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b901ee0fa63fa54ac199aaaf11b80b1bd6ecd402
mfem/examples/ex1p_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.
double E_exact(const Vector &);
void gradE_exact(const Vector &, Vector &);
double f_exact(const Vector &);
double freq = 1.0, kappa;
int dim;
#define COMPLEX_VERSION
#define NEUMANN
const double omega = 1.4;
const double eps = 1.0e-8;
/// General product operator: x -> A(x)+B(x)
class SumOperator : public Operator
{
const Operator *A, *B;
bool ownA, ownB;
mutable Vector z, w;
double cA, cB;
public:
SumOperator(const Operator *A_, const Operator *B_,
bool ownA_, bool ownB_, double cA_, double cB_)
: Operator(A_->Height(), B_->Width()),
A(A_), B(B_), ownA(ownA_), ownB(ownB_), z(A_->Height()), w(A_->Width()),
cA(cA_), cB(cB_)
{
MFEM_VERIFY(A->Width() == B->Width() && A->Height() == B->Height(),
"incompatible Operators: A->Width() = " << A->Width()
<< ", B->Height() = " << B->Height());
z.UseDevice(true);
w.UseDevice(true);
}
~SumOperator()
{
if (ownA) { delete A; }
if (ownB) { delete B; }
}
virtual void Mult(const Vector &x, Vector &y) const
{ B->Mult(x, z); A->Mult(x, y); y *= cA; z *= cB; y += z;}
virtual void MultTranspose(const Vector &x, Vector &y) const
{ B->MultTranspose(x, w); A->MultTranspose(x, y); y *= cA; w *= cB; y += w;}
};
class Complex_PMHSS : public Solver
{
public:
Complex_PMHSS(Operator *Re, Operator *Im, Solver *prec_Re, Solver *prec_Im,
double a_)
: Solver(2*Re->Height()), a(a_), A(Re, Im, false, false),
A_Re(Re, NULL, false, false),
A_Im(Im, NULL, false, false), u(2*Re->Height()), rhs(2*Re->Height()),
n(Re->Height())
{
MFEM_VERIFY(Re->Height() == Im->Height() && Re->Height() == Re->Width() &&
Im->Height() == Im->Width(), "");
MFEM_VERIFY(this->Height() == A.Height(), "");
// Create CG solver for real operator aV + A_Re in complex space.
V = useIdentityV ? (Operator*) new IdentityOperator(this->Height()) :
(Operator*) &A_Re;
// In the case V = A_Re, it is faster to use a scaled operator than a SumOperator
Operator *sumOpRe = useIdentityV ? (Operator*) new SumOperator(V, &A_Re, false,
false, a, 1.0)
: (Operator*) new ScaledOperator(&A_Re, a + 1.0);
SumOperator *sumOpIm = new SumOperator(V, &A_Im, false, false, a, 1.0);
CGSolver *cg = new CGSolver(MPI_COMM_WORLD);
cg->SetRelTol(1e-6);
cg->SetMaxIter(1000);
cg->SetPrintLevel(0);
cg->SetOperator(*sumOpRe);
cg->SetPreconditioner(*prec_Re);
cg->iterative_mode = false;
SRe = cg;
CGSolver *cgi = new CGSolver(MPI_COMM_WORLD);
cgi->SetRelTol(1e-6);
cgi->SetMaxIter(1000);
cgi->SetPrintLevel(0);
cgi->SetOperator(*sumOpIm);
if (prec_Im && useIdentityV) { cgi->SetPreconditioner(*prec_Im); }
if (!useIdentityV) { cgi->SetPreconditioner(*prec_Re); }
cgi->iterative_mode = false;
/*
// For negative definite imaginary part, but then PMHSS does not work?
MINRESSolver *cgi = new MINRESSolver(MPI_COMM_WORLD);
cgi->SetRelTol(1e-12);
cgi->SetMaxIter(1000);
cgi->SetPrintLevel(0);
cgi->SetOperator(*sumOpIm);
if (prec_Im) cgi->SetPreconditioner(*prec_Im);
*/
SIm = cgi;
}
void SetOperator(const Operator &op)
{
MFEM_VERIFY(false, "Don't call SetOperator");
}
void ComputeResidual(const Vector &b, const Vector &sol, Vector &res) const
{
A.Mult(sol, res);
res -= b;
}
void Mult(const Vector &x, Vector &y) const
{
MFEM_VERIFY(x.Size() == Height() && y.Size() == Height(), "");
const double initNorm = x.Norml2();
mfem::out << "MHSS RHS norm " << initNorm << '\n';
// With V = I, use modified HSS (MHSS) from Bai, Benzi, Chen 2010.
y = 0.0;
for (int it=0; it<maxiter; ++it)
{
// Solve (aI + Re) u = (aI - i Im) y + x
if (it == 0)
{
// Optimize the first iteration, when the initial guess is y=0.
SRe->Mult(x, u);
}
else
{
A_Im.Mult(y, u); // u = Im y
// Set rhs = -i Im y = -i u
for (int j=0; j<n; ++j)
{
rhs[j] = u[n+j];
rhs[n+j] = -u[j];
}
rhs += x;
V->Mult(y, u);
rhs.Add(a, u);
SRe->Mult(rhs, u);
}
// Solve (aI + Im) y = (aI + i Re) u - i x
A_Re.Mult(u, y); // y = Re u
// Set rhs = i (Re u - x) = i (y - x)
for (int j=0; j<n; ++j)
{
rhs[j] = -(y[n+j] - x[n+j]);
rhs[n+j] = y[j] - x[j];
}
if (useIdentityV)
{
//V->Mult(u, y);
//rhs.Add(a, y);
rhs.Add(a, u);
}
else
{
// Using V = A_Re
rhs.Add(a, y);
}
SIm->Mult(rhs, y);
ComputeResidual(x, y, rhs);
const double resNorm = rhs.Norml2();
mfem::out << "MHSS iter " << it << " residual norm " << resNorm << '\n';
if (resNorm / initNorm < tol)
{
mfem::out << "MHSS converged\n";
break;
}
}
}
private:
const double a;
const int maxiter = 1;
ComplexOperator A, A_Re, A_Im;
mutable Vector u, rhs;
const int n;
const double tol = 1.0e-8;
const bool useIdentityV = false;
Operator *V = NULL;
Solver *SRe = NULL;
Solver *SIm = NULL;
};
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 H1_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;
#ifndef NEUMANN
if (pmesh->bdr_attributes.Size())
{
Array<int> ess_bdr(pmesh->bdr_attributes.Max());
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
FunctionCoefficient E_coef(E_exact);
VectorFunctionCoefficient grad_E(sdim, gradE_exact);
ProductCoefficient omegaE(imscale, E_coef);
// 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.
FunctionCoefficient f(f_exact);
#ifdef COMPLEX_VERSION
ParComplexLinearForm *b = new ParComplexLinearForm(fespace);
b->AddDomainIntegrator(new DomainLFIntegrator(f), NULL);
#ifdef NEUMANN
b->AddBoundaryIntegrator(NULL, new BoundaryNormalLFIntegrator(grad_E));
#endif
b->AddBoundaryIntegrator(NULL, new BoundaryLFIntegrator(omegaE)); // im part
#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;
ConstantCoefficient E_im(0.0);
//x.ProjectBdrCoefficientTangent(E_Re, E_Im, ess_bdr);
x.ProjectCoefficient(E_coef, E_im);
#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);
Coefficient *epscoef = new ConstantCoefficient(eps);
Coefficient *imabs = new ConstantCoefficient(fabs(imscale)); // im part
#ifdef COMPLEX_VERSION
// Complex version
ParSesquilinearForm *a = new ParSesquilinearForm(fespace);
if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
a->AddDomainIntegrator(new DiffusionIntegrator(*muinv), NULL);
a->AddDomainIntegrator(new MassIntegrator(*epscoef), NULL);
a->AddBoundaryIntegrator(NULL, new MassIntegrator(*im)); // im part
#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 DiffusionIntegrator(*muinv));
a_Re.AddDomainIntegrator(new MassIntegrator(*epscoef));
if (pa) { 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 MassIntegrator(*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;
}
HypreBoomerAMG amg(*A_Re.As<HypreParMatrix>());
#ifdef COMPLEX_VERSION
BlockDiagonalPreconditioner BlockDP(offsets);
BlockDP.SetDiagonalBlock(0, &amg);
BlockDP.SetDiagonalBlock(1, &amg);
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);
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);
//gmres.SetPreconditioner(PMHSS);
gmres.SetPreconditioner(PMHSSgmres);
#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_coef);
#else
double err = x.ComputeL2Error(E_coef);
#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 muinv;
delete b;
delete fespace;
delete fec;
delete pmesh;
MPI_Finalize();
return 0;
}
#define VERSION_COS
double E_exact(const Vector &x)
{
if (dim == 3)
{
#ifdef VERSION_COS
return cos(kappa * x(0)) * cos(kappa * x(1)) * cos(kappa * x(2));
#else
return sin(kappa * x(0)) * sin(kappa * x(1)) * sin(kappa * x(2));
#endif
}
else
{
return 0.0;
}
}
void gradE_exact(const Vector &x, Vector &grad)
{
if (dim == 3)
{
#ifdef VERSION_COS
grad(0) = -kappa * sin(kappa * x(0)) * cos(kappa * x(1)) * cos(kappa * x(2));
grad(1) = -kappa * sin(kappa * x(1)) * cos(kappa * x(0)) * cos(kappa * x(2));
grad(2) = -kappa * sin(kappa * x(2)) * cos(kappa * x(0)) * cos(kappa * x(1));
#else
grad(0) = kappa * cos(kappa * x(0)) * sin(kappa * x(1)) * sin(kappa * x(2));
grad(1) = kappa * cos(kappa * x(1)) * sin(kappa * x(0)) * sin(kappa * x(2));
grad(2) = kappa * cos(kappa * x(2)) * sin(kappa * x(0)) * sin(kappa * x(1));
#endif
}
else
{
MFEM_VERIFY(false, "");
}
}
// (grad u, grad v) + eps (u, v) = <grad u . n, v> - (div grad u, v) + eps (u, v)
double f_exact(const Vector &x)
{
if (dim == 3)
{
const double c = 3.0 * kappa * kappa;
#ifdef VERSION_COS
return (eps + c) * cos(kappa * x(0)) * cos(kappa * x(1)) * cos(kappa * x(2));
#else
return (eps + c) * sin(kappa * x(0)) * sin(kappa * x(1)) * sin(kappa * x(2));
#endif
}
else
{
return 0.0;
}
}
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