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 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(&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);
// 3. 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;
ifstream imesh(mesh_file);
if (!imesh)
{
if (myid == 0)
cerr << "\nCan not open mesh file: " << mesh_file << '\n' << endl;
MPI_Finalize();
return 2;
}
mesh = new Mesh(imesh, 1, 1);
imesh.close();
int dim = mesh->Dimension();
if (dim != 3)
{
if (myid == 0)
cerr << "\nThis example requires a 3D mesh\n" << endl;
MPI_Finalize();
return 3;
}
// 4. 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();
}
// 5. 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 = 2;
for (int l = 0; l < par_ref_levels; l++)
pmesh->UniformRefinement();
}
pmesh->ReorientTetMesh();
// 6. Define a parallel finite element space on the parallel mesh. Here we
// use the lowest order Nedelec finite elements, but we can easily switch
// to higher-order spaces by changing the value of p.
FiniteElementCollection *fec = new ND_FECollection(order, dim);
ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
int size = fespace->GlobalTrueVSize();
if (myid == 0)
cout << "Number of unknowns: " << size << endl;
// 7. 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(3, f_exact);
ParLinearForm *b = new ParLinearForm(fespace);
b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
b->Assemble();
// 8. 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(3, E_exact);
x.ProjectCoefficient(E);
// 9. 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 and finally imposing non-homogeneous Dirichlet
// boundary conditions. The boundary conditions are implemented by
// marking all the boundary attributes from the mesh as essential
// (Dirichlet). After serial and parallel assembly we extract the
// parallel matrix A.
Coefficient *muinv = new ConstantCoefficient(1.0);
Coefficient *sigma = new ConstantCoefficient(1.0);
ParBilinearForm *a = new ParBilinearForm(fespace);
a->AddDomainIntegrator(new CurlCurlIntegrator(*muinv));
a->AddDomainIntegrator(new VectorFEMassIntegrator(*sigma));
a->Assemble();
Array<int> ess_bdr(pmesh->bdr_attributes.Max());
ess_bdr = 1;
a->EliminateEssentialBC(ess_bdr, x, *b);
a->Finalize();
// 10. Define the parallel (hypre) matrix and vectors representing a(.,.),
// b(.) and the finite element approximation.
HypreParMatrix *A = a->ParallelAssemble();
HypreParVector *B = b->ParallelAssemble();
HypreParVector *X = x.ParallelAverage();
*X = 0.0;
delete a;
delete sigma;
delete muinv;
delete b;
// 11. Define and apply a parallel PCG solver for AX=B with the AMS
// preconditioner from hypre.
HypreSolver *ams = new HypreAMS(*A, fespace);
HyprePCG *pcg = new HyprePCG(*A);
pcg->SetTol(1e-12);
pcg->SetMaxIter(500);
pcg->SetPrintLevel(2);
pcg->SetPreconditioner(*ams);
pcg->Mult(*B, *X);
// 12. Extract the parallel grid function corresponding to the finite element
// approximation X. This is the local solution on each processor.
x = *X;
// 13. Compute and print the L^2 norm of the error.
{
double err = x.ComputeL2Error(E);
if (myid == 0)
cout << "\n|| E_h - E ||_{L^2} = " << err << '\n' << endl;
}
// 14. 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);
x.Save(sol_ofs);
}
// 15. 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);
sol_sock << "solution\n" << *pmesh << x << flush;
}
// 16. Free the used memory.
delete pcg;
delete ams;
delete X;
delete B;
delete A;
delete fespace;
delete fec;
delete pmesh;
MPI_Finalize();
return 0;
}
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.
int elem_type = 1;
int ref_levels = 2;
int amr = 0;
int order = 2;
bool always_snap = false;
bool visualization = 1;
OptionsParser args(argc, argv);
args.AddOption(&elem_type, "-e", "--elem",
"Type of elements to use: 0 - triangles, 1 - quads.");
args.AddOption(&order, "-o", "--order",
"Finite element order (polynomial degree).");
args.AddOption(&ref_levels, "-r", "--refine",
"Number of times to refine the mesh uniformly.");
args.AddOption(&amr, "-amr", "--refine-locally",
"Additional local (non-conforming) refinement:"
" 1 = refine around north pole, 2 = refine randomly.");
args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
"--no-visualization",
"Enable or disable GLVis visualization.");
args.AddOption(&always_snap, "-snap", "--always-snap", "-no-snap",
"--snap-at-the-end",
"If true, snap nodes to the sphere initially and after each refinement "
"otherwise, snap only after the last refinement");
args.Parse();
if (!args.Good())
{
if (myid == 0)
{
args.PrintUsage(cout);
}
MPI_Finalize();
return 1;
}
if (myid == 0)
{
args.PrintOptions(cout);
}
// 3. Generate an initial high-order (surface) mesh on the unit sphere. The
// Mesh object represents a 2D mesh in 3 spatial dimensions. We first add
// the elements and the vertices of the mesh, and then make it high-order
// by specifying a finite element space for its nodes.
int Nvert = 8, Nelem = 6;
if (elem_type == 0)
{
Nvert = 6;
Nelem = 8;
}
Mesh *mesh = new Mesh(2, Nvert, Nelem, 0, 3);
if (elem_type == 0) // inscribed octahedron
{
const double tri_v[6][3] =
{
{ 1, 0, 0}, { 0, 1, 0}, {-1, 0, 0},
{ 0, -1, 0}, { 0, 0, 1}, { 0, 0, -1}
};
const int tri_e[8][3] =
{
{0, 1, 4}, {1, 2, 4}, {2, 3, 4}, {3, 0, 4},
{1, 0, 5}, {2, 1, 5}, {3, 2, 5}, {0, 3, 5}
};
for (int j = 0; j < Nvert; j++)
{
mesh->AddVertex(tri_v[j]);
}
for (int j = 0; j < Nelem; j++)
{
int attribute = j + 1;
mesh->AddTriangle(tri_e[j], attribute);
}
mesh->FinalizeTriMesh(1, 1, true);
}
else // inscribed cube
{
const double quad_v[8][3] =
{
{-1, -1, -1}, {+1, -1, -1}, {+1, +1, -1}, {-1, +1, -1},
{-1, -1, +1}, {+1, -1, +1}, {+1, +1, +1}, {-1, +1, +1}
};
const int quad_e[6][4] =
{
{3, 2, 1, 0}, {0, 1, 5, 4}, {1, 2, 6, 5},
{2, 3, 7, 6}, {3, 0, 4, 7}, {4, 5, 6, 7}
};
for (int j = 0; j < Nvert; j++)
{
mesh->AddVertex(quad_v[j]);
}
for (int j = 0; j < Nelem; j++)
{
int attribute = j + 1;
mesh->AddQuad(quad_e[j], attribute);
}
mesh->FinalizeQuadMesh(1, 1, true);
}
// Set the space for the high-order mesh nodes.
H1_FECollection fec(order, mesh->Dimension());
FiniteElementSpace nodal_fes(mesh, &fec, mesh->SpaceDimension());
mesh->SetNodalFESpace(&nodal_fes);
// 4. Refine the mesh while snapping nodes to the sphere. Number of parallel
// refinements is fixed to 2.
for (int l = 0; l <= ref_levels; l++)
{
if (l > 0) // for l == 0 just perform snapping
{
mesh->UniformRefinement();
}
// Snap the nodes of the refined mesh back to sphere surface.
if (always_snap)
{
SnapNodes(*mesh);
}
}
if (amr == 1)
{
for (int l = 0; l < 3; l++)
{
mesh->RefineAtVertex(Vertex(0, 0, 1));
}
SnapNodes(*mesh);
}
else if (amr == 2)
{
for (int l = 0; l < 2; l++)
{
mesh->RandomRefinement(0.5); // 50% probability
}
SnapNodes(*mesh);
}
ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
delete mesh;
{
int par_ref_levels = 2;
for (int l = 0; l < par_ref_levels; l++)
{
pmesh->UniformRefinement();
// Snap the nodes of the refined mesh back to sphere surface.
if (always_snap)
{
SnapNodes(*pmesh);
}
}
if (!always_snap || par_ref_levels < 1)
{
SnapNodes(*pmesh);
}
}
if (amr == 1)
{
for (int l = 0; l < 2; l++)
{
pmesh->RefineAtVertex(Vertex(0, 0, 1));
}
SnapNodes(*pmesh);
}
else if (amr == 2)
{
for (int l = 0; l < 2; l++)
{
pmesh->RandomRefinement(0.5); // 50% probability
}
SnapNodes(*pmesh);
}
// 5. Define a finite element space on the mesh. Here we use isoparametric
// finite elements -- the same as the mesh nodes.
ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, &fec);
HYPRE_Int size = fespace->GlobalTrueVSize();
if (myid == 0)
{
cout << "Number of unknowns: " << size << endl;
}
// 6. 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.
ParLinearForm *b = new ParLinearForm(fespace);
ConstantCoefficient one(1.0);
FunctionCoefficient rhs_coef (analytic_rhs);
FunctionCoefficient sol_coef (analytic_solution);
b->AddDomainIntegrator(new DomainLFIntegrator(rhs_coef));
b->Assemble();
// 7. Define the solution vector x as a finite element grid function
// corresponding to fespace. Initialize x with initial guess of zero.
ParGridFunction x(fespace);
x = 0.0;
// 8. Set up the bilinear form a(.,.) on the finite element space
// corresponding to the Laplacian operator -Delta, by adding the Diffusion
// and Mass domain integrators.
ParBilinearForm *a = new ParBilinearForm(fespace);
a->AddDomainIntegrator(new DiffusionIntegrator(one));
a->AddDomainIntegrator(new MassIntegrator(one));
// 9. Assemble the parallel linear system, applying any transformations
// such as: parallel assembly, applying conforming constraints, etc.
a->Assemble();
HypreParMatrix A;
Vector B, X;
Array<int> empty_tdof_list;
a->FormLinearSystem(empty_tdof_list, x, *b, A, X, B);
// 10. Define and apply a parallel PCG solver for AX=B with the BoomerAMG
// preconditioner from hypre. Extract the parallel grid function x
// corresponding to the finite element approximation X. This is the local
// solution on each processor.
HypreSolver *amg = new HypreBoomerAMG(A);
HyprePCG *pcg = new HyprePCG(A);
pcg->SetTol(1e-12);
pcg->SetMaxIter(200);
pcg->SetPrintLevel(2);
pcg->SetPreconditioner(*amg);
pcg->Mult(B, X);
a->RecoverFEMSolution(X, *b, x);
delete a;
delete b;
// 11. Compute and print the L^2 norm of the error.
double err = x.ComputeL2Error(sol_coef);
if (myid == 0)
{
cout << "\nL2 norm of error: " << err << endl;
}
// 12. Save the refined mesh and the solution. This output can be viewed
// later using GLVis: "glvis -np <np> -m sphere_refined -g sol".
{
ostringstream mesh_name, sol_name;
mesh_name << "sphere_refined." << 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);
x.Save(sol_ofs);
}
// 13. 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);
sol_sock << "solution\n" << *pmesh << x << flush;
}
// 14. Free the used memory.
delete pcg;
delete amg;
delete fespace;
delete pmesh;
MPI_Finalize();
return 0;
}
void
TeslaSolver::Solve()
{
if (myid_ == 0) { cout << "Running solver ... " << endl << flush; }
// Initialize the magnetic vector potential with its boundary conditions
*a_ = 0.0;
// Apply surface currents if available
if ( k_ )
{
SurfCur_->ComputeSurfaceCurrent(*k_);
*a_ = *k_;
}
// Apply uniform B boundary condition on remaining surfaces
a_->ProjectBdrCoefficientTangent(*aBCCoef_, non_k_bdr_);
// Initialize the RHS vector
HypreParVector *RHS = new HypreParVector(HCurlFESpace_);
*RHS = 0.0;
HypreParMatrix *MassHCurl = hCurlMass_->ParallelAssemble();
// Initialize the volumetric current density
if ( j_ )
{
j_->ProjectCoefficient(*jCoef_);
HypreParVector *J = j_->ParallelProject();
HypreParVector *JD = new HypreParVector(HCurlFESpace_);
MassHCurl->Mult(*J,*JD);
DivFreeProj_->Mult(*JD, *RHS);
delete J;
delete JD;
}
// Initialize the Magnetization
HypreParVector *M = NULL;
if ( m_ )
{
m_->ProjectCoefficient(*mCoef_);
M = m_->ParallelProject();
HypreParMatrix *MassHDiv = hDivMassMuInv_->ParallelAssemble();
HypreParVector *MD = new HypreParVector(HDivFESpace_);
MassHDiv->Mult(*M,*MD);
Curl_->MultTranspose(*MD,*RHS,mu0_,1.0);
delete MassHDiv;
delete MD;
}
// Apply Dirichlet BCs to matrix and right hand side
HypreParMatrix *CurlMuInvCurl = curlMuInvCurl_->ParallelAssemble();
HypreParVector *A = a_->ParallelProject();
// Apply the boundary conditions to the assembled matrix and vectors
curlMuInvCurl_->ParallelEliminateEssentialBC(ess_bdr_,
*CurlMuInvCurl,
*A, *RHS);
// Define and apply a parallel PCG solver for AX=B with the AMS
// preconditioner from hypre.
HypreAMS *ams = new HypreAMS(*CurlMuInvCurl, HCurlFESpace_);
ams->SetSingularProblem();
HyprePCG *pcg = new HyprePCG(*CurlMuInvCurl);
pcg->SetTol(1e-12);
pcg->SetMaxIter(500);
pcg->SetPrintLevel(2);
pcg->SetPreconditioner(*ams);
pcg->Mult(*RHS, *A);
delete ams;
delete pcg;
delete CurlMuInvCurl;
delete RHS;
// Extract the parallel grid function corresponding to the finite
// element approximation Phi. This is the local solution on each
// processor.
*a_ = *A;
// Compute the negative Gradient of the solution vector. This is
// the magnetic field corresponding to the scalar potential
// represented by phi.
HypreParVector *B = new HypreParVector(HDivFESpace_);
Curl_->Mult(*A,*B);
*b_ = *B;
// Compute magnetic field (H) from B and M
if (myid_ == 0) { cout << "Computing H ... " << flush; }
HypreParMatrix *HDivHCurlMuInv = hDivHCurlMuInv_->ParallelAssemble();
HypreParVector *BD = new HypreParVector(HCurlFESpace_);
HypreParVector *H = new HypreParVector(HCurlFESpace_);
HDivHCurlMuInv->Mult(*B,*BD);
if ( M )
{
HDivHCurlMuInv->Mult(*M,*BD,-1.0*mu0_,1.0);
}
HyprePCG * pcgM = new HyprePCG(*MassHCurl);
pcgM->SetTol(1e-12);
pcgM->SetMaxIter(500);
pcgM->SetPrintLevel(0);
HypreDiagScale *diagM = new HypreDiagScale;
pcgM->SetPreconditioner(*diagM);
pcgM->Mult(*BD,*H);
*h_ = *H;
if (myid_ == 0) { cout << "done." << flush; }
delete diagM;
delete pcgM;
delete HDivHCurlMuInv;
delete MassHCurl;
delete A;
delete B;
delete BD;
delete H;
delete M;
if (myid_ == 0) { cout << " Solver done. " << flush; }
}
void
VoltaSolver::Solve()
{
if (myid_ == 0) { cout << "Running solver ... " << endl << flush; }
// Initialize the electric potential with its boundary conditions
*phi_ = 0.0;
if ( dbcs_->Size() > 0 )
{
if ( phiBCCoef_ )
{
// Apply gradient boundary condition
phi_->ProjectBdrCoefficient(*phiBCCoef_, ess_bdr_);
}
else
{
// Apply piecewise constant boundary condition
Array<int> dbc_bdr_attr(pmesh_->bdr_attributes.Max());
for (int i=0; i<dbcs_->Size(); i++)
{
ConstantCoefficient voltage((*dbcv_)[i]);
dbc_bdr_attr = 0;
dbc_bdr_attr[(*dbcs_)[i]-1] = 1;
phi_->ProjectBdrCoefficient(voltage, dbc_bdr_attr);
}
}
}
// Initialize the RHS vector
HypreParVector *RHS = new HypreParVector(H1FESpace_);
*RHS = 0.0;
// Initialize the volumetric charge density
if ( rho_ )
{
rho_->ProjectCoefficient(*rhoCoef_);
HypreParMatrix *MassH1 = h1Mass_->ParallelAssemble();
HypreParVector *Rho = rho_->ParallelProject();
MassH1->Mult(*Rho,*RHS);
delete MassH1;
delete Rho;
}
// Initialize the Polarization
HypreParVector *P = NULL;
if ( p_ )
{
p_->ProjectCoefficient(*pCoef_);
P = p_->ParallelProject();
HypreParMatrix *MassHCurl = hCurlMass_->ParallelAssemble();
HypreParVector *PD = new HypreParVector(HCurlFESpace_);
MassHCurl->Mult(*P,*PD);
Grad_->MultTranspose(*PD,*RHS,-1.0,1.0);
delete MassHCurl;
delete PD;
}
// Initialize the surface charge density
if ( sigma_ )
{
*sigma_ = 0.0;
Array<int> nbc_bdr_attr(pmesh_->bdr_attributes.Max());
for (int i=0; i<nbcs_->Size(); i++)
{
ConstantCoefficient sigma_coef((*nbcv_)[i]);
nbc_bdr_attr = 0;
nbc_bdr_attr[(*nbcs_)[i]-1] = 1;
sigma_->ProjectBdrCoefficient(sigma_coef, nbc_bdr_attr);
}
HypreParMatrix *MassS = h1SurfMass_->ParallelAssemble();
HypreParVector *Sigma = sigma_->ParallelProject();
MassS->Mult(*Sigma,*RHS,1.0,1.0);
delete MassS;
delete Sigma;
}
// Apply Dirichlet BCs to matrix and right hand side
HypreParMatrix *DivEpsGrad = divEpsGrad_->ParallelAssemble();
HypreParVector *Phi = phi_->ParallelProject();
// Apply the boundary conditions to the assembled matrix and vectors
if ( dbcs_->Size() > 0 )
{
// According to the selected surfaces
divEpsGrad_->ParallelEliminateEssentialBC(ess_bdr_,
*DivEpsGrad,
*Phi, *RHS);
}
else
{
// No surfaces were labeled as Dirichlet so eliminate one DoF
Array<int> dof_list(0);
if ( myid_ == 0 )
{
dof_list.SetSize(1);
dof_list[0] = 0;
}
DivEpsGrad->EliminateRowsCols(dof_list, *Phi, *RHS);
}
// Define and apply a parallel PCG solver for AX=B with the AMG
// preconditioner from hypre.
HypreSolver *amg = new HypreBoomerAMG(*DivEpsGrad);
HyprePCG *pcg = new HyprePCG(*DivEpsGrad);
pcg->SetTol(1e-12);
pcg->SetMaxIter(500);
pcg->SetPrintLevel(2);
pcg->SetPreconditioner(*amg);
pcg->Mult(*RHS, *Phi);
delete amg;
delete pcg;
delete DivEpsGrad;
delete RHS;
// Extract the parallel grid function corresponding to the finite
// element approximation Phi. This is the local solution on each
// processor.
*phi_ = *Phi;
// Compute the negative Gradient of the solution vector. This is
// the magnetic field corresponding to the scalar potential
// represented by phi.
HypreParVector *E = new HypreParVector(HCurlFESpace_);
Grad_->Mult(*Phi,*E,-1.0);
*e_ = *E;
delete Phi;
// Compute electric displacement (D) from E and P
if (myid_ == 0) { cout << "Computing D ... " << flush; }
HypreParMatrix *HCurlHDivEps = hCurlHDivEps_->ParallelAssemble();
HypreParVector *ED = new HypreParVector(HDivFESpace_);
HypreParVector *D = new HypreParVector(HDivFESpace_);
HCurlHDivEps->Mult(*E,*ED);
if ( P )
{
HypreParMatrix *HCurlHDiv = hCurlHDiv_->ParallelAssemble();
HCurlHDiv->Mult(*P,*ED,-1.0,1.0);
delete HCurlHDiv;
}
HypreParMatrix * MassHDiv = hDivMass_->ParallelAssemble();
HyprePCG * pcgM = new HyprePCG(*MassHDiv);
pcgM->SetTol(1e-12);
pcgM->SetMaxIter(500);
pcgM->SetPrintLevel(0);
HypreDiagScale *diagM = new HypreDiagScale;
pcgM->SetPreconditioner(*diagM);
pcgM->Mult(*ED,*D);
*d_ = *D;
if (myid_ == 0) { cout << "done." << flush; }
delete diagM;
delete pcgM;
delete HCurlHDivEps;
delete MassHDiv;
delete E;
delete ED;
delete D;
delete P;
if (myid_ == 0) { cout << " Solver done. " << flush; }
}
double L2ZZErrorEstimator(BilinearFormIntegrator &flux_integrator,
const ParGridFunction &x,
ParFiniteElementSpace &smooth_flux_fes,
ParFiniteElementSpace &flux_fes,
Vector &errors,
int norm_p, double solver_tol, int solver_max_it)
{
// Compute fluxes in discontinuous space
GridFunction flux(&flux_fes);
flux = 0.0;
ParFiniteElementSpace *xfes = x.ParFESpace();
Array<int> xdofs, fdofs;
Vector el_x, el_f;
for (int i = 0; i < xfes->GetNE(); i++)
{
xfes->GetElementVDofs(i, xdofs);
x.GetSubVector(xdofs, el_x);
ElementTransformation *Transf = xfes->GetElementTransformation(i);
flux_integrator.ComputeElementFlux(*xfes->GetFE(i), *Transf, el_x,
*flux_fes.GetFE(i), el_f, false);
flux_fes.GetElementVDofs(i, fdofs);
flux.AddElementVector(fdofs, el_f);
}
// Assemble the linear system for L2 projection into the "smooth" space
ParBilinearForm *a = new ParBilinearForm(&smooth_flux_fes);
ParLinearForm *b = new ParLinearForm(&smooth_flux_fes);
VectorGridFunctionCoefficient f(&flux);
if (xfes->GetNE())
{
if (smooth_flux_fes.GetFE(0)->GetRangeType() == FiniteElement::SCALAR)
{
VectorMassIntegrator *vmass = new VectorMassIntegrator;
vmass->SetVDim(smooth_flux_fes.GetVDim());
a->AddDomainIntegrator(vmass);
b->AddDomainIntegrator(new VectorDomainLFIntegrator(f));
}
else
{
a->AddDomainIntegrator(new VectorFEMassIntegrator);
b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
}
}
b->Assemble();
a->Assemble();
a->Finalize();
// The destination of the projected discontinuous flux
ParGridFunction smooth_flux(&smooth_flux_fes);
smooth_flux = 0.0;
HypreParMatrix* A = a->ParallelAssemble();
HypreParVector* B = b->ParallelAssemble();
HypreParVector* X = smooth_flux.ParallelProject();
delete a;
delete b;
// Define and apply a parallel PCG solver for AX=B with the BoomerAMG
// preconditioner from hypre.
HypreBoomerAMG *amg = new HypreBoomerAMG(*A);
amg->SetPrintLevel(0);
HyprePCG *pcg = new HyprePCG(*A);
pcg->SetTol(solver_tol);
pcg->SetMaxIter(solver_max_it);
pcg->SetPrintLevel(0);
pcg->SetPreconditioner(*amg);
pcg->Mult(*B, *X);
// Extract the parallel grid function corresponding to the finite element
// approximation X. This is the local solution on each processor.
smooth_flux = *X;
delete A;
delete B;
delete X;
delete amg;
delete pcg;
// Proceed through the elements one by one, and find the Lp norm differences
// between the flux as computed per element and the flux projected onto the
// smooth_flux_fes space.
double total_error = 0.0;
errors.SetSize(xfes->GetNE());
for (int i = 0; i < xfes->GetNE(); i++)
{
errors(i) = ComputeElementLpDistance(norm_p, i, smooth_flux, flux);
total_error += pow(errors(i), norm_p);
}
double glob_error;
MPI_Allreduce(&total_error, &glob_error, 1, MPI_DOUBLE, MPI_SUM,
xfes->GetComm());
return pow(glob_error, 1.0/norm_p);
}