290 lines
11 KiB
C++
290 lines
11 KiB
C++
// MFEM Example 1
|
|
//
|
|
// Compile with: make ex1
|
|
//
|
|
// Sample runs: ex1 -m ../data/square-disc.mesh
|
|
// ex1 -m ../data/star.mesh
|
|
// ex1 -m ../data/star-mixed.mesh
|
|
// ex1 -m ../data/escher.mesh
|
|
// ex1 -m ../data/fichera.mesh
|
|
// ex1 -m ../data/fichera-mixed.mesh
|
|
// ex1 -m ../data/toroid-wedge.mesh
|
|
// ex1 -m ../data/octahedron.mesh -o 1
|
|
// ex1 -m ../data/periodic-annulus-sector.msh
|
|
// ex1 -m ../data/periodic-torus-sector.msh
|
|
// 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/star-mixed-p2.mesh -o 2
|
|
// ex1 -m ../data/disc-nurbs.mesh -o -1
|
|
// ex1 -m ../data/pipe-nurbs.mesh -o -1
|
|
// ex1 -m ../data/fichera-mixed-p2.mesh -o 2
|
|
// 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
|
|
// ex1 -m ../data/nc3-nurbs.mesh -o -1
|
|
//
|
|
// Device sample runs:
|
|
// ex1 -pa -d cuda
|
|
// ex1 -fa -d cuda
|
|
// ex1 -pa -d raja-cuda
|
|
// * ex1 -pa -d raja-hip
|
|
// ex1 -pa -d occa-cuda
|
|
// ex1 -pa -d raja-omp
|
|
// ex1 -pa -d occa-omp
|
|
// ex1 -pa -d ceed-cpu
|
|
// ex1 -pa -d ceed-cpu -o 4 -a
|
|
// ex1 -pa -d ceed-cpu -m ../data/square-mixed.mesh
|
|
// ex1 -pa -d ceed-cpu -m ../data/fichera-mixed.mesh
|
|
// * ex1 -pa -d ceed-cuda
|
|
// * ex1 -pa -d ceed-hip
|
|
// ex1 -pa -d ceed-cuda:/gpu/cuda/shared
|
|
// ex1 -pa -d ceed-cuda:/gpu/cuda/shared -m ../data/square-mixed.mesh
|
|
// ex1 -pa -d ceed-cuda:/gpu/cuda/shared -m ../data/fichera-mixed.mesh
|
|
// ex1 -m ../data/beam-hex.mesh -pa -d cuda
|
|
// ex1 -m ../data/beam-tet.mesh -pa -d ceed-cpu
|
|
// ex1 -m ../data/beam-tet.mesh -pa -d ceed-cuda:/gpu/cuda/ref
|
|
//
|
|
// Description: This example code demonstrates the use of MFEM to define a
|
|
// simple finite element discretization of the Poisson 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 pa = false;
|
|
bool fa = false;
|
|
const char *device_config = "cpu";
|
|
bool visualization = true;
|
|
bool algebraic_ceed = false;
|
|
|
|
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(&pa, "-pa", "--partial-assembly", "-no-pa",
|
|
"--no-partial-assembly", "Enable Partial Assembly.");
|
|
args.AddOption(&fa, "-fa", "--full-assembly", "-no-fa",
|
|
"--no-full-assembly", "Enable Full Assembly.");
|
|
args.AddOption(&device_config, "-d", "--device",
|
|
"Device configuration string, see Device::Configure().");
|
|
#ifdef MFEM_USE_CEED
|
|
args.AddOption(&algebraic_ceed, "-a", "--algebraic", "-no-a", "--no-algebraic",
|
|
"Use algebraic Ceed solver");
|
|
#endif
|
|
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. Enable hardware devices such as GPUs, and programming models such as
|
|
// CUDA, OCCA, RAJA and OpenMP based on command line options.
|
|
Device device(device_config);
|
|
device.Print();
|
|
|
|
// 3. 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(mesh_file, 1, 1);
|
|
int dim = mesh.Dimension();
|
|
|
|
// 4. 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();
|
|
}
|
|
}*/
|
|
|
|
// 5. 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;
|
|
bool delete_fec;
|
|
if (order > 0)
|
|
{
|
|
fec = new H1_FECollection(order, dim);
|
|
delete_fec = true;
|
|
}
|
|
else if (mesh.GetNodes())
|
|
{
|
|
fec = mesh.GetNodes()->OwnFEC();
|
|
delete_fec = false;
|
|
cout << "Using isoparametric FEs: " << fec->Name() << endl;
|
|
}
|
|
else
|
|
{
|
|
fec = new H1_FECollection(order = 1, dim);
|
|
delete_fec = true;
|
|
}
|
|
FiniteElementSpace fespace(&mesh, fec);
|
|
cout << "Number of finite element unknowns: "
|
|
<< fespace.GetTrueVSize() << endl;
|
|
|
|
// 6. Determine the list of true (i.e. conforming) essential boundary dofs.
|
|
// In this example, the boundary conditions are defined by marking all
|
|
// the external 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 = 0;
|
|
// Apply boundary conditions on all external boundaries:
|
|
mesh.MarkExternalBoundaries(ess_bdr);
|
|
// Boundary conditions can also be applied based on named attributes:
|
|
// mesh.MarkNamedBoundaries(set_name, ess_bdr)
|
|
|
|
fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
|
|
}
|
|
|
|
// 7. 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(&fespace);
|
|
ConstantCoefficient one(1.0);
|
|
b.AddDomainIntegrator(new DomainLFIntegrator(one));
|
|
b.Assemble();
|
|
|
|
// 8. 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;
|
|
|
|
// 9. 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(&fespace);
|
|
if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
|
|
if (fa)
|
|
{
|
|
a.SetAssemblyLevel(AssemblyLevel::FULL);
|
|
// Sort the matrix column indices when running on GPU or with OpenMP (i.e.
|
|
// when Device::IsEnabled() returns true). This makes the results
|
|
// bit-for-bit deterministic at the cost of somewhat longer run time.
|
|
a.EnableSparseMatrixSorting(Device::IsEnabled());
|
|
}
|
|
a.AddDomainIntegrator(new DiffusionIntegrator(one));
|
|
|
|
// 10. 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();
|
|
|
|
OperatorPtr A;
|
|
Vector B, X;
|
|
a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
|
|
|
|
cout << "Size of linear system: " << A->Height() << endl;
|
|
|
|
// 11. Solve the linear system A X = B.
|
|
if (!pa)
|
|
{
|
|
#ifndef MFEM_USE_SUITESPARSE
|
|
// Use a simple symmetric Gauss-Seidel preconditioner with PCG.
|
|
GSSmoother M((SparseMatrix&)(*A));
|
|
PCG(*A, M, B, X, 1, 200, 1e-12, 0.0);
|
|
#else
|
|
// 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
|
|
}
|
|
else
|
|
{
|
|
if (UsesTensorBasis(fespace))
|
|
{
|
|
if (algebraic_ceed)
|
|
{
|
|
ceed::AlgebraicSolver M(a, ess_tdof_list);
|
|
PCG(*A, M, B, X, 1, 400, 1e-12, 0.0);
|
|
}
|
|
else
|
|
{
|
|
OperatorJacobiSmoother M(a, ess_tdof_list);
|
|
PCG(*A, M, B, X, 1, 400, 1e-12, 0.0);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
CG(*A, B, X, 1, 400, 1e-12, 0.0);
|
|
}
|
|
}
|
|
|
|
// 12. Recover the solution as a finite element grid function.
|
|
a.RecoverFEMSolution(X, b, x);
|
|
|
|
// 13. 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);
|
|
|
|
// 14. Send the solution by socket to a GLVis server.
|
|
if (visualization)
|
|
{
|
|
char vishost[] = "localhost";
|
|
int visport = 19916;
|
|
glvis_stream sol_sock(vishost, visport);
|
|
sol_sock.precision(8);
|
|
sol_sock << "solution\n" << mesh << x << flush;
|
|
}
|
|
|
|
// 15. Free the used memory.
|
|
if (delete_fec)
|
|
{
|
|
delete fec;
|
|
}
|
|
|
|
return 0;
|
|
}
|