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mfem/examples/ex4D_DivSkew.cpp
T
aschaf b44ba89cc1 Fixed one example.
2019-10-21 14:24:32 +02:00

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// MFEM Example 3 - Parallel Version
//
// Compile with: make ex3p
//
// Sample runs: mpirun -np 4 ex3p -m ../data/star.mesh
// mpirun -np 4 ex3p -m ../data/square-disc.mesh -o 2
// mpirun -np 4 ex3p -m ../data/beam-tet.mesh
// mpirun -np 4 ex3p -m ../data/beam-hex.mesh
// mpirun -np 4 ex3p -m ../data/escher.mesh
// mpirun -np 4 ex3p -m ../data/fichera.mesh
// mpirun -np 4 ex3p -m ../data/fichera-q2.vtk
// mpirun -np 4 ex3p -m ../data/fichera-q3.mesh
// mpirun -np 4 ex3p -m ../data/square-disc-nurbs.mesh
// mpirun -np 4 ex3p -m ../data/beam-hex-nurbs.mesh
// mpirun -np 4 ex3p -m ../data/amr-quad.mesh -o 2
// mpirun -np 4 ex3p -m ../data/amr-hex.mesh
// mpirun -np 4 ex3p -m ../data/star-surf.mesh -o 2
// mpirun -np 4 ex3p -m ../data/mobius-strip.mesh -o 2 -f 0.1
// mpirun -np 4 ex3p -m ../data/klein-bottle.mesh -o 2 -f 0.1
//
// Description: This example code solves a simple electromagnetic diffusion
// problem corresponding to the second order definite Maxwell
// equation curl curl E + E = f with boundary condition
// E x n = <given tangential field>. Here, we use a given exact
// solution E and compute the corresponding r.h.s. f.
// We discretize with Nedelec finite elements in 2D or 3D.
//
// The example demonstrates the use of H(curl) finite element
// spaces with the curl-curl and the (vector finite element) mass
// bilinear form, as well as the computation of discretization
// error when the exact solution is known. Static condensation is
// also illustrated.
//
// We recommend viewing examples 1-2 before viewing this example.
#include "mfem.hpp"
#include <fstream>
#include <iostream>
#include "./spe10_coeff.cpp"
using namespace std;
using namespace mfem;
int* LoadIterations(int NRows, int NCol)
{
ifstream in("iter_DivSkew.txt");
//initialize
int *iters = new int[NCol*NRows];
for (int col = 0; col < NCol; col++)
{
for (int row = 0; row < NRows; row++)
{
iters[row*NCol+col] = -1;
}
}
if (!in)
{
cout << "Cannot open file.\n";
return iters;
}
for (int row = 0; row < NRows; row++)
for (int col = 0; col < NCol; col++)
{
if (in.eof())
{
in.close();
return iters;
}
in >> iters[row*NCol+col];
}
in.close();
return iters;
}
void putIterationsInArray(int iter, int row, int col, int NCol, int* iters)
{
iters[row*NCol+col] = iter;
}
void WriteIterations(int *iters, int NRows, int NCol)
{
ofstream out;
out.open("iter_DivSkew.txt",fstream::out);
if (!out)
{
cout << "Cannot open file.\n";
delete[] iters;
return;
}
for (int row = 0; row < NRows; row++)
{
for (int col = 0; col < NCol; col++)
{
out << iters[row*NCol+col] << "\t";
}
out << endl;
}
out.close();
delete[] iters;
}
// Exact solution, E, and r.h.s., f. See below for implementation.
void E_exact_vec(const Vector &x, Vector &E);
void E_exact(const Vector &, DenseMatrix &);
void f_exact(const Vector &, DenseMatrix &);
class DivSkew4dPrec : public Solver
{
private:
HypreParMatrix *A;
ParFiniteElementSpace *fespace;
Coefficient *alpha_, *beta_;
//kernel operators
HypreParMatrix *P_d_HCurl_HDivSkew;
HypreParMatrix *P_H1_HCurl;
HypreParMatrix *H1_KernelMat;
HypreBoomerAMG *amgH1_Kernel;
//"image" operators
HypreParMatrix *P_H1_HDivSkew;
HypreParMatrix *H1_ImageMat;
HypreBoomerAMG *amgH1_Image;
HypreParMatrix *HCurlMat;
HypreSmoother * smootherDivSkew;
HypreSmoother * smootherCurl;
CGSolver *pcgKernel;
CGSolver *pcgImage;
Vector *f;
Vector *fKernel, *uKernel;
Vector *fImage, *uImage;
Vector *fCurl, *uCurl;
bool exactSolves;
FiniteElementCollection* fecHCurlKernel;
ParFiniteElementSpace *HCurlKernelFESpace;
public:
~DivSkew4dPrec()
{
delete pcgImage, pcgKernel;
delete f, fKernel, uKernel, fImage, uImage, fCurl, uCurl;
delete smootherCurl, HCurlMat;
delete P_d_HCurl_HDivSkew, P_H1_HDivSkew, P_H1_HCurl;
delete amgH1_Image, H1_ImageMat;
delete amgH1_Kernel, H1_KernelMat;
delete smootherDivSkew;
delete HCurlKernelFESpace, fecHCurlKernel;
}
DivSkew4dPrec(HypreParMatrix *AUser, ParFiniteElementSpace *fespaceUser,
Coefficient *alpha, Coefficient *beta,
const Array<int> &essBnd, int orderKernel=1, bool exactSolvesUser=false)
{
A = AUser;
fespace = fespaceUser;
alpha_ = alpha;
beta_ = beta;
ParMesh *pmesh = fespace->GetParMesh();
int dim = pmesh->Dimension();
exactSolves = exactSolvesUser;
int orderIm=1; //H1 --> H(divSkew)
int orderKer=orderKernel; //curl V --> H(divSkew)
smootherDivSkew = new HypreSmoother(*A, 16, 3);
Array<int> HDivSkew_essDof(fespace->GetVSize()); HDivSkew_essDof = 0;
fespace->GetEssentialVDofs(essBnd, HDivSkew_essDof);
//setup the H1 FESpace for the kernel
FiniteElementCollection* fecH1Kernel = new H1_FECollection(orderKer, 4);
ParFiniteElementSpace *H1KernelFESpace = new ParFiniteElementSpace(pmesh,
fecH1Kernel, dim, Ordering::byVDIM);
Array<int> H1Kernel_essDof(H1KernelFESpace->GetVSize()); H1Kernel_essDof = 0;
H1KernelFESpace->GetEssentialVDofs(essBnd, H1Kernel_essDof);
//setup the H(curl) FESpace for the kernel
if (orderKer==1) { fecHCurlKernel = new ND1_4DFECollection; }
else { fecHCurlKernel = new ND2_4DFECollection; }
HCurlKernelFESpace = new ParFiniteElementSpace(pmesh,
fecHCurlKernel);
Array<int> HCurlKernel_essDof(HCurlKernelFESpace->GetVSize());
HCurlKernel_essDof = 0;
HCurlKernelFESpace->GetEssentialVDofs(essBnd, HCurlKernel_essDof);
//setup the FESpace for the H1 injection
FiniteElementCollection* fecH1Vec;
if (orderIm==1) { fecH1Vec = new LinearFECollection; }
else { fecH1Vec = new QuadraticFECollection; }
ParFiniteElementSpace *H1_ImageFESpace = new ParFiniteElementSpace(pmesh,
fecH1Vec, 6, Ordering::byVDIM);
Array<int> H1Image_essDof(H1_ImageFESpace->GetVSize()); H1Image_essDof = 0;
H1_ImageFESpace->GetEssentialVDofs(essBnd, H1Image_essDof);
//setup the H1 preconditioner for the kernel
ParBilinearForm* H1Varf = new ParBilinearForm(H1KernelFESpace);
H1Varf->AddDomainIntegrator(new VectorDiffusionIntegrator(*beta_));
// H1Varf->AddDomainIntegrator(new VectorMassIntegrator);
H1Varf->Assemble();
H1Varf->Finalize();
SparseMatrix &matH1(H1Varf->SpMat());
for (int dof = 0; dof < H1Kernel_essDof.Size(); dof++)
if (H1Kernel_essDof[dof] < 0)
{
matH1.EliminateRowCol(dof);
}
H1_KernelMat = H1Varf->ParallelAssemble();
delete H1Varf;
amgH1_Kernel = new HypreBoomerAMG(*H1_KernelMat);
amgH1_Kernel->SetSystemsOptions(dim);
amgH1_Kernel->SetPrintLevel(0);
//setup the H1 preconditioner for the image
ParBilinearForm* H1VecVarf = new ParBilinearForm(H1_ImageFESpace);
VectorDiffusionIntegrator *alpha_integ = new VectorDiffusionIntegrator(*alpha_);
alpha_integ->SetVDim(6);
H1VecVarf->AddDomainIntegrator(alpha_integ);
VectorMassIntegrator *beta_integ = new VectorMassIntegrator(*beta);
beta_integ->SetVDim(6);
H1VecVarf->AddDomainIntegrator(beta_integ);
H1VecVarf->Assemble();
H1VecVarf->Finalize();
SparseMatrix &matH1Vec(H1VecVarf->SpMat());
for (int dof=0; dof<H1Image_essDof.Size(); dof++) if (H1Image_essDof[dof]<0) { matH1Vec.EliminateRowCol(dof); }
H1_ImageMat = H1VecVarf->ParallelAssemble();
delete H1VecVarf;
amgH1_Image = new HypreBoomerAMG(*H1_ImageMat);
amgH1_Image->SetSystemsOptions(6);
amgH1_Image->SetPrintLevel(0);
//setup the injection of H1 into H(curl)
ParDiscreteLinearOperator *disInterpol = new ParDiscreteLinearOperator(
H1KernelFESpace, HCurlKernelFESpace);
disInterpol->AddDomainInterpolator(new IdentityInterpolator);
disInterpol->Assemble();
disInterpol->Finalize();
SparseMatrix* smatID = &(disInterpol->SpMat());
smatID->EliminateCols(H1Kernel_essDof);
for (int dof=0; dof<HCurlKernel_essDof.Size();
dof++) if (HCurlKernel_essDof[dof]<0) { smatID->EliminateRow(dof); }
P_H1_HCurl = disInterpol->ParallelAssemble();
delete disInterpol;
//setup the injection of H1 into H(DivSkew)
ParDiscreteLinearOperator *disInterpolIm = new ParDiscreteLinearOperator(
H1_ImageFESpace, fespace);
disInterpolIm->AddDomainInterpolator(new IdentityInterpolator);
disInterpolIm->Assemble();
disInterpolIm->Finalize();
SparseMatrix* smatIDIm = &(disInterpolIm->SpMat());
smatIDIm->EliminateCols(H1Image_essDof);
for (int dof=0; dof<HDivSkew_essDof.Size(); dof++) if (HDivSkew_essDof[dof]<0) { smatIDIm->EliminateRow(dof); }
P_H1_HDivSkew = disInterpolIm->ParallelAssemble();
delete disInterpolIm;
//setup the injection of the curl(H(curl)) into H(DivSkew)
ParDiscreteLinearOperator *disCurl = new ParDiscreteLinearOperator(
HCurlKernelFESpace, fespace);
disCurl->AddDomainInterpolator(new CurlInterpolator);
disCurl->Assemble();
disCurl->Finalize();
SparseMatrix* smatCurl = &(disCurl->SpMat());
smatCurl->EliminateCols(HCurlKernel_essDof);
for (int dof=0; dof<HDivSkew_essDof.Size(); dof++) if (HDivSkew_essDof[dof]<0) { smatCurl->EliminateRow(dof); }
P_d_HCurl_HDivSkew = disCurl->ParallelAssemble();
delete disCurl;
//setup the smoother for H(curl)
// Coefficient *massC = new ConstantCoefficient(1.0);
// Coefficient *CurlCurlC = new ConstantCoefficient(1.0);
ParBilinearForm *a_HCurl = new ParBilinearForm(HCurlKernelFESpace);
a_HCurl->AddDomainIntegrator(new CurlCurlIntegrator(*beta_));
// a_HCurl->AddDomainIntegrator(new CurlCurlIntegrator(*CurlCurlC));
// a_HCurl->AddDomainIntegrator(new VectorFEMassIntegrator(*massC));
a_HCurl->Assemble();
a_HCurl->Finalize();
SparseMatrix &matHCurl(a_HCurl->SpMat());
for (int dof=0; dof<HCurlKernel_essDof.Size();
dof++) if (HCurlKernel_essDof[dof]<0) { matHCurl.EliminateRowCol(dof); }
HCurlMat = a_HCurl->ParallelAssemble();
delete a_HCurl;
smootherCurl = new HypreSmoother(*HCurlMat, 16, 3);
f = new Vector(fespace->GetTrueVSize());
fKernel = new Vector(H1KernelFESpace->GetTrueVSize());
uKernel = new Vector(H1KernelFESpace->GetTrueVSize());
fImage = new Vector(H1_ImageFESpace->GetTrueVSize());
uImage = new Vector(H1_ImageFESpace->GetTrueVSize());
fCurl = new Vector(HCurlKernelFESpace->GetTrueVSize());
uCurl = new Vector(HCurlKernelFESpace->GetTrueVSize());
amgH1_Kernel->Mult(*fKernel, *uKernel);
amgH1_Image->Mult(*fImage, *uImage);
pcgKernel = new CGSolver(MPI_COMM_WORLD);
pcgKernel->SetOperator(*H1_KernelMat);
pcgKernel->SetPreconditioner(*amgH1_Kernel);
pcgKernel->SetRelTol(1e-16);
pcgKernel->SetMaxIter(100000000);
pcgKernel->SetPrintLevel(-2);
pcgImage = new CGSolver(MPI_COMM_WORLD);
pcgImage->SetOperator(*H1_ImageMat);
pcgImage->SetPreconditioner(*amgH1_Image);
pcgImage->SetRelTol(1e-16);
pcgImage->SetMaxIter(100000000);
pcgImage->SetPrintLevel(-2);
delete H1KernelFESpace, fecH1Kernel;
delete H1_ImageFESpace, fecH1Vec;
}
void setExactSolve(bool exSol)
{
exactSolves = exSol;
}
virtual void Mult(const Vector &x, Vector &y) const
{
smootherDivSkew->Mult(x,y);
P_H1_HDivSkew->MultTranspose(x,*fImage);
*uImage = 0.0;
if (exactSolves) { pcgImage->Mult(*fImage, *uImage); }
else { amgH1_Image->Mult(*fImage, *uImage); }
P_H1_HDivSkew->Mult(1.0, *uImage, 1.0, y);
*uCurl = 0.0;
P_d_HCurl_HDivSkew->MultTranspose(x,*fCurl);
smootherCurl->Mult(*fCurl, *uCurl);
P_H1_HCurl->MultTranspose(*fCurl,*fKernel);
*uKernel = 0.0;
if (exactSolves) { pcgKernel->Mult(*fKernel, *uKernel); }
else { amgH1_Kernel->Mult(*fKernel, *uKernel); }
P_H1_HCurl->Mult(1.0, *uKernel, 1.0, *uCurl);
P_d_HCurl_HDivSkew->Mult(1.0, *uCurl, 1.0, y);
}
virtual void SetOperator(const Operator &op) {};
};
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);
bool verbose = (myid==0);
// 2. Parse command-line options.
const char *mesh_file = "../data/cube4d_96.MFEM";
int order = 1;
bool set_bc = true;
bool static_cond = false;
bool visualization = 1;
int sequ_ref_levels = 0;
int par_ref_levels = 0;
double tol = 1e-6;
double coeffWeight = 1.0;
bool exactH1Solver = false;
bool spe10Coeff = false;
bool standardCG = true;
int NExpo = 8;
int weightStart = -NExpo;
int weightEnd = NExpo;
OptionsParser args(argc, argv);
args.AddOption(&mesh_file, "-m", "--mesh",
"Mesh file to use.");
args.AddOption(&sequ_ref_levels, "-sr", "--seqrefinement",
"Number of sequential refinement steps.");
args.AddOption(&par_ref_levels, "-pr", "--parrefinement",
"Number of parallel refinement steps.");
args.AddOption(&order, "-o", "--order",
"Polynomial order of the finite element space.");
args.AddOption(&set_bc, "-bc", "--impose-bc", "-no-bc", "--dont-impose-bc",
"Impose or not essential boundary conditions.");
args.AddOption(&tol, "-tol", "--tol",
"A parameter.");
args.AddOption(&coeffWeight, "-c", "--coeffMass",
"the weight for the mass term.");
args.AddOption(&exactH1Solver, "-exH1Sol", "--exactH1Solver", "-H1prec",
"--H1preconditioner",
"Use exact H1 solvers for the preconditioner.");
args.AddOption(&spe10Coeff, "-spe10", "--useSPE10Coeff", "-constCoeff",
"--constCoeff",
"Switch between the coefficients for the mass bilinear form.");
args.AddOption(&standardCG, "-sCG", "--stdCG", "-rCG", "--resCG",
"Switch between standard PCG or recompute residuals in every step and use the residuals itself for the stopping criteria.");
args.AddOption(&weightStart, "-ws", "--weightStart",
"the exponent for the starting weight (for the mass term).");
args.AddOption(&weightEnd, "-we", "--weightEnd",
"the exponent for the weight at the end (for the mass term).");
args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
"--no-visualization",
"Enable or disable GLVis visualization.");
args.Parse();
if (!args.Good())
{
args.PrintUsage(cout);
return 1;
}
if (verbose) { args.PrintOptions(cout); }
Mesh *mesh;
ifstream imesh(mesh_file);
if (!imesh)
{
cerr << "\nCan not open mesh file: " << mesh_file << '\n' << endl;
return 2;
}
mesh = new Mesh(imesh, 1, 1);
imesh.close();
int dim = mesh->Dimension();
int sdim = mesh->SpaceDimension();
if (dim !=4 || sdim != 4)
{
MPI_Finalize();
return 0;
}
for (int i=0; i<sequ_ref_levels; i++) { mesh->UniformRefinement(); }
if (verbose) { mesh->PrintCharacteristics(); }
if (verbose) { cout << "now we partition the mesh..." << endl << endl; }
ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
delete mesh;
for (int i=0; i<par_ref_levels; i++) { pmesh->UniformRefinement(); }
pmesh->PrintInfo(std::cout);
if (verbose) { cout << endl; }
// 6. Define a parallel finite element space on the parallel mesh. Here we
// use the Nedelec finite elements of the specified order.
FiniteElementCollection *fec;
if (order==1) { fec = new DivSkew1_4DFECollection; }
// else fec = new F2K1_4DFECollection;
ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
fespace->SetUpdateOperatorType(Operator::Hypre_ParCSR);
HYPRE_Int size = fespace->GlobalTrueVSize();
// 7. 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(pmesh->bdr_attributes.Max());
ess_bdr = set_bc ? 1 : 0;
if (pmesh->bdr_attributes.Size())
{
fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
}
if (myid == 0)
{
cout << "Number of finite element unknowns: " << size << endl;
}
// 8. 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.
MatrixFunctionCoefficient f(sdim, f_exact);
MatrixFunctionCoefficient solMat(sdim, E_exact);
VectorFunctionCoefficient solVec(6, E_exact_vec);
// 9. 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);
for (int expo=weightStart; expo<=weightEnd; expo++)
{
double weight = pow(10.0,expo);
x.ProjectCoefficient(solVec);
ParLinearForm *b = new ParLinearForm(fespace);
b->AddDomainIntegrator(new MatFEDomainLFIntegrator(f));
b->Assemble();
// cout << x << endl;
// x = 0.0;
// 10. 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.
// std::string permFile = "spe_perm.dat";
// InversePermeabilityFunction::ReadPermeabilityFile(permFile, MPI_COMM_WORLD);
Coefficient *alpha = new ConstantCoefficient(1.0);
Coefficient *beta;
// if(spe10Coeff) beta = new FunctionCoefficient(InversePermeabilityFunction::Norm2Permeability);
// else
beta = new ConstantCoefficient(weight);
ParBilinearForm *a = new ParBilinearForm(fespace);
a->AddDomainIntegrator(new DivSkewDivSkewIntegrator(*alpha));
a->AddDomainIntegrator(new VectorFE_DivSkewMassIntegrator(*beta));
// 11. 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();
HypreParMatrix A;
Vector B, X;
a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
if (myid == 0)
{
cout << "Size of linear system: " << A.GetGlobalNumRows() << endl;
}
//Define the preconditioner
if (myid == 0) { cout << "Set up the preconditioner" << endl; }
Solver *prec;
if (dim==4) { prec = new DivSkew4dPrec(&A, fespace, alpha, beta, ess_bdr, order, exactH1Solver); }
IterativeSolver *pcg = new CGSolver(MPI_COMM_WORLD);
pcg->SetOperator(A);
pcg->SetRelTol(tol);
pcg->SetMaxIter(500);
pcg->SetPrintLevel(1);
pcg->SetPreconditioner(*prec);
pcg->Mult(B, X);
delete prec;
int iter = pcg->GetNumIterations();
if (myid==0)
{
cout << "Weigth: " << weight << " " << iter << endl;
int *iters = LoadIterations(10, 2*NExpo+1);
putIterationsInArray(iter, sequ_ref_levels+par_ref_levels, expo+NExpo,
2*NExpo+1, iters);
WriteIterations(iters, 10, 2*NExpo+1);
}
// 13. Recover the parallel grid function corresponding to X. This is the
// local finite element solution on each processor.
a->RecoverFEMSolution(X, *b, x);
// 14. Compute and print the L^2 norm of the error.
{
double error = 0.0;
for (int i = 0; i < fespace->GetNE(); i++)
{
const FiniteElement* fe = fespace->GetFE(i);
int fdof = fe->GetDof();
ElementTransformation* transf = fespace->GetElementTransformation(i);
DenseMatrix shape(fdof,dim*dim);
int intorder = 2*fe->GetOrder() + 1; // <----------
const IntegrationRule *ir;
ir = &(IntRules.Get(fe->GetGeomType(), intorder));
Vector elSol(dim*dim);
DenseMatrix elSolMat(dim,dim);
DenseMatrix exactSol(dim,dim);
Vector exactSolVec(dim*dim);
Array<int> vdofs;
fespace->GetElementVDofs(i, vdofs);
for (int j = 0; j < ir->GetNPoints(); j++)
{
const IntegrationPoint &ip = ir->IntPoint(j);
transf->SetIntPoint(&ip);
fe->CalcVShape(*transf, shape);
elSol = 0.0;
for (int k = 0; k < fdof; k++)
{
if (vdofs[k] >= 0)
{
for (int l=0; l<dim*dim; l++) { elSol(l) += shape(k,l)*x(vdofs[k]); }
}
else
{
for (int l=0; l<dim*dim; l++) { elSol(l) -= shape(k,l)*x(-1-vdofs[k]); }
}
}
for (int k=0; k<dim; k++)
for (int l=0; l<dim; l++)
{
elSolMat(k,l) = elSol(dim*k+l);
}
solMat.Eval(exactSol,*transf, ip);
for (int k=0; k<dim; k++)
for (int l=0; l<dim; l++)
{
exactSolVec(dim*k+l) = exactSol(k,l);
}
elSol.Add(-1.0, exactSolVec);
error += ip.weight * fabs(transf->Weight()) * (elSol * elSol);
}
}
double globalError = 0.0;
MPI_Allreduce(&error, &globalError, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
if (myid==0) { std::cout << "L2 error: " << sqrt(globalError) << std::endl; }
}
delete pcg;
delete a;
delete alpha;
delete beta;
delete b;
}
// 17. Free the used memory.
delete fespace;
delete fec;
delete pmesh;
MPI_Finalize();
return 0;
}
void E_exact_vec(const Vector &x, Vector &E)
{
int dim = x.Size();
if (dim==4)
{
E.SetSize(6);
double s0 = sin(M_PI*x(0)), s1 = sin(M_PI*x(1)), s2 = sin(M_PI*x(2)),
s3 = sin(M_PI*x(3));
double c0 = cos(M_PI*x(0)), c1 = cos(M_PI*x(1)), c2 = cos(M_PI*x(2)),
c3 = cos(M_PI*x(3));
E(0) = c0*c1*s2*s3;
E(1) = -c0*s1*c2*s3;
E(2) = c0*s1*s2*c3;
E(3) = s0*c1*c2*s3;
E(4) = -s0*c1*s2*c3;
E(5) = s0*s1*c2*c3;
}
}
void E_exact(const Vector &x, DenseMatrix &E)
{
int dim = x.Size();
E.SetSize(dim*dim);
if (dim==4)
{
Vector vecE; E_exact_vec(x, vecE);
E = 0.0;
E(0,1) = vecE(0);
E(0,2) = vecE(1);
E(0,3) = vecE(2);
E(1,2) = vecE(3);
E(1,3) = vecE(4);
E(2,3) = vecE(5);
E(1,0) = -E(0,1);
E(2,0) = -E(0,2);
E(3,0) = -E(0,3);
E(2,1) = -E(1,2);
E(3,1) = -E(1,3);
E(3,2) = -E(2,3);
}
}
//f_exact = E + 0.5 * P( curl DivSkew E ), where P is the 4d permutation operator
void f_exact(const Vector &x, DenseMatrix &f)
{
int dim = x.Size();
f.SetSize(dim,dim);
if (dim==4)
{
f = 0.0;
double s0 = sin(M_PI*x(0)), s1 = sin(M_PI*x(1)), s2 = sin(M_PI*x(2)),
s3 = sin(M_PI*x(3));
double c0 = cos(M_PI*x(0)), c1 = cos(M_PI*x(1)), c2 = cos(M_PI*x(2)),
c3 = cos(M_PI*x(3));
f(0,1) = (1.0 + 1.0 * M_PI*M_PI)*c0*c1*s2*s3;
f(0,2) = -(1.0 + 0.0 * M_PI*M_PI)*c0*s1*c2*s3;
f(0,3) = (1.0 + 1.0 * M_PI*M_PI)*c0*s1*s2*c3;
f(1,2) = (1.0 - 1.0 * M_PI*M_PI)*s0*c1*c2*s3;
f(1,3) = -(1.0 + 0.0 * M_PI*M_PI)*s0*c1*s2*c3;
f(2,3) = (1.0 + 1.0 * M_PI*M_PI)*s0*s1*c2*c3;
f(1,0) = -f(0,1);
f(2,0) = -f(0,2);
f(3,0) = -f(0,3);
f(2,1) = -f(1,2);
f(3,1) = -f(1,3);
f(3,2) = -f(2,3);
}
}
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