4 ex21p
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// mpirun -np 4 ex21p -o 3
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// mpirun -np 4 ex21p -m ../data/beam-quad.mesh
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// mpirun -np 4 ex21p -m ../data/beam-quad.mesh -o 3
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// mpirun -np 4 ex21p -m ../data/beam-tet.mesh
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// mpirun -np 4 ex21p -m ../data/beam-tet.mesh -o 2
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// mpirun -np 4 ex21p -m ../data/beam-hex.mesh
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// mpirun -np 4 ex21p -m ../data/beam-hex.mesh -o 2
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//
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// Description: This is a version of Example 2p with a simple adaptive mesh
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// refinement loop. The problem being solved is again the linear
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// elasticity describing a multi-material cantilever beam.
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// 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 and curved meshes. Interpolation of functions from
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// 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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// We recommend viewing Examples 2p and 6p 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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int main(int argc, char *argv[])
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{
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// 0. Initialize MPI and HYPRE.
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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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Hypre::Init();
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// 1. Parse command-line options.
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const char *mesh_file = "../data/beam-tri.mesh";
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int serial_ref_levels = 0;
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int order = 1;
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bool static_cond = false;
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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(&serial_ref_levels, "-rs", "--refine-serial",
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"Number of uniform serial refinements (before parallel"
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" partitioning)");
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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(&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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// 2. Read the mesh from the given mesh file. We can handle triangular,
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// quadrilateral, tetrahedral, and hexahedral meshes with the same code.
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Mesh mesh(mesh_file, 1, 1);
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int dim = mesh.Dimension();
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MFEM_VERIFY(mesh.SpaceDimension() == dim, "invalid mesh");
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if (mesh.attributes.Max() < 2 || mesh.bdr_attributes.Max() < 2)
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{
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cerr << "\nInput mesh should have at least two materials and "
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<< "two boundary attributes! (See schematic in ex2.cpp)\n"
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<< endl;
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MPI_Finalize();
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return 3;
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}
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// 3. Refine the mesh before parallel partitioning. Since a NURBS mesh can
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// currently only be refined uniformly, we need to convert it to a
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// piecewise-polynomial curved mesh. First we refine the NURBS mesh a bit
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// more and then project the curvature to quadratic Nodes.
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if (mesh.NURBSext && serial_ref_levels == 0)
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{
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serial_ref_levels = 2;
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}
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for (int i = 0; i < serial_ref_levels; i++)
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{
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mesh.UniformRefinement();
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}
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if (mesh.NURBSext)
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{
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mesh.SetCurvature(2);
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}
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mesh.EnsureNCMesh();
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ParMesh pmesh(MPI_COMM_WORLD, mesh);
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mesh.Clear();
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// 4. 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, dim);
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// 5. As in Example 2, we set up the linear form b(.) which corresponds to
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// the right-hand side of the FEM linear system. In this case, b_i equals
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// the boundary integral of f*phi_i where f represents a "pull down"
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// force on the Neumann part of the boundary and phi_i are the basis
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// functions in the finite element fespace. The force is defined by the
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// VectorArrayCoefficient object f, which is a vector of Coefficient
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// objects. The fact that f is non-zero on boundary attribute 2 is
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// indicated by the use of piece-wise constants coefficient for its last
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// component. We don't assemble the discrete problem yet, this will be
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// done in the main loop.
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VectorArrayCoefficient f(dim);
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for (int i = 0; i < dim-1; i++)
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{
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f.Set(i, new ConstantCoefficient(0.0));
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}
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{
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Vector pull_force(pmesh.bdr_attributes.Max());
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pull_force = 0.0;
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pull_force(1) = -1.0e-2;
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f.Set(dim-1, new PWConstCoefficient(pull_force));
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}
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ParLinearForm b(&fespace);
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b.AddDomainIntegrator(new VectorBoundaryLFIntegrator(f));
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// 6. Set up the bilinear form a(.,.) on the finite element space
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// corresponding to the linear elasticity integrator with piece-wise
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// constants coefficient lambda and mu.
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Vector lambda(pmesh.attributes.Max());
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lambda = 1.0;
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lambda(0) = lambda(1)*50;
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PWConstCoefficient lambda_func(lambda);
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Vector mu(pmesh.attributes.Max());
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mu = 1.0;
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mu(0) = mu(1)*50;
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PWConstCoefficient mu_func(mu);
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ParBilinearForm a(&fespace);
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BilinearFormIntegrator *integ =
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new ElasticityIntegrator(lambda_func,mu_func);
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a.AddDomainIntegrator(integ);
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if (static_cond) { a.EnableStaticCondensation(); }
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// 7. 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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Vector zero_vec(dim);
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zero_vec = 0.0;
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VectorConstantCoefficient zero_vec_coeff(zero_vec);
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ParGridFunction x(&fespace);
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x = 0.0;
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// 8. Determine the list of true (i.e. conforming) essential boundary dofs.
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// In this example, the boundary conditions are defined by marking only
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// boundary attribute 1 from the mesh as essential and converting it to a
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// list of true dofs. The conversion to true dofs will be done in the
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// main loop.
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Array<int> ess_bdr(pmesh.bdr_attributes.Max());
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ess_bdr = 0;
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ess_bdr[0] = 1;
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// 9. GLVis visualization.
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char vishost[] = "localhost";
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int visport = 19916;
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socketstream sol_sock;
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// 10. Set up an error estimator. Here we use the Zienkiewicz-Zhu estimator
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// that uses the ComputeElementFlux method of the ElasticityIntegrator to
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// recover a smoothed flux (stress) that is subtracted from the element
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// flux to get an error indicator. We need to supply the space for the
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// smoothed flux: an (H1)^tdim (i.e., vector-valued) space is used here.
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// Here, tdim represents the number of components for a symmetric (dim x
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// dim) tensor.
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const int tdim = dim*(dim+1)/2;
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L2_FECollection flux_fec(order, dim);
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ParFiniteElementSpace flux_fespace(&pmesh, &flux_fec, tdim);
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ParFiniteElementSpace smooth_flux_fespace(&pmesh, &fec, tdim);
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L2ZienkiewiczZhuEstimator estimator(*integ, x, flux_fespace,
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smooth_flux_fespace);
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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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const int max_dofs = 50000;
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const int max_amr_itr = 20;
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for (int it = 0; it <= max_amr_itr; it++)
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{
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HYPRE_BigInt 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.
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a.Assemble();
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b.Assemble();
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// 14. Set Dirichlet boundary values in the GridFunction x.
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// Determine the list of Dirichlet true DOFs in the linear system.
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Array<int> ess_tdof_list;
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x.ProjectBdrCoefficient(zero_vec_coeff, ess_bdr);
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fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
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// 15. Create the linear system: eliminate boundary conditions, constrain
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// hanging nodes and possibly apply other transformations. The system
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// will be solved for true (unconstrained) DOFs only.
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HypreParMatrix A;
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Vector B, X;
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const int copy_interior = 1;
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a.FormLinearSystem(ess_tdof_list, x, b, A, X, B, copy_interior);
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// 16. 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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// amg.SetSystemsOptions(dim); // optional
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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(500);
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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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// 17. After solving the linear system, reconstruct the solution as a
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// finite element GridFunction. Constrained nodes are interpolated
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// from true DOFs (it may therefore happen that x.Size() >= X.Size()).
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a.RecoverFEMSolution(X, b, x);
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// 18. Send solution by socket to the GLVis server.
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if (visualization && it == 0)
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{
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sol_sock.open(vishost, visport);
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sol_sock.precision(8);
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}
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if (visualization && sol_sock.good())
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{
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GridFunction nodes(&fespace), *nodes_p = &nodes;
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pmesh.GetNodes(nodes);
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nodes += x;
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int own_nodes = 0;
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pmesh.SwapNodes(nodes_p, own_nodes);
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x.Neg(); // visualize the backward displacement
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sol_sock << "parallel " << num_procs << ' ' << myid << '\n';
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sol_sock << "solution\n" << pmesh << x << flush;
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x.Neg();
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pmesh.SwapNodes(nodes_p, own_nodes);
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if (it == 0)
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{
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sol_sock << "keys '" << ((dim == 2) ? "Rjl" : "") << "m'" << endl;
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}
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sol_sock << "window_title 'AMR iteration: " << it << "'\n"
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<< "pause" << endl;
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if (myid == 0)
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{
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cout << "Visualization paused. "
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"Press <space> in the GLVis window to continue." << endl;
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}
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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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break;
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}
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// 19. 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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break;
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}
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// 20. Update the space to reflect the new state of the mesh. Also,
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// interpolate the solution x so that it lies in the new space but
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// represents the same function. This saves solver iterations later
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// since we'll have a good initial guess of x in the next step.
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// Internally, FiniteElementSpace::Update() calculates an
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// interpolation matrix which is then used by GridFunction::Update().
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fespace.Update();
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x.Update();
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// 21. 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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{
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ostringstream mref_name, mesh_name, sol_name;
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mref_name << "ex21p_reference_mesh." << setfill('0') << setw(6) << myid;
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mesh_name << "ex21p_deformed_mesh." << setfill('0') << setw(6) << myid;
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sol_name << "ex21p_displacement." << setfill('0') << setw(6) << myid;
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ofstream mesh_ref_out(mref_name.str().c_str());
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mesh_ref_out.precision(16);
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pmesh.Print(mesh_ref_out);
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ofstream mesh_out(mesh_name.str().c_str());
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mesh_out.precision(16);
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GridFunction nodes(&fespace), *nodes_p = &nodes;
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pmesh.GetNodes(nodes);
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nodes += x;
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int own_nodes = 0;
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pmesh.SwapNodes(nodes_p, own_nodes);
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pmesh.Print(mesh_out);
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pmesh.SwapNodes(nodes_p, own_nodes);
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ofstream x_out(sol_name.str().c_str());
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x_out.precision(16);
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x.Save(x_out);
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}
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MPI_Finalize();
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return 0;
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}
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