ex1.cpp

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//                                MFEM Example 1
//
// Compile with: make ex1
//
// Sample runs:  ex1 -m ../data/square-disc.mesh
//               ex1 -m ../data/star.mesh
//               ex1 -m ../data/escher.mesh
//               ex1 -m ../data/fichera.mesh
//               ex1 -m ../data/square-disc-p2.vtk -o 2
//               ex1 -m ../data/square-disc-p3.mesh -o 3
//               ex1 -m ../data/square-disc-nurbs.mesh -o -1
//               ex1 -m ../data/disc-nurbs.mesh -o -1
//               ex1 -m ../data/pipe-nurbs.mesh -o -1
//               ex1 -m ../data/star-surf.mesh
//               ex1 -m ../data/square-disc-surf.mesh
//
// Description:  This example code demonstrates the use of MFEM to define a
//               simple finite element discretization of the Laplace problem
//               -Delta u = 1 with homogeneous Dirichlet boundary conditions.
//               Specifically, we discretize using a FE space of the specified
//               order, or if order < 1 using an isoparametric/isogeometric
//               space (i.e. quadratic for quadratic curvilinear mesh, NURBS for
//               NURBS mesh, etc.)
//
//               The example highlights the use of mesh refinement, finite
//               element grid functions, as well as linear and bilinear forms
//               corresponding to the left-hand side and right-hand side of the
//               discrete linear system. We also cover the explicit elimination
//               of boundary conditions on all boundary edges, and the optional
//               connection to the GLVis tool for visualization.

#include "mfem.hpp"
#include <fstream>
#include <iostream>

using namespace std;
using namespace mfem;

int main(int argc, char *argv[])
{
   // 1. Parse command-line options.
   const char *mesh_file = "../data/star.mesh";
   int order = 1;
   bool visualization = 1;

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
                  "Mesh file to use.");
   args.AddOption(&order, "-o", "--order",
                  "Finite element order (polynomial degree) or -1 for"
                  " isoparametric space.");
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
   args.Parse();
   if (!args.Good())
   {
      args.PrintUsage(cout);
      return 1;
   }
   args.PrintOptions(cout);

   // 2. Read the mesh from the given mesh file. We can handle triangular,
   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
   //    the same code.
   Mesh *mesh;
   ifstream imesh(mesh_file);
   if (!imesh)
   {
      cerr << "\nCan not open mesh file: " << mesh_file << '\n' << endl;
      return 2;
   }
   mesh = new Mesh(imesh, 1, 1);
   imesh.close();
   int dim = mesh->Dimension();

   // 3. Refine the mesh to increase the resolution. In this example we do
   //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
   //    largest number that gives a final mesh with no more than 50,000
   //    elements.
   {
      int ref_levels =
         (int)floor(log(50000./mesh->GetNE())/log(2.)/dim);
      for (int l = 0; l < ref_levels; l++)
         mesh->UniformRefinement();
   }

   // 4. Define a finite element space on the mesh. Here we use continuous
   //    Lagrange finite elements of the specified order. If order < 1, we
   //    instead use an isoparametric/isogeometric space.
   FiniteElementCollection *fec;
   if (order > 0)
      fec = new H1_FECollection(order, dim);
   else if (mesh->GetNodes())
      fec = mesh->GetNodes()->OwnFEC();
   else
      fec = new H1_FECollection(order = 1, dim);
   FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
   cout << "Number of unknowns: " << fespace->GetVSize() << endl;

   // 5. Set up the linear form b(.) which corresponds to the right-hand side of
   //    the FEM linear system, which in this case is (1,phi_i) where phi_i are
   //    the basis functions in the finite element fespace.
   LinearForm *b = new LinearForm(fespace);
   ConstantCoefficient one(1.0);
   b->AddDomainIntegrator(new DomainLFIntegrator(one));
   b->Assemble();

   // 6. Define the solution vector x as a finite element grid function
   //    corresponding to fespace. Initialize x with initial guess of zero,
   //    which satisfies the boundary conditions.
   GridFunction x(fespace);
   x = 0.0;

   // 7. Set up the bilinear form a(.,.) on the finite element space
   //    corresponding to the Laplacian operator -Delta, by adding the Diffusion
   //    domain integrator and imposing homogeneous Dirichlet boundary
   //    conditions. The boundary conditions are implemented by marking all the
   //    boundary attributes from the mesh as essential (Dirichlet). After
   //    assembly and finalizing we extract the corresponding sparse matrix A.
   BilinearForm *a = new BilinearForm(fespace);
   a->AddDomainIntegrator(new DiffusionIntegrator(one));
   a->Assemble();
   Array<int> ess_bdr(mesh->bdr_attributes.Max());
   ess_bdr = 1;
   a->EliminateEssentialBC(ess_bdr, x, *b);
   a->Finalize();
   const SparseMatrix &A = a->SpMat();

#ifndef MFEM_USE_SUITESPARSE
   // 8. Define a simple symmetric Gauss-Seidel preconditioner and use it to
   //    solve the system Ax=b with PCG.
   GSSmoother M(A);
   PCG(A, M, *b, x, 1, 200, 1e-12, 0.0);
#else
   // 8. If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
   UMFPackSolver umf_solver;
   umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
   umf_solver.SetOperator(A);
   umf_solver.Mult(*b, x);
#endif

   // 9. Save the refined mesh and the solution. This output can be viewed later
   //    using GLVis: "glvis -m refined.mesh -g sol.gf".
   ofstream mesh_ofs("refined.mesh");
   mesh_ofs.precision(8);
   mesh->Print(mesh_ofs);
   ofstream sol_ofs("sol.gf");
   sol_ofs.precision(8);
   x.Save(sol_ofs);

   // 10. Send the solution by socket to a GLVis server.
   if (visualization)
   {
      char vishost[] = "localhost";
      int  visport   = 19916;
      socketstream sol_sock(vishost, visport);
      sol_sock.precision(8);
      sol_sock << "solution\n" << *mesh << x << flush;
   }

   // 11. Free the used memory.
   delete a;
   delete b;
   delete fespace;
   if (order > 0)
      delete fec;
   delete mesh;

   return 0;
}