82 lines
2.8 KiB
C++
82 lines
2.8 KiB
C++
// MFEM Example 0
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//
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// Compile with: make ex0
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//
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// Sample runs: ex0
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// ex0 -m ../data/fichera.mesh
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// ex0 -m ../data/square-disc.mesh -o 2
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//
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// Description: This example code demonstrates the most basic usage of MFEM to
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// define a simple finite element discretization of the Laplace
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// problem -Delta u = 1 with zero Dirichlet boundary conditions.
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// General 2D/3D mesh files and finite element polynomial degrees
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// can be specified by command line options.
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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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OptionsParser args(argc, argv);
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args.AddOption(&mesh_file, "-m", "--mesh", "Mesh file to use.");
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args.AddOption(&order, "-o", "--order", "Finite element polynomial degree");
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args.ParseCheck();
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// 2. Read the mesh from the given mesh file, and refine once uniformly.
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Mesh mesh(mesh_file);
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mesh.UniformRefinement();
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// 3. Define a finite element space on the mesh. Here we use H1 continuous
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// high-order Lagrange finite elements of the given order.
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H1_FECollection fec(order, mesh.Dimension());
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FiniteElementSpace fespace(&mesh, &fec);
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cout << "Number of unknowns: " << fespace.GetTrueVSize() << endl;
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// 4. Extract the list of all the boundary DOFs. These will be marked as
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// Dirichlet in order to enforce zero boundary conditions.
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Array<int> boundary_dofs;
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fespace.GetBoundaryTrueDofs(boundary_dofs);
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// 5. Define the solution x as a finite element grid function in fespace. Set
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// the initial guess to zero, which also sets the boundary conditions.
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GridFunction x(&fespace);
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x = 0.0;
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// 6. Set up the linear form b(.) corresponding to the right-hand side.
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ConstantCoefficient one(1.0);
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LinearForm b(&fespace);
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b.AddDomainIntegrator(new DomainLFIntegrator(one));
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b.Assemble();
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// 7. Set up the bilinear form a(.,.) corresponding to the -Delta operator.
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BilinearForm a(&fespace);
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a.AddDomainIntegrator(new DiffusionIntegrator);
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a.Assemble();
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// 8. Form the linear system A X = B. This includes eliminating boundary
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// conditions, applying AMR constraints, and other transformations.
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SparseMatrix A;
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Vector B, X;
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a.FormLinearSystem(boundary_dofs, x, b, A, X, B);
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// 9. Solve the system using PCG with symmetric Gauss-Seidel preconditioner.
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GSSmoother M(A);
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PCG(A, M, B, X, 1, 200, 1e-12, 0.0);
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// 10. Recover the solution x as a grid function and save to file. The output
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// can be viewed using GLVis as follows: "glvis -m mesh.mesh -g sol.gf"
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a.RecoverFEMSolution(X, b, x);
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x.Save("sol.gf");
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mesh.Save("mesh.mesh");
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return 0;
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}
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