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125ff22 Jul 1, 2016
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@tzanio @jakubcerveny
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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
// ex1 -m ../data/inline-segment.mesh
// ex1 -m ../data/amr-quad.mesh
// ex1 -m ../data/amr-hex.mesh
// ex1 -m ../data/fichera-amr.mesh
// ex1 -m ../data/mobius-strip.mesh
// ex1 -m ../data/mobius-strip.mesh -o -1 -sc
//
// 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 essential boundary conditions, static condensation, 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 static_cond = false;
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(&static_cond, "-sc", "--static-condensation", "-no-sc",
"--no-static-condensation", "Enable static condensation.");
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 = new Mesh(mesh_file, 1, 1);
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();
cout << "Using isoparametric FEs: " << fec->Name() << endl;
}
else
{
fec = new H1_FECollection(order = 1, dim);
}
FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
cout << "Number of finite element unknowns: "
<< fespace->GetTrueVSize() << endl;
// 5. Determine the list of true (i.e. conforming) essential boundary dofs.
// In this example, the boundary conditions are defined by marking all
// the boundary attributes from the mesh as essential (Dirichlet) and
// converting them to a list of true dofs.
Array<int> ess_tdof_list;
if (mesh->bdr_attributes.Size())
{
Array<int> ess_bdr(mesh->bdr_attributes.Max());
ess_bdr = 1;
fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
}
// 6. 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();
// 7. 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;
// 8. Set up the bilinear form a(.,.) on the finite element space
// corresponding to the Laplacian operator -Delta, by adding the Diffusion
// domain integrator.
BilinearForm *a = new BilinearForm(fespace);
a->AddDomainIntegrator(new DiffusionIntegrator(one));
// 9. Assemble the bilinear form and the corresponding linear system,
// applying any necessary transformations such as: eliminating boundary
// conditions, applying conforming constraints for non-conforming AMR,
// static condensation, etc.
if (static_cond) { a->EnableStaticCondensation(); }
a->Assemble();
SparseMatrix A;
Vector B, X;
a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
cout << "Size of linear system: " << A.Height() << endl;
#ifndef MFEM_USE_SUITESPARSE
// 10. Define a simple symmetric Gauss-Seidel preconditioner and use it to
// solve the system A X = B with PCG.
GSSmoother M(A);
PCG(A, M, B, X, 1, 200, 1e-12, 0.0);
#else
// 10. 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
// 11. Recover the solution as a finite element grid function.
a->RecoverFEMSolution(X, *b, x);
// 12. 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);
// 13. 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;
}
// 14. Free the used memory.
delete a;
delete b;
delete fespace;
if (order > 0) { delete fec; }
delete mesh;
return 0;
}