275 lines
9.6 KiB
C++
275 lines
9.6 KiB
C++
// MFEM Example 6 - Parallel Version
|
|
//
|
|
// Compile with: make ex6p
|
|
//
|
|
// Sample runs: mpirun -np 4 ex6p -m ../data/square-disc.mesh -o 1
|
|
// mpirun -np 4 ex6p -m ../data/square-disc.mesh -o 2
|
|
// mpirun -np 4 ex6p -m ../data/square-disc-nurbs.mesh -o 2
|
|
// mpirun -np 4 ex6p -m ../data/star.mesh -o 3
|
|
// mpirun -np 4 ex6p -m ../data/escher.mesh -o 1
|
|
// mpirun -np 4 ex6p -m ../data/fichera.mesh -o 2
|
|
// mpirun -np 4 ex6p -m ../data/disc-nurbs.mesh -o 2
|
|
// mpirun -np 4 ex6p -m ../data/ball-nurbs.mesh
|
|
// mpirun -np 4 ex6p -m ../data/pipe-nurbs.mesh
|
|
// mpirun -np 4 ex6p -m ../data/star-surf.mesh -o 2
|
|
// mpirun -np 4 ex6p -m ../data/square-disc-surf.mesh -o 2
|
|
// mpirun -np 4 ex6p -m ../data/amr-quad.mesh
|
|
//
|
|
// Description: This is a version of Example 1 with a simple adaptive mesh
|
|
// refinement loop. The problem being solved is again the Laplace
|
|
// equation -Delta u = 1 with homogeneous Dirichlet boundary
|
|
// conditions. The problem is solved on a sequence of meshes which
|
|
// are locally refined in a conforming (triangles, tetrahedrons)
|
|
// or non-conforming (quadrilateral, hexahedrons) manner according
|
|
// to a simple ZZ error estimator.
|
|
//
|
|
// The example demonstrates MFEM's capability to work with both
|
|
// conforming and nonconforming refinements, in 2D and 3D, on
|
|
// linear, curved and surface meshes. Interpolation of functions
|
|
// from coarse to fine meshes, as well as persistent GLVis
|
|
// visualization are also illustrated.
|
|
//
|
|
// We recommend viewing Example 1 before viewing this example.
|
|
|
|
#include "mfem.hpp"
|
|
#include <fstream>
|
|
#include <iostream>
|
|
|
|
using namespace std;
|
|
using namespace mfem;
|
|
|
|
int main(int argc, char *argv[])
|
|
{
|
|
// 1. Initialize MPI.
|
|
int num_procs, myid;
|
|
MPI_Init(&argc, &argv);
|
|
MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
|
|
MPI_Comm_rank(MPI_COMM_WORLD, &myid);
|
|
|
|
// 2. Parse command-line options.
|
|
const char *mesh_file = "../data/star.mesh";
|
|
int order = 1;
|
|
bool visualization = true;
|
|
|
|
OptionsParser args(argc, argv);
|
|
args.AddOption(&mesh_file, "-m", "--mesh",
|
|
"Mesh file to use.");
|
|
args.AddOption(&order, "-o", "--order",
|
|
"Finite element order (polynomial degree).");
|
|
args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
|
|
"--no-visualization",
|
|
"Enable or disable GLVis visualization.");
|
|
args.Parse();
|
|
if (!args.Good())
|
|
{
|
|
if (myid == 0)
|
|
{
|
|
args.PrintUsage(cout);
|
|
}
|
|
MPI_Finalize();
|
|
return 1;
|
|
}
|
|
if (myid == 0)
|
|
{
|
|
args.PrintOptions(cout);
|
|
}
|
|
|
|
// 3. Read the (serial) mesh from the given mesh file on all processors. We
|
|
// can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
|
|
// and volume meshes with the same code.
|
|
Mesh *mesh;
|
|
ifstream imesh(mesh_file);
|
|
if (!imesh)
|
|
{
|
|
if (myid == 0)
|
|
{
|
|
cerr << "\nCan not open mesh file: " << mesh_file << '\n' << endl;
|
|
}
|
|
MPI_Finalize();
|
|
return 2;
|
|
}
|
|
mesh = new Mesh(imesh, 1, 1);
|
|
imesh.close();
|
|
int dim = mesh->Dimension();
|
|
int sdim = mesh->SpaceDimension();
|
|
|
|
// 4. Refine the serial mesh on all processors to increase the resolution.
|
|
// Also project a NURBS mesh to a piecewise-quadratic curved mesh. Make
|
|
// sure that the mesh is non-conforming.
|
|
if (mesh->NURBSext)
|
|
{
|
|
mesh->UniformRefinement();
|
|
mesh->SetCurvature(2);
|
|
}
|
|
mesh->EnsureNCMesh();
|
|
|
|
// 5. Define a parallel mesh by partitioning the serial mesh.
|
|
// Once the parallel mesh is defined, the serial mesh can be deleted.
|
|
ParMesh pmesh(MPI_COMM_WORLD, *mesh);
|
|
delete mesh;
|
|
|
|
MFEM_VERIFY(pmesh.bdr_attributes.Size() > 0,
|
|
"Boundary attributes required in the mesh.");
|
|
Array<int> ess_bdr(pmesh.bdr_attributes.Max());
|
|
ess_bdr = 1;
|
|
|
|
// 6. Define a finite element space on the mesh. The polynomial order is
|
|
// one (linear) by default, but this can be changed on the command line.
|
|
H1_FECollection fec(order, dim);
|
|
ParFiniteElementSpace fespace(&pmesh, &fec);
|
|
|
|
// 7. As in Example 1p, we set up bilinear and linear forms corresponding to
|
|
// the Laplace problem -\Delta u = 1. We don't assemble the discrete
|
|
// problem yet, this will be done in the main loop.
|
|
ParBilinearForm a(&fespace);
|
|
ParLinearForm b(&fespace);
|
|
|
|
ConstantCoefficient one(1.0);
|
|
|
|
a.AddDomainIntegrator(new DiffusionIntegrator(one));
|
|
b.AddDomainIntegrator(new DomainLFIntegrator(one));
|
|
|
|
// 8. The solution vector x and the associated finite element grid function
|
|
// will be maintained over the AMR iterations. We initialize it to zero.
|
|
ParGridFunction x(&fespace);
|
|
x = 0;
|
|
|
|
// 9. Connect to GLVis.
|
|
char vishost[] = "localhost";
|
|
int visport = 19916;
|
|
|
|
socketstream sout;
|
|
if (visualization)
|
|
{
|
|
sout.open(vishost, visport);
|
|
if (!sout)
|
|
{
|
|
if (myid == 0)
|
|
{
|
|
cout << "Unable to connect to GLVis server at "
|
|
<< vishost << ':' << visport << endl;
|
|
cout << "GLVis visualization disabled.\n";
|
|
}
|
|
visualization = false;
|
|
}
|
|
|
|
sout.precision(8);
|
|
}
|
|
|
|
// 10. The main AMR loop. In each iteration we solve the problem on the
|
|
// current mesh, visualize the solution, estimate the error on all
|
|
// elements, refine the worst elements and update all objects to work
|
|
// with the new mesh.
|
|
const int max_dofs = 100000;
|
|
for (int it = 0; ; it++)
|
|
{
|
|
HYPRE_Int global_dofs = fespace.GlobalTrueVSize();
|
|
if (myid == 0)
|
|
{
|
|
cout << "\nIteration " << it << endl;
|
|
cout << "Number of unknowns: " << global_dofs << endl;
|
|
}
|
|
|
|
// 11. Assemble the stiffness matrix and the right-hand side. Note that
|
|
// MFEM doesn't care at this point that the mesh is nonconforming
|
|
// and parallel. The FE space is considered 'cut' along hanging
|
|
// edges/faces, and also across processor boundaries.
|
|
a.Assemble();
|
|
b.Assemble();
|
|
|
|
// 12. Set the initial estimate of the solution and the Dirichlet DOFs,
|
|
// here we just use zero everywhere.
|
|
x = 0.0;
|
|
|
|
// 13. Create the parallel linear system: eliminate boundary conditions,
|
|
// constrain hanging nodes and nodes across processor boundaries.
|
|
// The system will be solved for true (unconstrained/unique) DOFs only.
|
|
Array<int> ess_tdof_list;
|
|
fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
|
|
|
|
HypreParMatrix A;
|
|
Vector B, X;
|
|
a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
|
|
|
|
// 14. Define and apply a parallel PCG solver for AX=B with the BoomerAMG
|
|
// preconditioner from hypre.
|
|
HypreBoomerAMG amg(A);
|
|
amg.SetPrintLevel(0);
|
|
HyprePCG pcg(A);
|
|
pcg.SetTol(1e-12);
|
|
pcg.SetMaxIter(200);
|
|
pcg.SetPrintLevel(0);
|
|
pcg.SetPreconditioner(amg);
|
|
pcg.Mult(B, X);
|
|
|
|
// 15. Extract the parallel grid function corresponding to the finite element
|
|
// approximation X. This is the local solution on each processor.
|
|
a.RecoverFEMSolution(X, b, x);
|
|
|
|
// 16. Send the solution by socket to a GLVis server.
|
|
if (visualization)
|
|
{
|
|
sout << "parallel " << num_procs << " " << myid << "\n";
|
|
sout << "solution\n" << pmesh << x << flush;
|
|
}
|
|
|
|
if (global_dofs > max_dofs)
|
|
{
|
|
break;
|
|
}
|
|
|
|
// 17. Estimate element errors using the Zienkiewicz-Zhu error estimator.
|
|
// The bilinear form integrator must have the 'ComputeElementFlux'
|
|
// method defined.
|
|
Vector errors(pmesh.GetNE());
|
|
{
|
|
// Space for the discontinuous (original) flux
|
|
DiffusionIntegrator flux_integrator(one);
|
|
L2_FECollection flux_fec(order, dim);
|
|
ParFiniteElementSpace flux_fes(&pmesh, &flux_fec, sdim);
|
|
|
|
// Space for the smoothed (conforming) flux
|
|
double norm_p = 1;
|
|
RT_FECollection smooth_flux_fec(order-1, dim);
|
|
ParFiniteElementSpace smooth_flux_fes(&pmesh, &smooth_flux_fec);
|
|
|
|
// Another possible set of options for the smoothed flux space:
|
|
// norm_p = 1;
|
|
// H1_FECollection smooth_flux_fec(order, dim);
|
|
// ParFiniteElementSpace smooth_flux_fes(&pmesh, &smooth_flux_fec, dim);
|
|
|
|
L2ZZErrorEstimator(flux_integrator, x,
|
|
smooth_flux_fes, flux_fes, errors, norm_p);
|
|
}
|
|
double local_max_err = errors.Max();
|
|
double global_max_err;
|
|
MPI_Allreduce(&local_max_err, &global_max_err, 1,
|
|
MPI_DOUBLE, MPI_MAX, pmesh.GetComm());
|
|
|
|
// 18. Make a list of elements whose error is larger than a fraction
|
|
// of the maximum element error. These elements will be refined.
|
|
Array<int> ref_list;
|
|
const double frac = 0.7;
|
|
double threshold = frac * global_max_err;
|
|
for (int i = 0; i < errors.Size(); i++)
|
|
{
|
|
if (errors[i] >= threshold) { ref_list.Append(i); }
|
|
}
|
|
|
|
// 19. Refine the selected elements. Since we are going to transfer the
|
|
// grid function x from the coarse mesh to the new fine mesh in the
|
|
// next step, we need to request the "two-level state" of the mesh.
|
|
pmesh.GeneralRefinement(ref_list);
|
|
|
|
// 20. Inform the space, grid function and also the bilinear and linear
|
|
// forms that the space has changed.
|
|
fespace.Update();
|
|
x.Update();
|
|
a.Update();
|
|
b.Update();
|
|
}
|
|
|
|
MPI_Finalize();
|
|
return 0;
|
|
}
|