569 lines
17 KiB
C++
569 lines
17 KiB
C++
|
|
|
|
#include "mfem.hpp"
|
|
#include <fstream>
|
|
#include <iostream>
|
|
#include "FOSLS.hpp"
|
|
|
|
using namespace std;
|
|
using namespace mfem;
|
|
|
|
void maxwell_solution(const Vector &x, std::vector<complex<double>> & sol,
|
|
std::vector<complex<double>> & curl,
|
|
std::vector<complex<double>> & curl2);
|
|
|
|
void E_exact_re(const Vector &x, Vector &E);
|
|
void H_exact_re(const Vector &x, Vector &H);
|
|
void E_exact_im(const Vector &x, Vector &E);
|
|
void H_exact_im(const Vector &x, Vector &H);
|
|
|
|
void f_exact_re(const Vector &x, Vector &f);
|
|
void g_exact_re(const Vector &x, Vector &g);
|
|
void f_exact_im(const Vector &x, Vector &f);
|
|
void g_exact_im(const Vector &x, Vector &g);
|
|
void plotfield(socketstream &,ParMesh * pmesh,const ParGridFunction & , string &);
|
|
|
|
int dim;
|
|
double omega;
|
|
int exact = 0;
|
|
|
|
// ----------------------------------------------------------------------
|
|
// | | E | H | RHS |
|
|
// ----------------------------------------------------------------------
|
|
// | F | (curlE,curlF)+w^2(E,F) | iw(curlH,F)+iw(H,curF) | -iw(J,F) |
|
|
// | | | | |
|
|
// | G |-iw(E,curlG)-iw(curlE,G) | (curlH,curlG)+w^2(H,G) | -(J,curlG) |
|
|
|
|
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/inline-hex.mesh";
|
|
int order = 1;
|
|
bool visualization = 1;
|
|
int sr = 1;
|
|
int pr = 1;
|
|
double rnum=1.0;
|
|
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(&sr, "-sr", "--serial_ref",
|
|
"Number of serial refinements.");
|
|
args.AddOption(&pr, "-pr", "--parallel_ref",
|
|
"Number of parallel refinements.");
|
|
args.AddOption(&rnum, "-rnum", "--number_of_wavelenths",
|
|
"Number of wavelengths");
|
|
args.AddOption(&exact, "-solution", "--exact_solution",
|
|
"Exact solution : 0-polynomial, 1-plane wave");
|
|
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);
|
|
}
|
|
|
|
omega = 2.0 * M_PI * rnum;
|
|
// omega = rnum;
|
|
Mesh *mesh = new Mesh(mesh_file, 1, 1);
|
|
|
|
dim = mesh->Dimension();
|
|
|
|
MFEM_VERIFY(dim == 3, "only 3D problems supported by this formulation");
|
|
|
|
for (int i = 0; i < sr; i++ )
|
|
{
|
|
mesh->UniformRefinement();
|
|
}
|
|
|
|
ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
|
|
delete mesh;
|
|
|
|
for (int i = 0; i < pr; i++ )
|
|
{
|
|
pmesh->UniformRefinement();
|
|
}
|
|
|
|
FiniteElementCollection *fec = new ND_FECollection(order,dim);
|
|
ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
|
|
|
|
HYPRE_Int size = fespace->GlobalTrueVSize();
|
|
|
|
if (myid == 0)
|
|
{
|
|
cout << "Number of True Dofs = " << size << endl;
|
|
}
|
|
|
|
Array<int> ess_tdof_list;
|
|
Array<int> ess_bdr;
|
|
if (pmesh->bdr_attributes.Size())
|
|
{
|
|
ess_bdr.SetSize(pmesh->bdr_attributes.Max());
|
|
ess_bdr = 1;
|
|
fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
|
|
}
|
|
|
|
|
|
VectorFunctionCoefficient E_ex_re(dim,E_exact_re);
|
|
VectorFunctionCoefficient H_ex_re(dim,H_exact_re);
|
|
VectorFunctionCoefficient E_ex_im(dim,E_exact_im);
|
|
VectorFunctionCoefficient H_ex_im(dim,H_exact_im);
|
|
|
|
VectorFunctionCoefficient f_ex_re(dim,f_exact_re);
|
|
VectorFunctionCoefficient g_ex_re(dim,g_exact_re);
|
|
VectorFunctionCoefficient f_ex_im(dim,f_exact_im);
|
|
VectorFunctionCoefficient g_ex_im(dim,g_exact_im);
|
|
|
|
int n = fespace->GetVSize();
|
|
int N = fespace->GetTrueVSize();
|
|
Array<int> block_offsets(5);
|
|
block_offsets[0] = 0;
|
|
block_offsets[1] = n;
|
|
block_offsets[2] = n;
|
|
block_offsets[3] = n;
|
|
block_offsets[4] = n;
|
|
block_offsets.PartialSum();
|
|
|
|
Array<int> block_trueOffsets(5);
|
|
block_trueOffsets[0] = 0;
|
|
block_trueOffsets[1] = N;
|
|
block_trueOffsets[2] = N;
|
|
block_trueOffsets[3] = N;
|
|
block_trueOffsets[4] = N;
|
|
block_trueOffsets.PartialSum();
|
|
|
|
BlockVector x(block_offsets), rhs(block_offsets);
|
|
BlockVector X(block_trueOffsets), Rhs(block_trueOffsets);
|
|
x = 0.0; rhs = 0.0; X = 0.0; Rhs = 0.0;
|
|
|
|
ParGridFunction E_gf_re, E_gf_im, H_gf_re, H_gf_im;
|
|
|
|
E_gf_re.MakeRef(fespace,x.GetBlock(0)); E_gf_re = 0.0;
|
|
H_gf_re.MakeRef(fespace,x.GetBlock(1)); H_gf_re = 0.0;
|
|
E_gf_im.MakeRef(fespace,x.GetBlock(2)); E_gf_im = 0.0;
|
|
H_gf_im.MakeRef(fespace,x.GetBlock(3)); H_gf_im = 0.0;
|
|
|
|
// E_gf_re.ProjectBdrCoefficientTangent(E_ex_re,ess_bdr);
|
|
// E_gf_im.ProjectBdrCoefficientTangent(E_ex_im,ess_bdr);
|
|
E_gf_re.ProjectCoefficient(E_ex_re);
|
|
E_gf_im.ProjectCoefficient(E_ex_im);
|
|
|
|
// ----------------------------------------------------------------------
|
|
// | | E | H | RHS |
|
|
// ----------------------------------------------------------------------
|
|
// | F | (curlE,curlF)+w^2(E,F) | iw(curlH,F)+iw(H,curF) | -iw(J,F) |
|
|
// | | | | |
|
|
// | G |-iw(E,curlG)-iw(curlE,G) | (curlH,curlG)+w^2(H,G) | -(J,curlG) |
|
|
// ----------------------------------------------------------------------
|
|
|
|
// for convinience we convert the above 2 x 2 blocks to 4 x 4 in order
|
|
// to accomodate complex valued operators
|
|
|
|
// A = (curlE,curlF)+w^2(E,F)
|
|
// B = w(curlH,F)+w(H,curF)
|
|
// b0 = w(J_im,F)
|
|
// b1 = -(J_re,curlG)
|
|
// b2 = -w(J_re,G)
|
|
// b3 = -(J_im,G)
|
|
|
|
// | A 0 0 -B | | E_re | | b0 |
|
|
// | 0 A B 0 | | H_re | = | b1 |
|
|
// | 0 B A 0 | | E_Im | | b2 |
|
|
// |-B 0 0 A | | H_im | | b3 |
|
|
|
|
ConstantCoefficient one(1.0);
|
|
ConstantCoefficient negone(-1.0);
|
|
ConstantCoefficient negomeg(-omega);
|
|
ConstantCoefficient omeg(omega);
|
|
ConstantCoefficient omeg2(omega * omega);
|
|
|
|
|
|
ScalarVectorProductCoefficient wJi(omeg,g_ex_im);
|
|
ScalarVectorProductCoefficient negJr(negone,g_ex_re);
|
|
ScalarVectorProductCoefficient negwJr(negomeg,g_ex_re);
|
|
ScalarVectorProductCoefficient negJi(negone,g_ex_im);
|
|
|
|
|
|
ParLinearForm b0(fespace);
|
|
ParLinearForm b1(fespace);
|
|
ParLinearForm b2(fespace);
|
|
ParLinearForm b3(fespace);
|
|
b0.Update(fespace,rhs.GetBlock(0),0);
|
|
b1.Update(fespace,rhs.GetBlock(1),0);
|
|
b2.Update(fespace,rhs.GetBlock(2),0);
|
|
b3.Update(fespace,rhs.GetBlock(3),0);
|
|
|
|
b0.AddDomainIntegrator(new VectorFEDomainLFIntegrator(wJi));
|
|
b1.AddDomainIntegrator(new VectorFEDomainLFCurlIntegrator(negJr));
|
|
b2.AddDomainIntegrator(new VectorFEDomainLFIntegrator(negwJr));
|
|
b3.AddDomainIntegrator(new VectorFEDomainLFCurlIntegrator(negJi));
|
|
|
|
b0.Assemble();
|
|
b1.Assemble();
|
|
b2.Assemble();
|
|
b3.Assemble();
|
|
|
|
Array2D<HypreParMatrix *> Ah(4,4);
|
|
for (int i = 0; i<4; i++)
|
|
{
|
|
for (int j = 0; j<4; j++)
|
|
{
|
|
Ah[i][j] = nullptr;
|
|
}
|
|
}
|
|
|
|
|
|
ParBilinearForm a00(fespace);
|
|
a00.AddDomainIntegrator(new CurlCurlIntegrator(one));
|
|
a00.AddDomainIntegrator(new VectorFEMassIntegrator(omeg2));
|
|
a00.Assemble();
|
|
a00.EliminateEssentialBC(ess_bdr,x.GetBlock(0),rhs.GetBlock(0),mfem::Operator::DIAG_ONE);
|
|
a00.Finalize();
|
|
Ah[0][0] = a00.ParallelAssemble();
|
|
|
|
ParMixedBilinearForm a03(fespace,fespace);
|
|
a03.AddDomainIntegrator(new MixedVectorCurlIntegrator(negomeg));
|
|
a03.AddDomainIntegrator(new MixedVectorWeakCurlIntegrator(negomeg));
|
|
a03.Assemble();
|
|
a03.EliminateTestDofs(ess_bdr);
|
|
a03.Finalize();
|
|
Ah[0][3] = a03.ParallelAssemble();
|
|
|
|
ParBilinearForm a11(fespace);
|
|
a11.AddDomainIntegrator(new CurlCurlIntegrator(one));
|
|
a11.AddDomainIntegrator(new VectorFEMassIntegrator(omeg2));
|
|
a11.Assemble();
|
|
a11.Finalize();
|
|
Ah[1][1] = a11.ParallelAssemble();
|
|
|
|
ParMixedBilinearForm a12(fespace,fespace);
|
|
a12.AddDomainIntegrator(new MixedVectorCurlIntegrator(omeg));
|
|
a12.AddDomainIntegrator(new MixedVectorWeakCurlIntegrator(omeg));
|
|
a12.Assemble();
|
|
a12.EliminateTrialDofs(ess_bdr,x.GetBlock(2),rhs.GetBlock(1));
|
|
a12.Finalize();
|
|
Ah[1][2] = a12.ParallelAssemble();
|
|
|
|
ParMixedBilinearForm a21(fespace,fespace);
|
|
a21.AddDomainIntegrator(new MixedVectorCurlIntegrator(omeg));
|
|
a21.AddDomainIntegrator(new MixedVectorWeakCurlIntegrator(omeg));
|
|
a21.Assemble();
|
|
a21.EliminateTestDofs(ess_bdr);
|
|
a21.Finalize();
|
|
Ah[2][1] = a21.ParallelAssemble();
|
|
// Ah[2][1] = Ah[1][2]->Transpose();
|
|
// (*Ah[2][1]) *=-1.0;
|
|
|
|
ParBilinearForm a22(fespace);
|
|
a22.AddDomainIntegrator(new CurlCurlIntegrator(one));
|
|
a22.AddDomainIntegrator(new VectorFEMassIntegrator(omeg2));
|
|
a22.Assemble();
|
|
a22.EliminateEssentialBC(ess_bdr,x.GetBlock(2),rhs.GetBlock(2),mfem::Operator::DIAG_ONE);
|
|
a22.Finalize();
|
|
Ah[2][2] = a22.ParallelAssemble();
|
|
|
|
ParMixedBilinearForm a30(fespace,fespace);
|
|
a30.AddDomainIntegrator(new MixedVectorCurlIntegrator(negomeg));
|
|
a30.AddDomainIntegrator(new MixedVectorWeakCurlIntegrator(negomeg));
|
|
a30.Assemble();
|
|
a30.EliminateTrialDofs(ess_bdr,x.GetBlock(0),rhs.GetBlock(3));
|
|
a30.Finalize();
|
|
Ah[3][0] = a30.ParallelAssemble();
|
|
// Ah[3][0] = Ah[0][3]->Transpose();
|
|
// (*Ah[3][0])*=-1.0;
|
|
|
|
ParBilinearForm a33(fespace);
|
|
a33.AddDomainIntegrator(new CurlCurlIntegrator(one));
|
|
a33.AddDomainIntegrator(new VectorFEMassIntegrator(omeg2));
|
|
a33.Assemble();
|
|
a33.Finalize();
|
|
Ah[3][3] = a33.ParallelAssemble();
|
|
// Ah[3][3] = Ah[2][2];
|
|
|
|
// HypreParMatrix * diff = new HypreParMatrix(*Ah[0][3]);
|
|
// *diff += *Ah[3][0];
|
|
|
|
|
|
for (int i = 0; i<4; i++)
|
|
{
|
|
fespace->GetRestrictionMatrix()->Mult(x.GetBlock(i), X.GetBlock(i));
|
|
fespace->GetProlongationMatrix()->MultTranspose(rhs.GetBlock(i),Rhs.GetBlock(i));
|
|
}
|
|
|
|
HypreParMatrix * A = HypreParMatrixFromBlocks(Ah);
|
|
|
|
HypreAMS ams0(*Ah[0][0],fespace);
|
|
HypreAMS ams1(*Ah[1][1],fespace);
|
|
|
|
BlockDiagonalPreconditioner prec(block_trueOffsets);
|
|
prec.SetDiagonalBlock(0,&ams0);
|
|
prec.SetDiagonalBlock(1,&ams1);
|
|
prec.SetDiagonalBlock(2,&ams0);
|
|
prec.SetDiagonalBlock(3,&ams1);
|
|
|
|
StopWatch chrono;
|
|
chrono.Clear();
|
|
chrono.Start();
|
|
CGSolver cg(MPI_COMM_WORLD);
|
|
cg.SetRelTol(1e-6);
|
|
// cg.SetAbsTol(1e-6);
|
|
cg.SetMaxIter(400);
|
|
cg.SetPrintLevel(1);
|
|
cg.SetOperator(*A);
|
|
cg.SetPreconditioner(prec);
|
|
cg.Mult(Rhs, X);
|
|
chrono.Stop();
|
|
double t1 = chrono.RealTime();
|
|
if (myid == 0)
|
|
{
|
|
cout << "PCG time = " << t1 << endl;
|
|
}
|
|
|
|
// {
|
|
// MUMPSSolver mumps;
|
|
// mumps.SetPrintLevel(0);
|
|
// mumps.SetOperator(*A);
|
|
// mumps.Mult(Rhs,X);
|
|
// }
|
|
E_gf_re = 0.0;
|
|
E_gf_im = 0.0;
|
|
H_gf_re = 0.0;
|
|
H_gf_im = 0.0;
|
|
|
|
E_gf_re.Distribute(&(X.GetBlock(0)));
|
|
H_gf_re.Distribute(&(X.GetBlock(1)));
|
|
E_gf_im.Distribute(&(X.GetBlock(2)));
|
|
H_gf_im.Distribute(&(X.GetBlock(3)));
|
|
|
|
double E_re_L2_Error = E_gf_re.ComputeL2Error(E_ex_re);
|
|
double E_im_L2_Error = E_gf_im.ComputeL2Error(E_ex_im);
|
|
double H_re_L2_Error = H_gf_re.ComputeL2Error(H_ex_re);
|
|
double H_im_L2_Error = H_gf_im.ComputeL2Error(H_ex_im);
|
|
|
|
ParGridFunction zero(fespace);
|
|
zero = 0.0;
|
|
double E_re_L2_norm = zero.ComputeL2Error(E_ex_re);
|
|
double E_im_L2_norm = zero.ComputeL2Error(E_ex_im);
|
|
double H_re_L2_norm = zero.ComputeL2Error(H_ex_re);
|
|
double H_im_L2_norm = zero.ComputeL2Error(H_ex_im);
|
|
if (myid == 0)
|
|
{
|
|
cout << "E_re L2 Error = " << E_re_L2_Error/E_re_L2_norm << endl;
|
|
cout << "E_im L2 Error = " << E_im_L2_Error/E_im_L2_norm << endl;
|
|
cout << "H_re L2 Error = " << H_re_L2_Error/H_re_L2_norm << endl;
|
|
cout << "H_im L2 Error = " << H_im_L2_Error/H_im_L2_norm << endl;
|
|
}
|
|
|
|
|
|
if (visualization)
|
|
{
|
|
char vishost[] = "localhost";
|
|
int visport = 19916;
|
|
socketstream sol_sock0(vishost, visport);
|
|
socketstream sol_sock1(vishost, visport);
|
|
socketstream sol_sock2(vishost, visport);
|
|
socketstream sol_sock3(vishost, visport);
|
|
string str0 = "E_re";
|
|
plotfield(sol_sock0,pmesh, E_gf_re,str0);
|
|
string str1 = "E_im";
|
|
plotfield(sol_sock1,pmesh,E_gf_im,str1);
|
|
string str2 = "H_re";
|
|
plotfield(sol_sock2,pmesh,H_gf_re,str2);
|
|
string str3 = "H_im";
|
|
plotfield(sol_sock3,pmesh,H_gf_im,str3);
|
|
|
|
ParGridFunction E_exact_re(fespace);
|
|
ParGridFunction E_exact_im(fespace);
|
|
ParGridFunction H_exact_re(fespace);
|
|
ParGridFunction H_exact_im(fespace);
|
|
E_exact_re.ProjectCoefficient(E_ex_re);
|
|
E_exact_im.ProjectCoefficient(E_ex_im);
|
|
H_exact_re.ProjectCoefficient(H_ex_re);
|
|
H_exact_im.ProjectCoefficient(H_ex_im);
|
|
|
|
socketstream sol_sock_ex0(vishost, visport);
|
|
socketstream sol_sock_ex1(vishost, visport);
|
|
socketstream sol_sock_ex2(vishost, visport);
|
|
socketstream sol_sock_ex3(vishost, visport);
|
|
str0 = "E_exact_re";
|
|
plotfield(sol_sock_ex0,pmesh,E_exact_re,str0);
|
|
str1 = "E_exact_im";
|
|
plotfield(sol_sock_ex1,pmesh,E_exact_im,str1);
|
|
str2 = "H_exact_re";
|
|
plotfield(sol_sock_ex2,pmesh,H_exact_re,str2);
|
|
str3 = "H_exact_im";
|
|
plotfield(sol_sock_ex3,pmesh,H_exact_im,str3);
|
|
}
|
|
|
|
MPI_Finalize();
|
|
return 0;
|
|
}
|
|
|
|
|
|
void maxwell_solution(const Vector &X, std::vector<complex<double>> &sol,
|
|
std::vector<complex<double>> &curl,
|
|
std::vector<complex<double>> &curl2)
|
|
{
|
|
double x = X(0), y = X(1), z = X(2);
|
|
|
|
complex<double> zi(0,1);
|
|
if (exact == 0)
|
|
{
|
|
sol[0] = y*(1.0-y)*z*(1.0-z) + zi * 2.0;
|
|
sol[1] = y*x*(1.0-x)*z*(1.0-z)+ zi * 2.0;
|
|
sol[2] = x*(1.0-x)*y*(1.0-y) + zi * 2.0;
|
|
|
|
curl[0] = (1.0-x)*x*(y*(2.0*z-3.0)+1.0);
|
|
curl[1] = 2.0*(1.0-y)*y*(x-z);
|
|
curl[2] = (z-1.0)*z*(y*(2*x-3)+1.0);
|
|
|
|
curl2[0] = (2.0*x-3.0)*(z-1.0)*z-2.0*y*y+2*y;
|
|
curl2[1] = -2.0*y*(x*x-x+(z-1.0)*z);
|
|
curl2[2] = 2*(x*(1.5-z)+x*x*(z-1.5)-y*y+y);
|
|
}
|
|
else
|
|
{
|
|
complex<double> alpha = zi * omega / sqrt(3);
|
|
sol[0] = exp(alpha*(x+y+z));
|
|
sol[1] = 0.0;
|
|
sol[2] = 0.0;
|
|
|
|
curl[0] = 0.0;
|
|
curl[1] = alpha * sol[0];
|
|
curl[2] = -alpha * sol[0];
|
|
|
|
curl2[0] = -2.0 * alpha * alpha * sol[0];
|
|
curl2[1] = alpha * alpha * sol[0];
|
|
curl2[2] = curl2[1];
|
|
}
|
|
|
|
|
|
// sol[0] = 1.0 + 2.0*zi;
|
|
// sol[1] = 1.0 + 2.0*zi;
|
|
// sol[2] = 1.0 + 2.0*zi;
|
|
// curl[0] = 0.0;
|
|
// curl[1] =0.0;
|
|
// curl[2] =0.0;
|
|
// curl2[0] =0.0;
|
|
// curl2[1] =0.0;
|
|
// curl2[2] =0.0;
|
|
|
|
}
|
|
|
|
void E_exact_re(const Vector &x, Vector &E)
|
|
{
|
|
std::vector<complex<double>>sol(3);
|
|
std::vector<complex<double>>curl(3);
|
|
std::vector<complex<double>>curl2(3);
|
|
maxwell_solution(x,sol,curl,curl2);
|
|
for (int i=0; i<dim; i++)
|
|
{
|
|
E(i) = sol[i].real();
|
|
}
|
|
}
|
|
void H_exact_re(const Vector &x, Vector &H)
|
|
{
|
|
complex<double> zi(0,1);
|
|
std::vector<complex<double>>sol(3);
|
|
std::vector<complex<double>>curl(3);
|
|
std::vector<complex<double>>curl2(3);
|
|
// H = i curlE / w
|
|
maxwell_solution(x,sol,curl,curl2);
|
|
for (int i=0; i<dim; i++)
|
|
{
|
|
H[i] = (zi * curl[i]/omega).real();
|
|
}
|
|
}
|
|
void E_exact_im(const Vector &x, Vector &E)
|
|
{
|
|
std::vector<complex<double>>sol(3);
|
|
std::vector<complex<double>>curl(3);
|
|
std::vector<complex<double>>curl2(3);
|
|
maxwell_solution(x,sol,curl,curl2);
|
|
for (int i=0; i<dim; i++)
|
|
{
|
|
E(i) = sol[i].imag();
|
|
}
|
|
}
|
|
void H_exact_im(const Vector &x, Vector &H)
|
|
{
|
|
complex<double> zi(0,1);
|
|
std::vector<complex<double>>sol(3);
|
|
std::vector<complex<double>>curl(3);
|
|
std::vector<complex<double>>curl2(3);
|
|
// H = i curlE / w
|
|
maxwell_solution(x,sol,curl,curl2);
|
|
for (int i=0; i<dim; i++)
|
|
{
|
|
H[i] = (zi * curl[i]/omega).imag();
|
|
}
|
|
}
|
|
|
|
void f_exact_re(const Vector &x, Vector &f)
|
|
{
|
|
f = 0.0;
|
|
}
|
|
void g_exact_re(const Vector &x, Vector &g)
|
|
{
|
|
// J = i omega E - curl H
|
|
// J = - i / omega (curl curl E - omega * omega E)
|
|
complex<double> zi(0,1);
|
|
std::vector<complex<double>>sol(3);
|
|
std::vector<complex<double>>curl(3);
|
|
std::vector<complex<double>>curl2(3);
|
|
maxwell_solution(x,sol,curl,curl2);
|
|
for (int i=0; i<dim; i++)
|
|
{
|
|
g(i) = (-zi / omega *(curl2[i] - omega * omega * sol[i])).real();
|
|
}
|
|
}
|
|
void f_exact_im(const Vector &x, Vector &f)
|
|
{
|
|
f = 0.0;
|
|
}
|
|
void g_exact_im(const Vector &x, Vector &g)
|
|
{
|
|
// J = i omega E - curl H
|
|
// J = - i / omega (curl curl E - omega * omega E)
|
|
complex<double> zi(0,1);
|
|
std::vector<complex<double>>sol(3);
|
|
std::vector<complex<double>>curl(3);
|
|
std::vector<complex<double>>curl2(3);
|
|
maxwell_solution(x,sol,curl,curl2);
|
|
for (int i=0; i<dim; i++)
|
|
{
|
|
g(i) = (-zi / omega *(curl2[i] - omega * omega * sol[i])).imag();
|
|
}
|
|
}
|
|
|
|
|
|
void plotfield(socketstream & socket, ParMesh * pmesh, const ParGridFunction & pgf, string & title )
|
|
{
|
|
int num_procs, myid;
|
|
MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
|
|
MPI_Comm_rank(MPI_COMM_WORLD, &myid);
|
|
ostringstream oss;
|
|
oss << title;
|
|
socket << "parallel " << num_procs << " " << myid << "\n";
|
|
socket.precision(8);
|
|
socket << "solution\n" << *pmesh << pgf
|
|
<< "window_title '" << oss.str() << "'" << flush;
|
|
}
|