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mfem/examples/ex3p_complex.cpp
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// MFEM Example 3 - Parallel Version
//
// Compile with: make ex3p_complex
//
#include "mfem.hpp"
#include <fstream>
#include <iostream>
using namespace std;
using namespace mfem;
// Exact solution, E, and r.h.s., f. See below for implementation.
void E_exact(const Vector &, Vector &);
void curlE_exact(const Vector &, Vector &);
void f_exact(const Vector &, Vector &);
double freq = 1.0, kappa;
int dim;
#define COMPLEX_VERSION
#define NEUMANN
#define INDEFINITE
const double omega = 1.4;
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/beam-tet.mesh";
int order = 1;
bool static_cond = false;
bool pa = false;
const char *device_config = "cpu";
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).");
args.AddOption(&freq, "-f", "--frequency", "Set the frequency for the exact"
" solution.");
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(&device_config, "-d", "--device",
"Device configuration string, see Device::Configure().");
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);
}
kappa = freq * M_PI;
// 3. 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);
if (myid == 0) { device.Print(); }
// 4. 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 = new Mesh(mesh_file, 1, 1);
dim = mesh->Dimension();
int sdim = mesh->SpaceDimension();
// 5. Refine the serial mesh on all processors 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 1,000 elements.
{
int ref_levels = (int)floor(log(1000./mesh->GetNE())/log(2.)/dim);
for (int l = 0; l < ref_levels; l++)
{
mesh->UniformRefinement();
}
}
// 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
// this mesh further in parallel to increase the resolution. Once the
// parallel mesh is defined, the serial mesh can be deleted. Tetrahedral
// meshes need to be reoriented before we can define high-order Nedelec
// spaces on them.
ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
delete mesh;
{
int par_ref_levels = 0;
for (int l = 0; l < par_ref_levels; l++)
{
pmesh->UniformRefinement();
}
}
pmesh->ReorientTetMesh();
// 7. Define a parallel finite element space on the parallel mesh. Here we
// use the Nedelec finite elements of the specified order.
FiniteElementCollection *fec = new ND_FECollection(order, dim);
ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
HYPRE_Int size = fespace->GlobalTrueVSize();
if (myid == 0)
{
cout << "Number of finite element unknowns: " << size << endl;
}
// 8. Determine the list of true (i.e. parallel 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;
Array<int> ess_bdr;
ess_bdr.SetSize(pmesh->bdr_attributes.Max());
ess_bdr = 0;
#ifndef NEUMANN
if (pmesh->bdr_attributes.Size())
{
ess_bdr = 1;
fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
}
#endif
//const double imscale = 0.0;
const double imscale = omega;
Coefficient *im = new ConstantCoefficient(imscale); // im part
//Coefficient *im = new ConstantCoefficient(0.0); // im part
VectorFunctionCoefficient E_Re(sdim, E_exact);
VectorFunctionCoefficient curlE_Re(sdim, curlE_exact);
ScalarVectorProductCoefficient omegaE(imscale, E_Re); // im part
//ScalarVectorProductCoefficient omegaE(0.0, E_Re); // im part
// 9. Set up the parallel linear form b(.) which corresponds to the
// right-hand side of the FEM linear system, which in this case is
// (f,phi_i) where f is given by the function f_exact and phi_i are the
// basis functions in the finite element fespace.
VectorFunctionCoefficient f(sdim, f_exact);
#ifdef COMPLEX_VERSION
ParComplexLinearForm *b = new ParComplexLinearForm(fespace);
b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f), NULL);
b->AddBoundaryIntegrator(NULL,
new VectorFEDomainLFIntegrator(omegaE)); // im part
#else
// Real version
ParLinearForm *b = new ParLinearForm(fespace);
b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
#endif
#ifdef NEUMANN
b->AddBoundaryIntegrator(new VectorFEBoundaryTangentLFIntegrator(curlE_Re),
NULL);
#endif
b->Assemble();
// 10. Define the solution vector x as a parallel finite element grid function
// corresponding to fespace. Initialize x by projecting the exact
// solution. Note that only values from the boundary edges will be used
// when eliminating the non-homogeneous boundary condition to modify the
// r.h.s. vector b.
/*
ParGridFunction x(fespace);
VectorFunctionCoefficient E(sdim, E_exact);
x.ProjectCoefficient(E);
*/
#ifdef COMPLEX_VERSION
// Complex version
ParComplexGridFunction x(fespace);
x = 0.0;
Vector zero(sdim);
zero = 0.0;
VectorConstantCoefficient E_Im(zero);
//x.ProjectBdrCoefficientTangent(E_Re, E_Im, ess_bdr);
x.ProjectCoefficient(E_Re, E_Im);
#else
ParGridFunction x(fespace);
x = 0.0;
x.ProjectCoefficient(E_Re);
#endif
// 11. Set up the parallel bilinear form corresponding to the EM diffusion
// operator curl muinv curl + sigma I, by adding the curl-curl and the
// mass domain integrators.
Coefficient *muinv = new ConstantCoefficient(1.0);
#ifdef INDEFINITE
Coefficient *sigma = new ConstantCoefficient(
-omega*omega); // indefinite -, definite +
#else
Coefficient *sigma = new ConstantCoefficient(
omega*omega); // indefinite -, definite +
#endif
Coefficient *abssigma = new ConstantCoefficient(omega*omega);
Coefficient *imabs = new ConstantCoefficient(imscale); // im part
//Coefficient *imabs = new ConstantCoefficient(0.0); // im part
//Coefficient *im = new ConstantCoefficient(0.0);
#ifdef COMPLEX_VERSION
// Complex version
ParSesquilinearForm *a = new ParSesquilinearForm(fespace);
if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
a->AddDomainIntegrator(new CurlCurlIntegrator(*muinv), NULL);
//a->AddDomainIntegrator(new VectorFEMassIntegrator(*sigma), new VectorFEMassIntegrator(*im));
a->AddDomainIntegrator(new VectorFEMassIntegrator(*sigma), NULL);
a->AddBoundaryIntegrator(NULL, new VectorFEMassIntegrator(*im)); // im part
#else
// Real version
ParBilinearForm *a = new ParBilinearForm(fespace);
if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
a->AddDomainIntegrator(new CurlCurlIntegrator(*muinv));
//a->AddDomainIntegrator(new VectorFEMassIntegrator(*sigma), new VectorFEMassIntegrator(*im));
a->AddDomainIntegrator(new VectorFEMassIntegrator(*sigma));
#endif
// 12. Assemble the parallel bilinear form and the corresponding linear
// system, applying any necessary transformations such as: parallel
// assembly, 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);
ParBilinearForm a_Re(fespace);
a_Re.AddDomainIntegrator(new CurlCurlIntegrator(*muinv));
a_Re.AddDomainIntegrator(new VectorFEMassIntegrator(*abssigma));
//if (pa) { a_Re.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
a_Re.SetAssemblyLevel(AssemblyLevel::PARTIAL);
a_Re.Assemble();
OperatorPtr A_Re;
a_Re.FormSystemMatrix(ess_tdof_list, A_Re);
ParBilinearForm a_Im(fespace);
a_Im.AddBoundaryIntegrator(new VectorFEMassIntegrator(*imabs));
a_Im.Assemble();
OperatorPtr A_Im;
a_Im.FormSystemMatrix(ess_tdof_list, A_Im);
// 13. Solve the system AX=B using PCG with the AMS preconditioner from hypre
// (in the full assembly case) or CG with Jacobi preconditioner (in the
// partial assembly case).
Array<int> offsets(3);
offsets[0] = 0;
offsets[1] = fespace->GetTrueVSize();
offsets[2] = fespace->GetTrueVSize();
offsets.PartialSum();
//OperatorJacobiSmoother massJacobi(a_Im, ess_tdof_list);
StopWatch sw;
sw.Clear();
sw.Start();
if (pa) // Jacobi preconditioning in partial assembly mode
{
MFEM_VERIFY(false, "TODO");
//OperatorJacobiSmoother Jacobi(*a, ess_tdof_list);
CGSolver cg(MPI_COMM_WORLD);
cg.SetRelTol(1e-12);
cg.SetMaxIter(1000);
cg.SetPrintLevel(1);
cg.SetOperator(*A);
//cg.SetPreconditioner(Jacobi);
cg.Mult(B, X);
}
else
{
if (myid == 0)
{
cout << "Size of linear system: "
<< A.As<HypreParMatrix>()->GetGlobalNumRows() << endl;
}
//HypreAMS ams(*A_Re.As<HypreParMatrix>(), fespace);
// One option is to use the standard real-valued MatrixFreeAMS to precondition
// the real part of the complex system in the PMHSS preconditioner (BlockDiagonalPreconditioner).
// Another option is to use complex MatrixFreeAMS to precondition the
// complex system without PMHSS and without a BlockDiagonalPreconditioner.
//#define COMPLEX_AMS
#ifdef MFEM_USE_AMGX
bool useAmgX = false;
cout << "Built with AMGX, using AMGX " << useAmgX << endl;
MatrixFreeAMS ams(a_Re, *A_Re, *fespace, muinv, abssigma, im, imabs, NULL,
ess_bdr, useAmgX);
MatrixFreeAMS ams(a_Re, *A_Re, *fespace, muinv, abssigma, NULL, NULL, ess_bdr,
useAmgX);
#ifdef COMPLEX_AMS
MFEM_VERIFY(false, "TODO");
#endif
#else
cout << "Not built with AMGX" << endl;
#ifdef COMPLEX_AMS
MatrixFreeAMS ams(a_Re, *A_Re, A.Ptr(), *fespace, muinv, abssigma, im, imabs,
NULL, ess_bdr);
#else
MatrixFreeAMS ams(a_Re, *A_Re, NULL, *fespace, muinv, abssigma, NULL, NULL,
NULL, ess_bdr);
#endif
#endif
#ifdef COMPLEX_VERSION
#ifdef COMPLEX_AMS
//MFEM_VERIFY(false, "TODO");
#else
BlockDiagonalPreconditioner BlockDP(offsets);
BlockDP.SetDiagonalBlock(0, &ams);
BlockDP.SetDiagonalBlock(1, &ams);
/*
BlockDiagonalPreconditioner BlockDP_Im(offsets);
BlockDP_Im.SetDiagonalBlock(0, &massJacobi); // TODO: this won't work if it has zeros on diagonal
BlockDP_Im.SetDiagonalBlock(1, &massJacobi);
*/
//Complex_PMHSS PMHSS(A_Re, A_Im, &BlockDP, &BlockDP_Im);
//Complex_PMHSS PMHSS(A_Re, A_Im, &BlockDP, NULL, 2.0 * omega);
//Complex_PMHSS PMHSS(A_Re, A_Im, &BlockDP, NULL, omega);
Complex_PMHSS PMHSS(A_Re.Ptr(), A_Im.Ptr(), &BlockDP, NULL, 1.0);
ComplexOperator AspdComplex(A_Re.Ptr(), A_Im.Ptr(), false, false);
GMRESSolver PMHSSgmres(MPI_COMM_WORLD);
PMHSSgmres.SetPrintLevel(1);
PMHSSgmres.SetKDim(100);
PMHSSgmres.SetMaxIter(100);
PMHSSgmres.SetRelTol(1e-6);
PMHSSgmres.SetAbsTol(0.0);
PMHSSgmres.SetOperator(AspdComplex);
PMHSSgmres.SetPreconditioner(PMHSS);
#endif
GMRESSolver gmres(MPI_COMM_WORLD);
gmres.SetPrintLevel(1);
gmres.SetKDim(1000);
gmres.SetMaxIter(100);
gmres.SetRelTol(1e-8);
gmres.SetAbsTol(0.0);
gmres.SetOperator(*A);
//gmres.SetPreconditioner(BlockDP);
#ifdef COMPLEX_AMS
//MFEM_VERIFY(false, "TODO");
gmres.SetPreconditioner(ams);
#else
gmres.SetPreconditioner(PMHSS);
//gmres.SetPreconditioner(PMHSSgmres);
#endif
#else
GMRESSolver gmres(MPI_COMM_WORLD);
gmres.SetPrintLevel(1);
gmres.SetKDim(1000);
gmres.SetMaxIter(100);
gmres.SetRelTol(1e-8);
gmres.SetAbsTol(0.0);
gmres.SetOperator(*A);
gmres.SetPreconditioner(ams);
#endif
gmres.Mult(B, X);
}
sw.Stop();
mfem::out << "Total solve time " <<sw.RealTime() << endl;
// 14. Recover the parallel grid function corresponding to X. This is the
// local finite element solution on each processor.
a->RecoverFEMSolution(X, *b, x);
// 15. Compute and print the L^2 norm of the error.
{
#ifdef COMPLEX_VERSION
double err = x.real().ComputeL2Error(E_Re);
#else
double err = x.ComputeL2Error(E_Re);
#endif
if (myid == 0)
{
cout << "\n|| E_h - E ||_{L^2} = " << err << '\n' << endl;
}
}
// 16. Save the refined mesh and the solution in parallel. This output can
// be viewed later using GLVis: "glvis -np <np> -m mesh -g sol".
{
ostringstream mesh_name, sol_name;
mesh_name << "mesh." << setfill('0') << setw(6) << myid;
sol_name << "sol." << setfill('0') << setw(6) << myid;
ofstream mesh_ofs(mesh_name.str().c_str());
mesh_ofs.precision(8);
pmesh->Print(mesh_ofs);
ofstream sol_ofs(sol_name.str().c_str());
sol_ofs.precision(8);
#ifdef COMPLEX_VERSION
x.real().Save(sol_ofs);
#else
x.Save(sol_ofs);
#endif
}
// 17. Send the solution by socket to a GLVis server.
if (visualization)
{
char vishost[] = "localhost";
int visport = 19916;
socketstream sol_sock(vishost, visport);
sol_sock << "parallel " << num_procs << " " << myid << "\n";
sol_sock.precision(8);
#ifdef COMPLEX_VERSION
sol_sock << "solution\n" << *pmesh << x.real() << flush;
#else
sol_sock << "solution\n" << *pmesh << x << flush;
#endif
}
// 18. Free the used memory.
delete a;
delete sigma;
delete muinv;
delete b;
delete fespace;
delete fec;
delete pmesh;
MPI_Finalize();
return 0;
}
void E_exact(const Vector &x, Vector &E)
{
if (dim == 3)
{
E(0) = sin(kappa * x(1));
E(1) = sin(kappa * x(2));
E(2) = sin(kappa * x(0));
}
else
{
E(0) = sin(kappa * x(1));
E(1) = sin(kappa * x(0));
if (x.Size() == 3) { E(2) = 0.0; }
}
}
void curlE_exact(const Vector &x, Vector &curl)
{
if (dim == 3)
{
curl(0) = kappa * cos(kappa * x(2));
curl(1) = kappa * cos(kappa * x(0));
curl(2) = kappa * cos(kappa * x(1));
}
else
{
MFEM_VERIFY(false, "");
}
}
void f_exact(const Vector &x, Vector &f)
{
if (dim == 3)
{
// indefinite -m, definite +m
const double c = kappa * kappa;
#ifdef INDEFINITE
const double m = -omega * omega;
#else
const double m = omega * omega;
#endif
f(0) = (c + m) * sin(kappa * x(1));
f(1) = (c + m) * sin(kappa * x(2));
f(2) = (c + m) * sin(kappa * x(0));
}
else
{
f(0) = (1. + kappa * kappa) * sin(kappa * x(1));
f(1) = (1. + kappa * kappa) * sin(kappa * x(0));
if (x.Size() == 3) { f(2) = 0.0; }
}
}
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