284 lines
9.8 KiB
C++
284 lines
9.8 KiB
C++
// MFEM Example 1
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//
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// Compile with: make ex1
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//
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// Sample runs: ex1 -m ../data/square-disc.mesh
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// ex1 -m ../data/star.mesh
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// ex1 -m ../data/star-mixed.mesh
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// ex1 -m ../data/escher.mesh
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// ex1 -m ../data/fichera.mesh
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// ex1 -m ../data/fichera-mixed.mesh
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// ex1 -m ../data/toroid-wedge.mesh
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// ex1 -m ../data/square-disc-p2.vtk -o 2
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// ex1 -m ../data/square-disc-p3.mesh -o 3
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// ex1 -m ../data/square-disc-nurbs.mesh -o -1
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// ex1 -m ../data/star-mixed-p2.mesh -o 2
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// ex1 -m ../data/disc-nurbs.mesh -o -1
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// ex1 -m ../data/pipe-nurbs.mesh -o -1
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// ex1 -m ../data/fichera-mixed-p2.mesh -o 2
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// ex1 -m ../data/star-surf.mesh
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// ex1 -m ../data/square-disc-surf.mesh
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// ex1 -m ../data/inline-segment.mesh
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// ex1 -m ../data/amr-quad.mesh
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// ex1 -m ../data/amr-hex.mesh
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// ex1 -m ../data/fichera-amr.mesh
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// ex1 -m ../data/mobius-strip.mesh
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// ex1 -m ../data/mobius-strip.mesh -o -1 -sc
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//
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// Description: This example code demonstrates the use of MFEM to define a
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// simple finite element discretization of the Laplace problem
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// -Delta u = 1 with homogeneous Dirichlet boundary conditions.
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// Specifically, we discretize using a FE space of the specified
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// order, or if order < 1 using an isoparametric/isogeometric
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// space (i.e. quadratic for quadratic curvilinear mesh, NURBS for
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// NURBS mesh, etc.)
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//
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// The example highlights the use of mesh refinement, finite
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// element grid functions, as well as linear and bilinear forms
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// corresponding to the left-hand side and right-hand side of the
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// discrete linear system. We also cover the explicit elimination
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// of essential boundary conditions, static condensation, and the
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// optional connection to the GLVis tool for visualization.
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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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// 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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int level = -1;
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int max_iter = 2000;
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bool static_cond = false;
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bool pa = false;
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bool gpu = false;
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bool nvvp = false;
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bool sync = 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(&order, "-o", "--order",
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"Finite element order (polynomial degree) or -1 for"
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" isoparametric space.");
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args.AddOption(&level, "-l", "--level", "Refinement level");
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args.AddOption(&max_iter, "-mi", "--max-iter",
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"Maximum number of CG iterations");
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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, "-p", "--pa", "-no-p", "--no-pa",
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"Enable Partial Assembly.");
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args.AddOption(&gpu, "-g", "--gpu", "-no-g", "--no-gpu", "Enable GPU.");
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args.AddOption(&nvvp, "-n", "--nvvp", "-no-n", "--no-nvvp", "Enable NVVP.");
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args.AddOption(&sync, "-s", "--sync", "-no-s", "--no-sync", "Enable SYNC.");
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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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if (nvvp) { config::Get().Nvvp(true); }
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if (sync) { config::Get().Sync(true); }
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// 2. 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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int dim = mesh->Dimension();
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// 3. 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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push(Refine,Indigo);
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int ref_levels = level>=0 ? level :
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(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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pop();
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}
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// 4. Define a finite element space on the mesh. Here we use continuous
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// Lagrange finite elements of the specified order. If order < 1, we
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// instead use an isoparametric/isogeometric space.
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push(FEC,LightSalmon);
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FiniteElementCollection *fec;
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if (order > 0)
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{
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fec = new H1_FECollection(order, dim);
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}
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else if (mesh->GetNodes())
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{
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fec = mesh->GetNodes()->OwnFEC();
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cout << "Using isoparametric FEs: " << fec->Name() << endl;
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}
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else
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{
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fec = new H1_FECollection(order = 1, dim);
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}
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pop();
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push(FES,Plum);
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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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pop();
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// 5. 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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push(BC,Tomato);
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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 = 1;
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fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
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}
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pop();
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// 6. Set up the linear form b(.) which corresponds to the right-hand side of
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// the FEM linear system, which in this case is (1,phi_i) where phi_i are
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// the basis functions in the finite element fespace.
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push(b,DarkMagenta);
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LinearForm *b = new LinearForm(fespace);
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ConstantCoefficient one(1.0);
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b->AddDomainIntegrator(new DomainLFIntegrator(one));
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b->Assemble();
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pop();
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// **************************************************************************
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push(SetCurvature,OliveDrab);
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mesh->SetCurvature(1, false, -1, Ordering::byVDIM);
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pop();
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if (gpu) { config::Get().Cuda(true); }
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if (pa) { config::Get().PA(true); }
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// 7. Define the solution vector x as a finite element grid function
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// corresponding to fespace. Initialize x with initial guess of zero,
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// which satisfies the boundary conditions.
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push(GridFunction,Fuchsia);
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GridFunction x(fespace);
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x = 0.0;
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pop();
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// 8. Set up the bilinear form a(.,.) on the finite element space
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// corresponding to the Laplacian operator -Delta, by adding the Diffusion
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// domain integrator.
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push(BilinearForm,Fuchsia);
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BilinearForm *a = new BilinearForm(fespace); // On piece here
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pop();
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push(AddDomainIntegrator,Fuchsia);
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if (pa) { a->AddDomainIntegrator(new PADiffusionIntegrator(one)); }
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else { a->AddDomainIntegrator(new DiffusionIntegrator(one)); }
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pop();
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// 9. 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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push(Assemble,Fuchsia);
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tic_toc.Clear();
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tic_toc.Start();
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a->Assemble(); // On piece here
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pop();
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Vector B, X;
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Operator *A;
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push(Operator,Fuchsia);
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if (pa) { A = new PABilinearForm(fespace); }
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else { A = new SparseMatrix(); }
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pop();
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push(FormLinearSystem,Fuchsia);
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a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
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pop();
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double my_rt = tic_toc.RealTime();
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cout << "\nTotal BilinearForm time: " << my_rt << " sec.";
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cout << "\n\"DOFs/sec\" in assembly: "
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<< 1e-6*A->Height()/my_rt << " million.\n"
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<< endl;
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cout << "Size of linear system: " << A->Height() << endl;
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CGSolver *cg;
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cg = new CGSolver;
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cg->SetRelTol(1e-6);
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cg->SetMaxIter(max_iter);
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cg->SetPrintLevel(3);
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cg->SetOperator(*A);
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tic_toc.Clear();
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tic_toc.Start();
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#ifndef MFEM_USE_SUITESPARSE
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push();
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cg->Mult(B, X);
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pop();
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#else
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// 10. 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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my_rt = tic_toc.RealTime();
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cout << "\nTotal CG time: " << my_rt << " sec." << endl;
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cout << "Time per CG step: "
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<< my_rt / cg->GetNumIterations() << " sec." << endl;
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cout << "\n\"DOFs/sec\" in CG: "
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<< 1e-6*A->Height()*cg->GetNumIterations()/my_rt << " million.\n"
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<< endl;
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delete cg;
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// 11. Recover the solution as a finite element grid function.
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a->RecoverFEMSolution(X, *b, x);
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// 12. Save the refined mesh and the solution. This output can be viewed later
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// 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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// 13. 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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// 14. Free the used memory.
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delete a;
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delete b;
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delete fespace;
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if (order > 0) { delete fec; }
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delete mesh;
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delete A;
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return 0;
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}
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