452 lines
13 KiB
C++
452 lines
13 KiB
C++
// MFEM Example 24
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//
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// Compile with: make ex24
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//
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// Sample runs: ex24 -m ../data/star.mesh
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// ex24 -m ../data/square-disc.mesh -o 2
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// ex24 -m ../data/beam-tet.mesh
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// ex24 -m ../data/beam-hex.mesh -o 2 -pa
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// ex24 -m ../data/beam-hex.mesh -o 2 -pa -p 1
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// ex24 -m ../data/beam-hex.mesh -o 2 -pa -p 2
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// ex24 -m ../data/escher.mesh
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// ex24 -m ../data/escher.mesh -o 2
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// ex24 -m ../data/fichera.mesh
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// ex24 -m ../data/fichera-q2.vtk
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// ex24 -m ../data/fichera-q3.mesh
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// ex24 -m ../data/square-disc-nurbs.mesh
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// ex24 -m ../data/beam-hex-nurbs.mesh
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// ex24 -m ../data/amr-quad.mesh -o 2
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// ex24 -m ../data/amr-hex.mesh
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//
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// Device sample runs:
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// ex24 -m ../data/star.mesh -pa -d cuda
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// ex24 -m ../data/star.mesh -pa -d raja-cuda
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// ex24 -m ../data/star.mesh -pa -d raja-omp
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// ex24 -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, with three variants:
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//
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// 1) (grad p, u) for p in H^1 tested against u in H(curl)
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// 2) (curl v, u) for v in H(curl) tested against u in H(div), 3D
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// 3) (div v, q) for v in H(div) tested against q in L_2
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//
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// Using different approaches, we project the gradient, curl, or
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// divergence to the appropriate space.
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//
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// We recommend viewing examples 1, 3, and 5 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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real_t p_exact(const Vector &x);
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void gradp_exact(const Vector &, Vector &);
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real_t div_gradp_exact(const Vector &x);
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void v_exact(const Vector &x, Vector &v);
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void curlv_exact(const Vector &x, Vector &cv);
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int dim;
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real_t freq = 1.0, kappa;
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int main(int argc, char *argv[])
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{
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// 1. 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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int prob = 0;
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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(&prob, "-p", "--problem-type",
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"Choose between 0: grad, 1: curl, 2: div");
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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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args.PrintUsage(cout);
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return 1;
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}
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args.PrintOptions(cout);
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kappa = freq * M_PI;
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// 2. 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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device.Print();
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// 3. Read the mesh from the given mesh file. We can handle triangular,
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// quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
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// 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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// 4. Refine the mesh to increase the resolution. In this example we do
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// 'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
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// largest number that gives a final mesh with no more than 50,000
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// elements.
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{
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int ref_levels = (int)floor(log(50000./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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// 5. Define a finite element space on the mesh. Here we use Nedelec or
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// Raviart-Thomas finite elements of the specified order.
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FiniteElementCollection *trial_fec = NULL;
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FiniteElementCollection *test_fec = NULL;
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if (prob == 0)
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{
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trial_fec = new H1_FECollection(order, dim);
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test_fec = new ND_FECollection(order, dim);
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}
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else if (prob == 1)
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{
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trial_fec = new ND_FECollection(order, dim);
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test_fec = new RT_FECollection(order-1, dim);
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}
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else
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{
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trial_fec = new RT_FECollection(order-1, dim);
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test_fec = new L2_FECollection(order-1, dim);
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}
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FiniteElementSpace trial_fes(mesh, trial_fec);
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FiniteElementSpace test_fes(mesh, test_fec);
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int trial_size = trial_fes.GetTrueVSize();
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int test_size = test_fes.GetTrueVSize();
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if (prob == 0)
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{
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cout << "Number of Nedelec finite element unknowns: " << test_size << endl;
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cout << "Number of H1 finite element unknowns: " << trial_size << endl;
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}
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else if (prob == 1)
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{
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cout << "Number of Nedelec finite element unknowns: " << trial_size << endl;
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cout << "Number of Raviart-Thomas finite element unknowns: " << test_size <<
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endl;
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}
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else
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{
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cout << "Number of Raviart-Thomas finite element unknowns: "
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<< trial_size << endl;
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cout << "Number of L2 finite element unknowns: " << test_size << endl;
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}
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// 6. Define the solution vector as a finite element grid function
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// corresponding to the trial fespace.
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GridFunction gftest(&test_fes);
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GridFunction gftrial(&trial_fes);
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GridFunction x(&test_fes);
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FunctionCoefficient p_coef(p_exact);
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VectorFunctionCoefficient gradp_coef(sdim, gradp_exact);
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VectorFunctionCoefficient v_coef(sdim, v_exact);
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VectorFunctionCoefficient curlv_coef(sdim, curlv_exact);
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FunctionCoefficient divgradp_coef(div_gradp_exact);
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if (prob == 0)
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{
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gftrial.ProjectCoefficient(p_coef);
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}
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else if (prob == 1)
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{
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gftrial.ProjectCoefficient(v_coef);
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}
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else
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{
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gftrial.ProjectCoefficient(gradp_coef);
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}
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gftrial.SetTrueVector();
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gftrial.SetFromTrueVector();
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// 7. Set up the bilinear forms for L2 projection.
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ConstantCoefficient one(1.0);
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BilinearForm a(&test_fes);
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MixedBilinearForm a_mixed(&trial_fes, &test_fes);
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if (pa)
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{
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a.SetAssemblyLevel(AssemblyLevel::PARTIAL);
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a_mixed.SetAssemblyLevel(AssemblyLevel::PARTIAL);
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}
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if (prob == 0)
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{
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a.AddDomainIntegrator(new VectorFEMassIntegrator(one));
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a_mixed.AddDomainIntegrator(new MixedVectorGradientIntegrator(one));
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}
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else if (prob == 1)
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{
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a.AddDomainIntegrator(new VectorFEMassIntegrator(one));
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a_mixed.AddDomainIntegrator(new MixedVectorCurlIntegrator(one));
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}
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else
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{
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a.AddDomainIntegrator(new MassIntegrator(one));
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a_mixed.AddDomainIntegrator(new VectorFEDivergenceIntegrator(one));
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}
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// 8. Assemble the bilinear form and the corresponding linear system,
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// applying any necessary transformations such as: eliminating boundary
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// conditions, applying conforming constraints for non-conforming AMR,
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// 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_mixed.Assemble();
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if (!pa) { a_mixed.Finalize(); }
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if (pa)
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{
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a_mixed.Mult(gftrial, x);
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}
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else
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{
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SparseMatrix& mixed = a_mixed.SpMat();
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mixed.Mult(gftrial, x);
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}
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// 9. Define and apply a PCG solver for Ax = b with Jacobi preconditioner.
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{
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GridFunction rhs(&test_fes);
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rhs = x;
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x = 0.0;
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CGSolver cg;
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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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if (pa)
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{
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Array<int> ess_tdof_list; // empty
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OperatorJacobiSmoother Jacobi(a, ess_tdof_list);
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cg.SetOperator(a);
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cg.SetPreconditioner(Jacobi);
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cg.Mult(rhs, x);
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}
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else
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{
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SparseMatrix& Amat = a.SpMat();
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DSmoother Jacobi(Amat);
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cg.SetOperator(Amat);
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cg.SetPreconditioner(Jacobi);
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cg.Mult(rhs, x);
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}
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}
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// 10. Compute the same field by applying a DiscreteInterpolator.
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GridFunction discreteInterpolant(&test_fes);
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DiscreteLinearOperator dlo(&trial_fes, &test_fes);
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if (prob == 0)
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{
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dlo.AddDomainInterpolator(new GradientInterpolator());
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}
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else if (prob == 1)
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{
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dlo.AddDomainInterpolator(new CurlInterpolator());
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}
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else
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{
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dlo.AddDomainInterpolator(new DivergenceInterpolator());
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}
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dlo.Assemble();
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dlo.Mult(gftrial, discreteInterpolant);
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// 11. Compute the projection of the exact field.
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GridFunction exact_proj(&test_fes);
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if (prob == 0)
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{
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exact_proj.ProjectCoefficient(gradp_coef);
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}
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else if (prob == 1)
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{
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exact_proj.ProjectCoefficient(curlv_coef);
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}
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else
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{
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exact_proj.ProjectCoefficient(divgradp_coef);
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}
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exact_proj.SetTrueVector();
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exact_proj.SetFromTrueVector();
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// 12. Compute and print the L_2 norm of the error.
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if (prob == 0)
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{
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real_t errSol = x.ComputeL2Error(gradp_coef);
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real_t errInterp = discreteInterpolant.ComputeL2Error(gradp_coef);
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real_t errProj = exact_proj.ComputeL2Error(gradp_coef);
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cout << "\n Solution of (E_h,v) = (grad p_h,v) for E_h and v in H(curl): "
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"|| 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 - grad p"
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" ||_{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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else if (prob == 1)
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{
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real_t errSol = x.ComputeL2Error(curlv_coef);
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real_t errInterp = discreteInterpolant.ComputeL2Error(curlv_coef);
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real_t errProj = exact_proj.ComputeL2Error(curlv_coef);
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cout << "\n Solution of (E_h,w) = (curl v_h,w) for E_h and w in H(div): "
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"|| E_h - curl v ||_{L_2} = " << errSol << '\n' << endl;
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cout << " Curl interpolant E_h = curl v_h in H(div): || E_h - curl v "
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"||_{L_2} = " << errInterp << '\n' << endl;
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cout << " Projection E_h of exact curl v in H(div): || E_h - curl v "
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"||_{L_2} = " << errProj << '\n' << endl;
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}
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else
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{
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int order_quad = max(2, 2*order+1);
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const IntegrationRule *irs[Geometry::NumGeom];
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for (int i=0; i < Geometry::NumGeom; ++i)
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{
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irs[i] = &(IntRules.Get(i, order_quad));
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}
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real_t errSol = x.ComputeL2Error(divgradp_coef, irs);
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real_t errInterp = discreteInterpolant.ComputeL2Error(divgradp_coef, irs);
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real_t errProj = exact_proj.ComputeL2Error(divgradp_coef, irs);
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cout << "\n Solution of (f_h,q) = (div v_h,q) for f_h and q in L_2: "
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"|| f_h - div v ||_{L_2} = " << errSol << '\n' << endl;
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cout << " Divergence interpolant f_h = div v_h in L_2: || f_h - div v "
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"||_{L_2} = " << errInterp << '\n' << endl;
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cout << " Projection f_h of exact div v in L_2: || f_h - div v "
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"||_{L_2} = " << errProj << '\n' << endl;
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}
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// 13. Save the refined mesh and the solution. This output can be viewed
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// later using GLVis: "glvis -m refined.mesh -g sol.gf".
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ofstream mesh_ofs("refined.mesh");
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mesh_ofs.precision(8);
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mesh->Print(mesh_ofs);
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ofstream sol_ofs("sol.gf");
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sol_ofs.precision(8);
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x.Save(sol_ofs);
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// 14. 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.precision(8);
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sol_sock << "solution\n" << *mesh << x << flush;
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}
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// 15. Free the used memory.
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delete trial_fec;
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delete test_fec;
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delete mesh;
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return 0;
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}
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real_t 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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real_t div_gradp_exact(const Vector &x)
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{
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if (dim == 3)
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{
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return -3.0 * 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 -2.0 * 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 v_exact(const Vector &x, Vector &v)
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{
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if (dim == 3)
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{
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v(0) = sin(kappa * x(1));
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v(1) = sin(kappa * x(2));
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v(2) = sin(kappa * x(0));
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}
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else
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{
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v(0) = sin(kappa * x(1));
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v(1) = sin(kappa * x(0));
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if (x.Size() == 3) { v(2) = 0.0; }
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}
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}
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void curlv_exact(const Vector &x, Vector &cv)
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{
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if (dim == 3)
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{
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cv(0) = -kappa * cos(kappa * x(2));
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cv(1) = -kappa * cos(kappa * x(0));
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cv(2) = -kappa * cos(kappa * x(1));
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}
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else
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{
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cv = 0.0;
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}
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}
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