304 lines
11 KiB
C++
304 lines
11 KiB
C++
// MFEM Example 4
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//
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// Compile with: make ex4
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//
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// Sample runs: ex4 -m ../data/square-disc.mesh
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// ex4 -m ../data/star.mesh
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// ex4 -m ../data/beam-tet.mesh
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// ex4 -m ../data/beam-hex.mesh
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// ex4 -m ../data/beam-hex.mesh -o 2 -pa
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// ex4 -m ../data/escher.mesh
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// ex4 -m ../data/fichera.mesh -o 2 -hb
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// ex4 -m ../data/fichera.mesh -o 2 -hb -ea
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// ex4 -m ../data/fichera-q2.vtk
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// ex4 -m ../data/fichera-q3.mesh -o 2 -sc
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// ex4 -m ../data/square-disc-nurbs.mesh
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// ex4 -m ../data/beam-hex-nurbs.mesh
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// ex4 -m ../data/periodic-square.mesh -no-bc
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// ex4 -m ../data/periodic-cube.mesh -no-bc
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// ex4 -m ../data/amr-quad.mesh
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// ex4 -m ../data/amr-hex.mesh
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// ex4 -m ../data/amr-hex.mesh -o 2 -hb
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// ex4 -m ../data/amr-hex.mesh -o 2 -hb -ea
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// ex4 -m ../data/fichera-amr.mesh -o 2 -sc
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// ex4 -m ../data/ref-prism.mesh -o 1
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// ex4 -m ../data/octahedron.mesh -o 1
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// ex4 -m ../data/star-surf.mesh -o 1
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//
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// Device sample runs:
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// ex4 -m ../data/star.mesh -pa -d cuda
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// ex4 -m ../data/star.mesh -hb -ea -d cuda
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// ex4 -m ../data/amr-quad.mesh -hb -ea -d cuda
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// ex4 -m ../data/star.mesh -pa -d raja-cuda
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// ex4 -m ../data/star.mesh -pa -d raja-omp
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// ex4 -m ../data/beam-hex.mesh -pa -d cuda
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//
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// Description: This example code solves a simple 2D/3D H(div) diffusion
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// problem corresponding to the second order definite equation
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// -grad(alpha div F) + beta F = f with boundary condition F dot n
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// = <given normal field>. Here, we use a given exact solution F
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// and compute the corresponding r.h.s. f. We discretize with
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// Raviart-Thomas finite elements.
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//
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// The example demonstrates the use of H(div) finite element
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// spaces with the grad-div and H(div) vector finite element mass
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// bilinear form, as well as the computation of discretization
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// error when the exact solution is known. Bilinear form
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// hybridization and static condensation are also illustrated.
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//
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// We recommend viewing examples 1-3 before viewing this example.
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#include "mfem.hpp"
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#include <fstream>
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#include <iostream>
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using namespace std;
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using namespace mfem;
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// Exact solution, F, and r.h.s., f. See below for implementation.
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void F_exact(const Vector &, Vector &);
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void f_exact(const Vector &, Vector &);
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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/star.mesh";
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int order = 1;
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bool set_bc = true;
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bool static_cond = false;
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bool hybridization = false;
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bool pa = false;
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bool ea = 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(&set_bc, "-bc", "--impose-bc", "-no-bc", "--dont-impose-bc",
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"Impose or not essential boundary conditions.");
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args.AddOption(&freq, "-f", "--frequency", "Set the frequency for the exact"
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" solution.");
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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(&hybridization, "-hb", "--hybridization", "-no-hb",
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"--no-hybridization", "Enable hybridization.");
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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(&ea, "-ea", "--element-assembly", "-no-ea",
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"--no-element-assembly", "Enable Element 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.ParseCheck();
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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, as well as
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// periodic meshes with the same code.
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Mesh *mesh = new Mesh(mesh_file, 1, 1);
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int dim = mesh->Dimension();
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int sdim = mesh->SpaceDimension();
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// 4. Refine the 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 25,000
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// elements.
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{
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int ref_levels =
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(int)floor(log(25000./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 the
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// Raviart-Thomas finite elements of the specified order.
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FiniteElementCollection *fec = new RT_FECollection(order-1, dim);
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FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
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cout << "Number of finite element unknowns: "
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<< fespace->GetTrueVSize() << endl;
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// 6. 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 all
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// the boundary attributes from the mesh as essential (Dirichlet) and
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// converting them to a list of true dofs.
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Array<int> ess_tdof_list;
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if (mesh->bdr_attributes.Size())
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{
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Array<int> ess_bdr(mesh->bdr_attributes.Max());
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ess_bdr = set_bc ? 1 : 0;
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fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
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}
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// 7. Set up the linear form b(.) which corresponds to the right-hand side
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// of the FEM linear system, which in this case is (f,phi_i) where f is
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// given by the function f_exact and phi_i are the basis functions in the
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// finite element fespace.
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VectorFunctionCoefficient f(sdim, f_exact);
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LinearForm *b = new LinearForm(fespace);
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b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
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b->Assemble();
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// 8. Define the solution vector x as a 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 faces 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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GridFunction x(fespace);
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VectorFunctionCoefficient F(sdim, F_exact);
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x.ProjectCoefficient(F);
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// 9. Set up the bilinear form corresponding to the H(div) diffusion operator
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// grad alpha div + beta I, by adding the div-div and the mass domain
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// integrators.
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Coefficient *alpha = new ConstantCoefficient(1.0);
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Coefficient *beta = new ConstantCoefficient(1.0);
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BilinearForm *a = new BilinearForm(fespace);
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if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
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if (ea) { a->SetAssemblyLevel(AssemblyLevel::ELEMENT); }
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a->AddDomainIntegrator(new DivDivIntegrator(*alpha));
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a->AddDomainIntegrator(new VectorFEMassIntegrator(*beta));
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// 10. 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, hybridization, etc.
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FiniteElementCollection *hfec = NULL;
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FiniteElementSpace *hfes = NULL;
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if (static_cond)
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{
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a->EnableStaticCondensation();
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}
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else if (hybridization)
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{
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hfec = new DG_Interface_FECollection(order-1, dim);
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hfes = new FiniteElementSpace(mesh, hfec);
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a->EnableHybridization(hfes, new NormalTraceJumpIntegrator(),
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ess_tdof_list);
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}
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a->Assemble();
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OperatorPtr A;
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Vector B, X;
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a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
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cout << "Size of linear system: " << A->Height() << endl;
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// 11. Solve the linear system A X = B.
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if (!pa && (!ea || hybridization))
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{
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#ifndef MFEM_USE_SUITESPARSE
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// Use a simple symmetric Gauss-Seidel preconditioner with PCG.
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GSSmoother M((SparseMatrix&)(*A));
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PCG(*A, M, B, X, 1, 10000, 1e-20, 0.0);
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#else
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// If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
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UMFPackSolver umf_solver;
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umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
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umf_solver.SetOperator(*A);
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umf_solver.Mult(B, X);
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#endif
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}
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else // Jacobi preconditioning in partial assembly mode
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{
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if (UsesTensorBasis(*fespace))
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{
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OperatorJacobiSmoother M(*a, ess_tdof_list);
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PCG(*A, M, B, X, 1, 10000, 1e-20, 0.0);
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}
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else
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{
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CG(*A, B, X, 1, 10000, 1e-20, 0.0);
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}
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}
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// 12. Recover the solution as a finite element grid function.
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a->RecoverFEMSolution(X, *b, x);
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// 13. Compute and print the L^2 norm of the error.
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cout << "\n|| F_h - F ||_{L^2} = " << x.ComputeL2Error(F) << '\n' << endl;
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// 14. 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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{
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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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}
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// 15. 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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// 16. Free the used memory.
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delete hfes;
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delete hfec;
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delete a;
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delete alpha;
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delete beta;
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delete b;
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delete fespace;
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delete fec;
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delete mesh;
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return 0;
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}
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// The exact solution (for non-surface meshes)
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void F_exact(const Vector &p, Vector &F)
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{
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int dim = p.Size();
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real_t x = p(0);
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real_t y = p(1);
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// real_t z = (dim == 3) ? p(2) : 0.0; // Uncomment if F is changed to depend on z
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F(0) = cos(kappa*x)*sin(kappa*y);
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F(1) = cos(kappa*y)*sin(kappa*x);
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if (dim == 3)
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{
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F(2) = 0.0;
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}
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}
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// The right hand side
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void f_exact(const Vector &p, Vector &f)
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{
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int dim = p.Size();
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real_t x = p(0);
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real_t y = p(1);
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// real_t z = (dim == 3) ? p(2) : 0.0; // Uncomment if f is changed to depend on z
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real_t temp = 1 + 2*kappa*kappa;
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f(0) = temp*cos(kappa*x)*sin(kappa*y);
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f(1) = temp*cos(kappa*y)*sin(kappa*x);
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if (dim == 3)
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{
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f(2) = 0;
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}
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}
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