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