void ParGridFunction::ExchangeFaceNbrData()
{
pfes->ExchangeFaceNbrData();
if (pfes->GetFaceNbrVSize() <= 0)
{
return;
}
ParMesh *pmesh = pfes->GetParMesh();
face_nbr_data.SetSize(pfes->GetFaceNbrVSize());
Vector send_data(pfes->send_face_nbr_ldof.Size_of_connections());
int *send_offset = pfes->send_face_nbr_ldof.GetI();
int *send_ldof = pfes->send_face_nbr_ldof.GetJ();
int *recv_offset = pfes->face_nbr_ldof.GetI();
MPI_Comm MyComm = pfes->GetComm();
int num_face_nbrs = pmesh->GetNFaceNeighbors();
MPI_Request *requests = new MPI_Request[2*num_face_nbrs];
MPI_Request *send_requests = requests;
MPI_Request *recv_requests = requests + num_face_nbrs;
MPI_Status *statuses = new MPI_Status[num_face_nbrs];
for (int i = 0; i < send_data.Size(); i++)
{
send_data[i] = data[send_ldof[i]];
}
for (int fn = 0; fn < num_face_nbrs; fn++)
{
int nbr_rank = pmesh->GetFaceNbrRank(fn);
int tag = 0;
MPI_Isend(&send_data(send_offset[fn]),
send_offset[fn+1] - send_offset[fn],
MPI_DOUBLE, nbr_rank, tag, MyComm, &send_requests[fn]);
MPI_Irecv(&face_nbr_data(recv_offset[fn]),
recv_offset[fn+1] - recv_offset[fn],
MPI_DOUBLE, nbr_rank, tag, MyComm, &recv_requests[fn]);
}
MPI_Waitall(num_face_nbrs, send_requests, statuses);
MPI_Waitall(num_face_nbrs, recv_requests, statuses);
delete [] statuses;
delete [] requests;
}
void ParNonlinearForm::Mult(const Vector &x, Vector &y) const
{
NonlinearForm::Mult(x, y); // x --(P)--> aux1 --(A_local)--> aux2
Y.SetData(aux2.GetData()); // aux2 contains A_local.P.x
if (fnfi.Size())
{
// Terms over shared interior faces in parallel.
ParFiniteElementSpace *pfes = ParFESpace();
ParMesh *pmesh = pfes->GetParMesh();
FaceElementTransformations *tr;
const FiniteElement *fe1, *fe2;
Array<int> vdofs1, vdofs2;
Vector el_x, el_y;
X.SetData(aux1.GetData()); // aux1 contains P.x
X.ExchangeFaceNbrData();
const int n_shared_faces = pmesh->GetNSharedFaces();
for (int i = 0; i < n_shared_faces; i++)
{
tr = pmesh->GetSharedFaceTransformations(i, true);
fe1 = pfes->GetFE(tr->Elem1No);
fe2 = pfes->GetFaceNbrFE(tr->Elem2No);
pfes->GetElementVDofs(tr->Elem1No, vdofs1);
pfes->GetFaceNbrElementVDofs(tr->Elem2No, vdofs2);
el_x.SetSize(vdofs1.Size() + vdofs2.Size());
X.GetSubVector(vdofs1, el_x.GetData());
X.FaceNbrData().GetSubVector(vdofs2, el_x.GetData() + vdofs1.Size());
for (int k = 0; k < fnfi.Size(); k++)
{
fnfi[k]->AssembleFaceVector(*fe1, *fe2, *tr, el_x, el_y);
Y.AddElementVector(vdofs1, el_y.GetData());
}
}
}
P->MultTranspose(Y, y);
for (int i = 0; i < ess_tdof_list.Size(); i++)
{
y(ess_tdof_list[i]) = 0.0;
}
}
void VisualizeMesh(socketstream &sock, const char *vishost, int visport,
ParMesh &pmesh, const char *title,
int x, int y, int w, int h, const char *keys, bool vec)
{
MPI_Comm comm = pmesh.GetComm();
int num_procs, myid;
MPI_Comm_size(comm, &num_procs);
MPI_Comm_rank(comm, &myid);
bool newly_opened = false;
int connection_failed;
do
{
if (myid == 0)
{
if (!sock.is_open() || !sock)
{
sock.open(vishost, visport);
sock.precision(8);
newly_opened = true;
}
sock << "solution\n";
}
pmesh.PrintAsOne(sock);
if (myid == 0 && newly_opened)
{
sock << "window_title '" << title << "'\n"
<< "window_geometry "
<< x << " " << y << " " << w << " " << h << "\n";
if ( keys ) { sock << "keys " << keys << "\n"; }
else { sock << "keys maaAc"; }
if ( vec ) { sock << "vvv"; }
sock << endl;
}
if (myid == 0)
{
connection_failed = !sock && !newly_opened;
}
MPI_Bcast(&connection_failed, 1, MPI_INT, 0, comm);
}
while (connection_failed);
}
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/star.mesh";
int order = 1;
bool set_bc = true;
bool static_cond = false;
bool hybridization = false;
bool visualization = 1;
bool use_petsc = true;
const char *petscrc_file = "";
bool use_nonoverlapping = false;
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(&set_bc, "-bc", "--impose-bc", "-no-bc", "--dont-impose-bc",
"Impose or not essential boundary conditions.");
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(&hybridization, "-hb", "--hybridization", "-no-hb",
"--no-hybridization", "Enable hybridization.");
args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
"--no-visualization",
"Enable or disable GLVis visualization.");
args.AddOption(&use_petsc, "-usepetsc", "--usepetsc", "-no-petsc",
"--no-petsc",
"Use or not PETSc to solve the linear system.");
args.AddOption(&petscrc_file, "-petscopts", "--petscopts",
"PetscOptions file to use.");
args.AddOption(&use_nonoverlapping, "-nonoverlapping", "--nonoverlapping",
"-no-nonoverlapping", "--no-nonoverlapping",
"Use or not the block diagonal PETSc's matrix format "
"for non-overlapping domain decomposition.");
args.Parse();
if (!args.Good())
{
if (myid == 0)
{
args.PrintUsage(cout);
}
MPI_Finalize();
return 1;
}
if (myid == 0)
{
args.PrintOptions(cout);
}
// 2b. We initialize PETSc
if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }
kappa = freq * M_PI;
// 3. Read the (serial) mesh from the given mesh file on all processors. We
// can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
// and volume, as well as periodic meshes with the same code.
Mesh *mesh = new Mesh(mesh_file, 1, 1);
int dim = mesh->Dimension();
int sdim = mesh->SpaceDimension();
// 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 (this is needed in the ADS solver below).
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 Raviart-Thomas finite elements of the specified order.
FiniteElementCollection *fec = new RT_FECollection(order-1, dim);
ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
HYPRE_Int size = fespace->GlobalTrueVSize();
if (myid == 0)
{
cout << "Number of finite element unknowns: " << size << endl;
}
// 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;
if (pmesh->bdr_attributes.Size())
{
Array<int> ess_bdr(pmesh->bdr_attributes.Max());
ess_bdr = set_bc ? 1 : 0;
fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
}
// 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.
VectorFunctionCoefficient f(sdim, f_exact);
ParLinearForm *b = new ParLinearForm(fespace);
b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
b->Assemble();
// 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 faces will be used
// when eliminating the non-homogeneous boundary condition to modify the
// r.h.s. vector b.
ParGridFunction x(fespace);
VectorFunctionCoefficient F(sdim, F_exact);
x.ProjectCoefficient(F);
// 10. Set up the parallel bilinear form corresponding to the H(div)
// diffusion operator grad alpha div + beta I, by adding the div-div and
// the mass domain integrators.
Coefficient *alpha = new ConstantCoefficient(1.0);
Coefficient *beta = new ConstantCoefficient(1.0);
ParBilinearForm *a = new ParBilinearForm(fespace);
a->AddDomainIntegrator(new DivDivIntegrator(*alpha));
a->AddDomainIntegrator(new VectorFEMassIntegrator(*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,
// hybridization, etc.
FiniteElementCollection *hfec = NULL;
ParFiniteElementSpace *hfes = NULL;
if (static_cond)
{
a->EnableStaticCondensation();
}
else if (hybridization)
{
hfec = new DG_Interface_FECollection(order-1, dim);
hfes = new ParFiniteElementSpace(pmesh, hfec);
a->EnableHybridization(hfes, new NormalTraceJumpIntegrator(),
ess_tdof_list);
}
a->Assemble();
Vector B, X;
CGSolver *pcg = new CGSolver(MPI_COMM_WORLD);
pcg->SetRelTol(1e-12);
pcg->SetMaxIter(500);
pcg->SetPrintLevel(1);
if (!use_petsc)
{
HypreParMatrix A;
a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
HYPRE_Int glob_size = A.GetGlobalNumRows();
if (myid == 0)
{
cout << "Size of linear system: " << glob_size << endl;
}
// 12. Define and apply a parallel PCG solver for A X = B with the 2D AMS or
// the 3D ADS preconditioners from hypre. If using hybridization, the
// system is preconditioned with hypre's BoomerAMG.
HypreSolver *prec = NULL;
pcg->SetOperator(A);
if (hybridization) { prec = new HypreBoomerAMG(A); }
else
{
ParFiniteElementSpace *prec_fespace =
(a->StaticCondensationIsEnabled() ? a->SCParFESpace() : fespace);
if (dim == 2) { prec = new HypreAMS(A, prec_fespace); }
else { prec = new HypreADS(A, prec_fespace); }
}
pcg->SetPreconditioner(*prec);
pcg->Mult(B, X);
delete prec;
}
else
{
PetscParMatrix A;
PetscPreconditioner *prec = NULL;
a->SetOperatorType(use_nonoverlapping ?
Operator::PETSC_MATIS : Operator::PETSC_MATAIJ);
a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
if (myid == 0)
{
cout << "Size of linear system: " << A.M() << endl;
}
pcg->SetOperator(A);
if (use_nonoverlapping)
{
ParFiniteElementSpace *prec_fespace =
(a->StaticCondensationIsEnabled() ? a->SCParFESpace() : fespace);
// Auxiliary class for BDDC customization
PetscBDDCSolverParams opts;
// Inform the solver about the finite element space
opts.SetSpace(prec_fespace);
// Inform the solver about essential dofs
opts.SetEssBdrDofs(&ess_tdof_list);
// Create a BDDC solver with parameters
prec = new PetscBDDCSolver(A, opts);
}
else
{
// Create an empty preconditioner that can be customized at runtime.
prec = new PetscPreconditioner(A, "solver_");
}
pcg->SetPreconditioner(*prec);
pcg->Mult(B, X);
delete prec;
}
delete pcg;
// 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 err = x.ComputeL2Error(F);
if (myid == 0)
{
cout << "\n|| F_h - F ||_{L^2} = " << err << '\n' << endl;
}
}
// 15. 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);
}
// 16. 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;
}
// 17. Free the used memory.
delete hfes;
delete hfec;
delete a;
delete alpha;
delete beta;
delete b;
delete fespace;
delete fec;
delete pmesh;
// We finalize PETSc
if (use_petsc) { MFEMFinalizePetsc(); }
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.
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;
}
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-quad.mesh";
int ser_ref_levels = 2;
int par_ref_levels = 0;
int order = 2;
int ode_solver_type = 3;
double t_final = 300.0;
double dt = 3;
double visc = 1e-2;
bool visualization = true;
int vis_steps = 1;
OptionsParser args(argc, argv);
args.AddOption(&mesh_file, "-m", "--mesh",
"Mesh file to use.");
args.AddOption(&ser_ref_levels, "-rs", "--refine-serial",
"Number of times to refine the mesh uniformly in serial.");
args.AddOption(&par_ref_levels, "-rp", "--refine-parallel",
"Number of times to refine the mesh uniformly in parallel.");
args.AddOption(&order, "-o", "--order",
"Order (degree) of the finite elements.");
args.AddOption(&ode_solver_type, "-s", "--ode-solver",
"ODE solver: 1 - Backward Euler, 2 - SDIRK2, 3 - SDIRK3,\n\t"
"\t 11 - Forward Euler, 12 - RK2, 13 - RK3 SSP, 14 - RK4.");
args.AddOption(&t_final, "-tf", "--t-final",
"Final time; start time is 0.");
args.AddOption(&dt, "-dt", "--time-step",
"Time step.");
args.AddOption(&visc, "-v", "--viscosity",
"Viscosity coefficient.");
args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
"--no-visualization",
"Enable or disable GLVis visualization.");
args.AddOption(&vis_steps, "-vs", "--visualization-steps",
"Visualize every n-th timestep.");
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 and hexahedral 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();
// 4. Define the ODE solver used for time integration. Several implicit
// singly diagonal implicit Runge-Kutta (SDIRK) methods, as well as
// explicit Runge-Kutta methods are available.
ODESolver *ode_solver;
switch (ode_solver_type)
{
// Implicit L-stable methods
case 1: ode_solver = new BackwardEulerSolver; break;
case 2: ode_solver = new SDIRK23Solver(2); break;
case 3: ode_solver = new SDIRK33Solver; break;
// Explicit methods
case 11: ode_solver = new ForwardEulerSolver; break;
case 12: ode_solver = new RK2Solver(0.5); break; // midpoint method
case 13: ode_solver = new RK3SSPSolver; break;
case 14: ode_solver = new RK4Solver; break;
// Implicit A-stable methods (not L-stable)
case 22: ode_solver = new ImplicitMidpointSolver; break;
case 23: ode_solver = new SDIRK23Solver; break;
case 24: ode_solver = new SDIRK34Solver; break;
default:
if (myid == 0)
cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
MPI_Finalize();
return 3;
}
// 5. Refine the mesh in serial to increase the resolution. In this example
// we do 'ser_ref_levels' of uniform refinement, where 'ser_ref_levels' is
// a command-line parameter.
for (int lev = 0; lev < ser_ref_levels; lev++)
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.
ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
delete mesh;
for (int lev = 0; lev < par_ref_levels; lev++)
pmesh->UniformRefinement();
// 7. Define the parallel vector finite element spaces representing the mesh
// deformation x_gf, the velocity v_gf, and the initial configuration,
// x_ref. Define also the elastic energy density, w_gf, which is in a
// discontinuous higher-order space. Since x and v are integrated in time
// as a system, we group them together in block vector vx, on the unique
// parallel degrees of freedom, with offsets given by array true_offset.
H1_FECollection fe_coll(order, dim);
ParFiniteElementSpace fespace(pmesh, &fe_coll, dim);
int glob_size = fespace.GlobalTrueVSize();
if (myid == 0)
cout << "Number of velocity/deformation unknowns: " << glob_size << endl;
int true_size = fespace.TrueVSize();
Array<int> true_offset(3);
true_offset[0] = 0;
true_offset[1] = true_size;
true_offset[2] = 2*true_size;
BlockVector vx(true_offset);
ParGridFunction v_gf(&fespace), x_gf(&fespace);
ParGridFunction x_ref(&fespace);
pmesh->GetNodes(x_ref);
L2_FECollection w_fec(order + 1, dim);
ParFiniteElementSpace w_fespace(pmesh, &w_fec);
ParGridFunction w_gf(&w_fespace);
// 8. Set the initial conditions for v_gf, x_gf and vx, and define the
// boundary conditions on a beam-like mesh (see description above).
VectorFunctionCoefficient velo(dim, InitialVelocity);
v_gf.ProjectCoefficient(velo);
VectorFunctionCoefficient deform(dim, InitialDeformation);
x_gf.ProjectCoefficient(deform);
v_gf.GetTrueDofs(vx.GetBlock(0));
x_gf.GetTrueDofs(vx.GetBlock(1));
Array<int> ess_bdr(fespace.GetMesh()->bdr_attributes.Max());
ess_bdr = 0;
ess_bdr[0] = 1; // boundary attribute 1 (index 0) is fixed
// 9. Initialize the hyperelastic operator, the GLVis visualization and print
// the initial energies.
HyperelasticOperator oper(fespace, ess_bdr, visc);
socketstream vis_v, vis_w;
if (visualization)
{
char vishost[] = "localhost";
int visport = 19916;
vis_v.open(vishost, visport);
vis_v.precision(8);
visualize(vis_v, pmesh, &x_gf, &v_gf, "Velocity", true);
// Make sure all ranks have sent their 'v' solution before initiating
// another set of GLVis connections (one from each rank):
MPI_Barrier(pmesh->GetComm());
vis_w.open(vishost, visport);
if (vis_w)
{
oper.GetElasticEnergyDensity(x_gf, w_gf);
vis_w.precision(8);
visualize(vis_w, pmesh, &x_gf, &w_gf, "Elastic energy density", true);
}
}
double ee0 = oper.ElasticEnergy(x_gf);
double ke0 = oper.KineticEnergy(v_gf);
if (myid == 0)
{
cout << "initial elastic energy (EE) = " << ee0 << endl;
cout << "initial kinetic energy (KE) = " << ke0 << endl;
cout << "initial total energy (TE) = " << (ee0 + ke0) << endl;
}
// 10. Perform time-integration (looping over the time iterations, ti, with a
// time-step dt).
ode_solver->Init(oper);
double t = 0.0;
bool last_step = false;
for (int ti = 1; !last_step; ti++)
{
if (t + dt >= t_final - dt/2)
last_step = true;
ode_solver->Step(vx, t, dt);
if (last_step || (ti % vis_steps) == 0)
{
v_gf.Distribute(vx.GetBlock(0));
x_gf.Distribute(vx.GetBlock(1));
double ee = oper.ElasticEnergy(x_gf);
double ke = oper.KineticEnergy(v_gf);
if (myid == 0)
cout << "step " << ti << ", t = " << t << ", EE = " << ee
<< ", KE = " << ke << ", ΔTE = " << (ee+ke)-(ee0+ke0) << endl;
if (visualization)
{
visualize(vis_v, pmesh, &x_gf, &v_gf);
if (vis_w)
{
oper.GetElasticEnergyDensity(x_gf, w_gf);
visualize(vis_w, pmesh, &x_gf, &w_gf);
}
}
}
}
// 11. Save the displaced mesh, the velocity and elastic energy.
{
GridFunction *nodes = &x_gf;
int owns_nodes = 0;
pmesh->SwapNodes(nodes, owns_nodes);
ostringstream mesh_name, velo_name, ee_name;
mesh_name << "deformed." << setfill('0') << setw(6) << myid;
velo_name << "velocity." << setfill('0') << setw(6) << myid;
ee_name << "elastic_energy." << setfill('0') << setw(6) << myid;
ofstream mesh_ofs(mesh_name.str().c_str());
mesh_ofs.precision(8);
pmesh->Print(mesh_ofs);
pmesh->SwapNodes(nodes, owns_nodes);
ofstream velo_ofs(velo_name.str().c_str());
velo_ofs.precision(8);
v_gf.Save(velo_ofs);
ofstream ee_ofs(ee_name.str().c_str());
ee_ofs.precision(8);
oper.GetElasticEnergyDensity(x_gf, w_gf);
w_gf.Save(ee_ofs);
}
// 10. Free the used memory.
delete ode_solver;
delete pmesh;
MPI_Finalize();
return 0;
}
int main(int argc, char *argv[])
{
// 1. Initialize MPI.
MPI_Session mpi(argc, argv);
int myid = mpi.WorldRank();
// print the cool banner
if (mpi.Root()) { display_banner(cout); }
// 2. Parse command-line options.
const char *mesh_file = "cylinder-hex.mesh";
int ser_ref_levels = 0;
int par_ref_levels = 0;
int order = 2;
int ode_solver_type = 1;
double t_final = 100.0;
double dt = 0.5;
double amp = 2.0;
double mu = 1.0;
double sigma = 2.0*M_PI*10;
double Tcapacity = 1.0;
double Tconductivity = 0.01;
double alpha = Tconductivity/Tcapacity;
double freq = 1.0/60.0;
bool visualization = true;
bool visit = true;
int vis_steps = 1;
int gfprint = 0;
const char *basename = "Joule";
int amr = 0;
int debug = 0;
const char *problem = "rod";
OptionsParser args(argc, argv);
args.AddOption(&mesh_file, "-m", "--mesh",
"Mesh file to use.");
args.AddOption(&ser_ref_levels, "-rs", "--refine-serial",
"Number of times to refine the mesh uniformly in serial.");
args.AddOption(&par_ref_levels, "-rp", "--refine-parallel",
"Number of times to refine the mesh uniformly in parallel.");
args.AddOption(&order, "-o", "--order",
"Order (degree) of the finite elements.");
args.AddOption(&ode_solver_type, "-s", "--ode-solver",
"ODE solver: 1 - Backward Euler, 2 - SDIRK2, 3 - SDIRK3\n\t."
"\t 22 - Mid-Point, 23 - SDIRK23, 34 - SDIRK34.");
args.AddOption(&t_final, "-tf", "--t-final",
"Final time; start time is 0.");
args.AddOption(&dt, "-dt", "--time-step",
"Time step.");
args.AddOption(&mu, "-mu", "--permeability",
"Magnetic permeability coefficient.");
args.AddOption(&sigma, "-cnd", "--sigma",
"Conductivity coefficient.");
args.AddOption(&freq, "-f", "--frequency",
"Frequency of oscillation.");
args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
"--no-visualization",
"Enable or disable GLVis visualization.");
args.AddOption(&visit, "-visit", "--visit", "-no-visit", "--no-visit",
"Enable or disable VisIt visualization.");
args.AddOption(&vis_steps, "-vs", "--visualization-steps",
"Visualize every n-th timestep.");
args.AddOption(&basename, "-k", "--outputfilename",
"Name of the visit dump files");
args.AddOption(&gfprint, "-print", "--print",
"Print results (grid functions) to disk.");
args.AddOption(&amr, "-amr", "--amr",
"Enable AMR");
args.AddOption(&STATIC_COND, "-sc", "--static-condensation",
"Enable static condensation");
args.AddOption(&debug, "-debug", "--debug",
"Print matrices and vectors to disk");
args.AddOption(&SOLVER_PRINT_LEVEL, "-hl", "--hypre-print-level",
"Hypre print level");
args.AddOption(&problem, "-p", "--problem",
"Name of problem to run");
args.Parse();
if (!args.Good())
{
if (mpi.Root())
{
args.PrintUsage(cout);
}
return 1;
}
if (mpi.Root())
{
args.PrintOptions(cout);
}
aj_ = amp;
mj_ = mu;
sj_ = sigma;
wj_ = 2.0*M_PI*freq;
kj_ = sqrt(0.5*wj_*mj_*sj_);
hj_ = alpha;
dtj_ = dt;
rj_ = 1.0;
if (mpi.Root())
{
cout << "\nSkin depth sqrt(2.0/(wj*mj*sj)) = " << sqrt(2.0/(wj_*mj_*sj_))
<< "\nSkin depth sqrt(2.0*dt/(mj*sj)) = " << sqrt(2.0*dt/(mj_*sj_))
<< endl;
}
// 3. Here material properties are assigned to mesh attributes. This code is
// not general, it is assumed the mesh has 3 regions each with a different
// integer attribute: 1, 2 or 3.
//
// The coil problem has three regions: 1) coil, 2) air, 3) the rod.
// The rod problem has two regions: 1) rod, 2) air.
//
// We can use the same material maps for both problems.
std::map<int, double> sigmaMap, InvTcondMap, TcapMap, InvTcapMap;
double sigmaAir;
double TcondAir;
double TcapAir;
if (strcmp(problem,"rod")==0 || strcmp(problem,"coil")==0)
{
sigmaAir = 1.0e-6 * sigma;
TcondAir = 1.0e6 * Tconductivity;
TcapAir = 1.0 * Tcapacity;
}
else
{
cerr << "Problem " << problem << " not recognized\n";
mfem_error();
}
if (strcmp(problem,"rod")==0 || strcmp(problem,"coil")==0)
{
sigmaMap.insert(pair<int, double>(1, sigma));
sigmaMap.insert(pair<int, double>(2, sigmaAir));
sigmaMap.insert(pair<int, double>(3, sigmaAir));
InvTcondMap.insert(pair<int, double>(1, 1.0/Tconductivity));
InvTcondMap.insert(pair<int, double>(2, 1.0/TcondAir));
InvTcondMap.insert(pair<int, double>(3, 1.0/TcondAir));
TcapMap.insert(pair<int, double>(1, Tcapacity));
TcapMap.insert(pair<int, double>(2, TcapAir));
TcapMap.insert(pair<int, double>(3, TcapAir));
InvTcapMap.insert(pair<int, double>(1, 1.0/Tcapacity));
InvTcapMap.insert(pair<int, double>(2, 1.0/TcapAir));
InvTcapMap.insert(pair<int, double>(3, 1.0/TcapAir));
}
else
{
cerr << "Problem " << problem << " not recognized\n";
mfem_error();
}
// 4. Read the serial mesh from the given mesh file on all processors. We can
// handle triangular, quadrilateral, tetrahedral and hexahedral meshes
// with the same code.
Mesh *mesh;
mesh = new Mesh(mesh_file, 1, 1);
int dim = mesh->Dimension();
// 5. Assign the boundary conditions
Array<int> ess_bdr(mesh->bdr_attributes.Max());
Array<int> thermal_ess_bdr(mesh->bdr_attributes.Max());
Array<int> poisson_ess_bdr(mesh->bdr_attributes.Max());
if (strcmp(problem,"coil")==0)
{
// BEGIN CODE FOR THE COIL PROBLEM
// For the coil in a box problem we have surfaces 1) coil end (+),
// 2) coil end (-), 3) five sides of box, 4) side of box with coil BC
ess_bdr = 0;
ess_bdr[0] = 1; // boundary attribute 4 (index 3) is fixed
ess_bdr[1] = 1; // boundary attribute 4 (index 3) is fixed
ess_bdr[2] = 1; // boundary attribute 4 (index 3) is fixed
ess_bdr[3] = 1; // boundary attribute 4 (index 3) is fixed
// Same as above, but this is for the thermal operator for HDiv
// formulation the essential BC is the flux
thermal_ess_bdr = 0;
thermal_ess_bdr[2] = 1; // boundary attribute 4 (index 3) is fixed
// Same as above, but this is for the poisson eq for H1 formulation the
// essential BC is the value of Phi
poisson_ess_bdr = 0;
poisson_ess_bdr[0] = 1; // boundary attribute 1 (index 0) is fixed
poisson_ess_bdr[1] = 1; // boundary attribute 2 (index 1) is fixed
// END CODE FOR THE COIL PROBLEM
}
else if (strcmp(problem,"rod")==0)
{
// BEGIN CODE FOR THE STRAIGHT ROD PROBLEM
// the boundary conditions below are for the straight rod problem
ess_bdr = 0;
ess_bdr[0] = 1; // boundary attribute 1 (index 0) is fixed (front)
ess_bdr[1] = 1; // boundary attribute 2 (index 1) is fixed (rear)
ess_bdr[2] = 1; // boundary attribute 3 (index 2) is fixed (outer)
// Same as above, but this is for the thermal operator. For HDiv
// formulation the essential BC is the flux, which is zero on the front
// and sides. Note the Natural BC is T = 0 on the outer surface.
thermal_ess_bdr = 0;
thermal_ess_bdr[0] = 1; // boundary attribute 1 (index 0) is fixed (front)
thermal_ess_bdr[1] = 1; // boundary attribute 2 (index 1) is fixed (rear)
// Same as above, but this is for the poisson eq for H1 formulation the
// essential BC is the value of Phi
poisson_ess_bdr = 0;
poisson_ess_bdr[0] = 1; // boundary attribute 1 (index 0) is fixed (front)
poisson_ess_bdr[1] = 1; // boundary attribute 2 (index 1) is fixed (back)
// END CODE FOR THE STRAIGHT ROD PROBLEM
}
else
{
cerr << "Problem " << problem << " not recognized\n";
mfem_error();
}
// The following is required for mesh refinement
mesh->EnsureNCMesh();
// 6. Define the ODE solver used for time integration. Several implicit
// methods are available, including singly diagonal implicit Runge-Kutta
// (SDIRK).
ODESolver *ode_solver;
switch (ode_solver_type)
{
// Implicit L-stable methods
case 1: ode_solver = new BackwardEulerSolver; break;
case 2: ode_solver = new SDIRK23Solver(2); break;
case 3: ode_solver = new SDIRK33Solver; break;
// Implicit A-stable methods (not L-stable)
case 22: ode_solver = new ImplicitMidpointSolver; break;
case 23: ode_solver = new SDIRK23Solver; break;
case 34: ode_solver = new SDIRK34Solver; break;
default:
if (mpi.Root())
{
cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
}
delete mesh;
return 3;
}
// 7. Refine the mesh in serial to increase the resolution. In this example
// we do 'ser_ref_levels' of uniform refinement, where 'ser_ref_levels' is
// a command-line parameter.
for (int lev = 0; lev < ser_ref_levels; lev++)
{
mesh->UniformRefinement();
}
// 8. 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.
ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
delete mesh;
for (int lev = 0; lev < par_ref_levels; lev++)
{
pmesh->UniformRefinement();
}
// Make sure tet-only meshes are marked for local refinement.
pmesh->Finalize(true);
// 9. Apply non-uniform non-conforming mesh refinement to the mesh. The
// whole metal region is refined once, before the start of the time loop,
// i.e. this is not based on any error estimator.
if (amr == 1)
{
Array<int> ref_list;
int numElems = pmesh->GetNE();
for (int ielem = 0; ielem < numElems; ielem++)
{
int thisAtt = pmesh->GetAttribute(ielem);
if (thisAtt == 1)
{
ref_list.Append(ielem);
}
}
pmesh->GeneralRefinement(ref_list);
ref_list.DeleteAll();
}
// 10. Reorient the mesh. Must be done after refinement but before definition
// of higher order Nedelec spaces
pmesh->ReorientTetMesh();
// 11. Rebalance the mesh. Since the mesh was adaptively refined in a
// non-uniform way it will be computationally unbalanced.
if (pmesh->Nonconforming())
{
pmesh->Rebalance();
}
// 12. Define the parallel finite element spaces. We use:
//
// H(curl) for electric field,
// H(div) for magnetic flux,
// H(div) for thermal flux,
// H(grad)/H1 for electrostatic potential,
// L2 for temperature
// L2 contains discontinuous "cell-center" finite elements, type 2 is
// "positive"
L2_FECollection L2FEC(order-1, dim);
// ND contains Nedelec "edge-centered" vector finite elements with continuous
// tangential component.
ND_FECollection HCurlFEC(order, dim);
// RT contains Raviart-Thomas "face-centered" vector finite elements with
// continuous normal component.
RT_FECollection HDivFEC(order-1, dim);
// H1 contains continuous "node-centered" Lagrange finite elements.
H1_FECollection HGradFEC(order, dim);
ParFiniteElementSpace L2FESpace(pmesh, &L2FEC);
ParFiniteElementSpace HCurlFESpace(pmesh, &HCurlFEC);
ParFiniteElementSpace HDivFESpace(pmesh, &HDivFEC);
ParFiniteElementSpace HGradFESpace(pmesh, &HGradFEC);
// The terminology is TrueVSize is the unique (non-redundant) number of dofs
HYPRE_Int glob_size_l2 = L2FESpace.GlobalTrueVSize();
HYPRE_Int glob_size_nd = HCurlFESpace.GlobalTrueVSize();
HYPRE_Int glob_size_rt = HDivFESpace.GlobalTrueVSize();
HYPRE_Int glob_size_h1 = HGradFESpace.GlobalTrueVSize();
if (mpi.Root())
{
cout << "Number of Temperature Flux unknowns: " << glob_size_rt << endl;
cout << "Number of Temperature unknowns: " << glob_size_l2 << endl;
cout << "Number of Electric Field unknowns: " << glob_size_nd << endl;
cout << "Number of Magnetic Field unknowns: " << glob_size_rt << endl;
cout << "Number of Electrostatic unknowns: " << glob_size_h1 << endl;
}
int Vsize_l2 = L2FESpace.GetVSize();
int Vsize_nd = HCurlFESpace.GetVSize();
int Vsize_rt = HDivFESpace.GetVSize();
int Vsize_h1 = HGradFESpace.GetVSize();
// the big BlockVector stores the fields as
// 0 Temperature
// 1 Temperature Flux
// 2 P field
// 3 E field
// 4 B field
// 5 Joule Heating
Array<int> true_offset(7);
true_offset[0] = 0;
true_offset[1] = true_offset[0] + Vsize_l2;
true_offset[2] = true_offset[1] + Vsize_rt;
true_offset[3] = true_offset[2] + Vsize_h1;
true_offset[4] = true_offset[3] + Vsize_nd;
true_offset[5] = true_offset[4] + Vsize_rt;
true_offset[6] = true_offset[5] + Vsize_l2;
// The BlockVector is a large contiguous chunk of memory for storing required
// data for the hypre vectors, in this case: the temperature L2, the T-flux
// HDiv, the E-field HCurl, and the B-field HDiv, and scalar potential P.
BlockVector F(true_offset);
// grid functions E, B, T, F, P, and w which is the Joule heating
ParGridFunction E_gf, B_gf, T_gf, F_gf, w_gf, P_gf;
T_gf.MakeRef(&L2FESpace,F, true_offset[0]);
F_gf.MakeRef(&HDivFESpace,F, true_offset[1]);
P_gf.MakeRef(&HGradFESpace,F,true_offset[2]);
E_gf.MakeRef(&HCurlFESpace,F,true_offset[3]);
B_gf.MakeRef(&HDivFESpace,F, true_offset[4]);
w_gf.MakeRef(&L2FESpace,F, true_offset[5]);
// 13. Get the boundary conditions, set up the exact solution grid functions
// These VectorCoefficients have an Eval function. Note that e_exact and
// b_exact in this case are exact analytical solutions, taking a 3-vector
// point as input and returning a 3-vector field
VectorFunctionCoefficient E_exact(3, e_exact);
VectorFunctionCoefficient B_exact(3, b_exact);
FunctionCoefficient T_exact(t_exact);
E_exact.SetTime(0.0);
B_exact.SetTime(0.0);
// 14. Initialize the Diffusion operator, the GLVis visualization and print
// the initial energies.
MagneticDiffusionEOperator oper(true_offset[6], L2FESpace, HCurlFESpace,
HDivFESpace, HGradFESpace,
ess_bdr, thermal_ess_bdr, poisson_ess_bdr,
mu, sigmaMap, TcapMap, InvTcapMap,
InvTcondMap);
// This function initializes all the fields to zero or some provided IC
oper.Init(F);
socketstream vis_T, vis_E, vis_B, vis_w, vis_P;
char vishost[] = "localhost";
int visport = 19916;
if (visualization)
{
// Make sure all ranks have sent their 'v' solution before initiating
// another set of GLVis connections (one from each rank):
MPI_Barrier(pmesh->GetComm());
vis_T.precision(8);
vis_E.precision(8);
vis_B.precision(8);
vis_P.precision(8);
vis_w.precision(8);
int Wx = 0, Wy = 0; // window position
int Ww = 350, Wh = 350; // window size
int offx = Ww+10, offy = Wh+45; // window offsets
miniapps::VisualizeField(vis_P, vishost, visport,
P_gf, "Electric Potential (Phi)", Wx, Wy, Ww, Wh);
Wx += offx;
miniapps::VisualizeField(vis_E, vishost, visport,
E_gf, "Electric Field (E)", Wx, Wy, Ww, Wh);
Wx += offx;
miniapps::VisualizeField(vis_B, vishost, visport,
B_gf, "Magnetic Field (B)", Wx, Wy, Ww, Wh);
Wx = 0;
Wy += offy;
miniapps::VisualizeField(vis_w, vishost, visport,
w_gf, "Joule Heating", Wx, Wy, Ww, Wh);
Wx += offx;
miniapps::VisualizeField(vis_T, vishost, visport,
T_gf, "Temperature", Wx, Wy, Ww, Wh);
}
// VisIt visualization
VisItDataCollection visit_dc(basename, pmesh);
if ( visit )
{
visit_dc.RegisterField("E", &E_gf);
visit_dc.RegisterField("B", &B_gf);
visit_dc.RegisterField("T", &T_gf);
visit_dc.RegisterField("w", &w_gf);
visit_dc.RegisterField("Phi", &P_gf);
visit_dc.RegisterField("F", &F_gf);
visit_dc.SetCycle(0);
visit_dc.SetTime(0.0);
visit_dc.Save();
}
E_exact.SetTime(0.0);
B_exact.SetTime(0.0);
// 15. Perform time-integration (looping over the time iterations, ti, with a
// time-step dt). The object oper is the MagneticDiffusionOperator which
// has a Mult() method and an ImplicitSolve() method which are used by
// the time integrators.
ode_solver->Init(oper);
double t = 0.0;
bool last_step = false;
for (int ti = 1; !last_step; ti++)
{
if (t + dt >= t_final - dt/2)
{
last_step = true;
}
// F is the vector of dofs, t is the current time, and dt is the time step
// to advance.
ode_solver->Step(F, t, dt);
if (debug == 1)
{
oper.Debug(basename,t);
}
if (gfprint == 1)
{
ostringstream T_name, E_name, B_name, F_name, w_name, P_name, mesh_name;
T_name << basename << "_" << setfill('0') << setw(6) << t << "_"
<< "T." << setfill('0') << setw(6) << myid;
E_name << basename << "_" << setfill('0') << setw(6) << t << "_"
<< "E." << setfill('0') << setw(6) << myid;
B_name << basename << "_" << setfill('0') << setw(6) << t << "_"
<< "B." << setfill('0') << setw(6) << myid;
F_name << basename << "_" << setfill('0') << setw(6) << t << "_"
<< "F." << setfill('0') << setw(6) << myid;
w_name << basename << "_" << setfill('0') << setw(6) << t << "_"
<< "w." << setfill('0') << setw(6) << myid;
P_name << basename << "_" << setfill('0') << setw(6) << t << "_"
<< "P." << setfill('0') << setw(6) << myid;
mesh_name << basename << "_" << setfill('0') << setw(6) << t << "_"
<< "mesh." << setfill('0') << setw(6) << myid;
ofstream mesh_ofs(mesh_name.str().c_str());
mesh_ofs.precision(8);
pmesh->Print(mesh_ofs);
mesh_ofs.close();
ofstream T_ofs(T_name.str().c_str());
T_ofs.precision(8);
T_gf.Save(T_ofs);
T_ofs.close();
ofstream E_ofs(E_name.str().c_str());
E_ofs.precision(8);
E_gf.Save(E_ofs);
E_ofs.close();
ofstream B_ofs(B_name.str().c_str());
B_ofs.precision(8);
B_gf.Save(B_ofs);
B_ofs.close();
ofstream F_ofs(F_name.str().c_str());
F_ofs.precision(8);
F_gf.Save(B_ofs);
F_ofs.close();
ofstream P_ofs(P_name.str().c_str());
P_ofs.precision(8);
P_gf.Save(P_ofs);
P_ofs.close();
ofstream w_ofs(w_name.str().c_str());
w_ofs.precision(8);
w_gf.Save(w_ofs);
w_ofs.close();
}
if (last_step || (ti % vis_steps) == 0)
{
double el = oper.ElectricLosses(E_gf);
if (mpi.Root())
{
cout << fixed;
cout << "step " << setw(6) << ti << ",\tt = " << setw(6)
<< setprecision(3) << t
<< ",\tdot(E, J) = " << setprecision(8) << el << endl;
}
// Make sure all ranks have sent their 'v' solution before initiating
// another set of GLVis connections (one from each rank):
MPI_Barrier(pmesh->GetComm());
if (visualization)
{
int Wx = 0, Wy = 0; // window position
int Ww = 350, Wh = 350; // window size
int offx = Ww+10, offy = Wh+45; // window offsets
miniapps::VisualizeField(vis_P, vishost, visport,
P_gf, "Electric Potential (Phi)", Wx, Wy, Ww, Wh);
Wx += offx;
miniapps::VisualizeField(vis_E, vishost, visport,
E_gf, "Electric Field (E)", Wx, Wy, Ww, Wh);
Wx += offx;
miniapps::VisualizeField(vis_B, vishost, visport,
B_gf, "Magnetic Field (B)", Wx, Wy, Ww, Wh);
Wx = 0;
Wy += offy;
miniapps::VisualizeField(vis_w, vishost, visport,
w_gf, "Joule Heating", Wx, Wy, Ww, Wh);
Wx += offx;
miniapps::VisualizeField(vis_T, vishost, visport,
T_gf, "Temperature", Wx, Wy, Ww, Wh);
}
if (visit)
{
visit_dc.SetCycle(ti);
visit_dc.SetTime(t);
visit_dc.Save();
}
}
}
if (visualization)
{
vis_T.close();
vis_E.close();
vis_B.close();
vis_w.close();
vis_P.close();
}
// 16. Free the used memory.
delete ode_solver;
delete pmesh;
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.
const char *mesh_file = "../data/beam-tet.mesh";
int ser_ref_levels = 2;
int par_ref_levels = 1;
int order = 1;
int nev = 5;
bool visualization = 1;
OptionsParser args(argc, argv);
args.AddOption(&mesh_file, "-m", "--mesh",
"Mesh file to use.");
args.AddOption(&ser_ref_levels, "-rs", "--refine-serial",
"Number of times to refine the mesh uniformly in serial.");
args.AddOption(&par_ref_levels, "-rp", "--refine-parallel",
"Number of times to refine the mesh uniformly in parallel.");
args.AddOption(&order, "-o", "--order",
"Finite element order (polynomial degree) or -1 for"
" isoparametric space.");
args.AddOption(&nev, "-n", "--num-eigs",
"Number of desired eigenmodes.");
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();
// 4. Refine the serial mesh on all processors to increase the resolution. In
// this example we do 'ref_levels' of uniform refinement (2 by default, or
// specified on the command line with -rs).
for (int lev = 0; lev < ser_ref_levels; lev++)
{
mesh->UniformRefinement();
}
// 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
// this mesh further in parallel to increase the resolution (1 time by
// default, or specified on the command line with -rp). Once the parallel
// mesh is defined, the serial mesh can be deleted.
ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
delete mesh;
for (int lev = 0; lev < par_ref_levels; lev++)
{
pmesh->UniformRefinement();
}
// 6. 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 unknowns: " << size << endl;
}
// 7. Set up the parallel bilinear forms a(.,.) and m(.,.) on the finite
// element space. The first corresponds to the curl curl, while the second
// is a simple mass matrix needed on the right hand side of the
// generalized eigenvalue problem below. The boundary conditions are
// implemented by marking all the boundary attributes from the mesh as
// essential. The corresponding degrees of freedom are eliminated with
// special values on the diagonal to shift the Dirichlet eigenvalues out
// of the computational range. After serial and parallel assembly we
// extract the corresponding parallel matrices A and M.
ConstantCoefficient one(1.0);
Array<int> ess_bdr;
if (pmesh->bdr_attributes.Size())
{
ess_bdr.SetSize(pmesh->bdr_attributes.Max());
ess_bdr = 1;
}
ParBilinearForm *a = new ParBilinearForm(fespace);
a->AddDomainIntegrator(new CurlCurlIntegrator(one));
if (pmesh->bdr_attributes.Size() == 0)
{
// Add a mass term if the mesh has no boundary, e.g. periodic mesh or
// closed surface.
a->AddDomainIntegrator(new VectorFEMassIntegrator(one));
}
a->Assemble();
a->EliminateEssentialBCDiag(ess_bdr, 1.0);
a->Finalize();
ParBilinearForm *m = new ParBilinearForm(fespace);
m->AddDomainIntegrator(new VectorFEMassIntegrator(one));
m->Assemble();
// shift the eigenvalue corresponding to eliminated dofs to a large value
m->EliminateEssentialBCDiag(ess_bdr, numeric_limits<double>::min());
m->Finalize();
HypreParMatrix *A = a->ParallelAssemble();
HypreParMatrix *M = m->ParallelAssemble();
delete a;
delete m;
// 8. Define and configure the AME eigensolver and the AMS preconditioner for
// A to be used within the solver. Set the matrices which define the
// generalized eigenproblem A x = lambda M x.
HypreAMS *ams = new HypreAMS(*A,fespace);
ams->SetPrintLevel(0);
ams->SetSingularProblem();
HypreAME *ame = new HypreAME(MPI_COMM_WORLD);
ame->SetNumModes(nev);
ame->SetPreconditioner(*ams);
ame->SetMaxIter(100);
ame->SetTol(1e-8);
ame->SetPrintLevel(1);
ame->SetMassMatrix(*M);
ame->SetOperator(*A);
// 9. Compute the eigenmodes and extract the array of eigenvalues. Define a
// parallel grid function to represent each of the eigenmodes returned by
// the solver.
Array<double> eigenvalues;
ame->Solve();
ame->GetEigenvalues(eigenvalues);
ParGridFunction x(fespace);
// 10. Save the refined mesh and the modes in parallel. This output can be
// viewed later using GLVis: "glvis -np <np> -m mesh -g mode".
{
ostringstream mesh_name, mode_name;
mesh_name << "mesh." << setfill('0') << setw(6) << myid;
ofstream mesh_ofs(mesh_name.str().c_str());
mesh_ofs.precision(8);
pmesh->Print(mesh_ofs);
for (int i=0; i<nev; i++)
{
// convert eigenvector from HypreParVector to ParGridFunction
x = ame->GetEigenvector(i);
mode_name << "mode_" << setfill('0') << setw(2) << i << "."
<< setfill('0') << setw(6) << myid;
ofstream mode_ofs(mode_name.str().c_str());
mode_ofs.precision(8);
x.Save(mode_ofs);
mode_name.str("");
}
}
// 11. Send the solution by socket to a GLVis server.
if (visualization)
{
char vishost[] = "localhost";
int visport = 19916;
socketstream mode_sock(vishost, visport);
mode_sock.precision(8);
for (int i=0; i<nev; i++)
{
if ( myid == 0 )
{
cout << "Eigenmode " << i+1 << '/' << nev
<< ", Lambda = " << eigenvalues[i] << endl;
}
// convert eigenvector from HypreParVector to ParGridFunction
x = ame->GetEigenvector(i);
mode_sock << "parallel " << num_procs << " " << myid << "\n"
<< "solution\n" << *pmesh << x << flush
<< "window_title 'Eigenmode " << i+1 << '/' << nev
<< ", Lambda = " << eigenvalues[i] << "'" << endl;
char c;
if (myid == 0)
{
cout << "press (q)uit or (c)ontinue --> " << flush;
cin >> c;
}
MPI_Bcast(&c, 1, MPI_CHAR, 0, MPI_COMM_WORLD);
if (c != 'c')
{
break;
}
}
mode_sock.close();
}
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-tri.mesh";
int order = 1;
int nev = 5;
bool visualization = 1;
bool amg_elast = 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(&nev, "-n", "--num-eigs",
"Number of desired eigenmodes.");
args.AddOption(&amg_elast, "-elast", "--amg-for-elasticity", "-sys",
"--amg-for-systems",
"Use the special AMG elasticity solver (GM/LN approaches), "
"or standard AMG for systems (unknown approach).");
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 = new Mesh(mesh_file, 1, 1);
int dim = mesh->Dimension();
if (mesh->attributes.Max() < 2)
{
if (myid == 0)
cerr << "\nInput mesh should have at least two materials!"
<< " (See schematic in ex12p.cpp)\n"
<< endl;
MPI_Finalize();
return 3;
}
// 4. Select the order of the finite element discretization space. For NURBS
// meshes, we increase the order by degree elevation.
if (mesh->NURBSext && order > mesh->NURBSext->GetOrder())
{
mesh->DegreeElevate(order - mesh->NURBSext->GetOrder());
}
// 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.
ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
delete mesh;
{
int par_ref_levels = 1;
for (int l = 0; l < par_ref_levels; l++)
{
pmesh->UniformRefinement();
}
}
// 7. Define a parallel finite element space on the parallel mesh. Here we
// use vector finite elements, i.e. dim copies of a scalar finite element
// space. We use the ordering by vector dimension (the last argument of
// the FiniteElementSpace constructor) which is expected in the systems
// version of BoomerAMG preconditioner. For NURBS meshes, we use the
// (degree elevated) NURBS space associated with the mesh nodes.
FiniteElementCollection *fec;
ParFiniteElementSpace *fespace;
const bool use_nodal_fespace = pmesh->NURBSext && !amg_elast;
if (use_nodal_fespace)
{
fec = NULL;
fespace = (ParFiniteElementSpace *)pmesh->GetNodes()->FESpace();
}
else
{
fec = new H1_FECollection(order, dim);
fespace = new ParFiniteElementSpace(pmesh, fec, dim, Ordering::byVDIM);
}
HYPRE_Int size = fespace->GlobalTrueVSize();
if (myid == 0)
{
cout << "Number of unknowns: " << size << endl
<< "Assembling: " << flush;
}
// 8. Set up the parallel bilinear forms a(.,.) and m(.,.) on the finite
// element space corresponding to the linear elasticity integrator with
// piece-wise constants coefficient lambda and mu, a simple mass matrix
// needed on the right hand side of the generalized eigenvalue problem
// below. The boundary conditions are implemented by marking only boundary
// attribute 1 as essential. We use special values on the diagonal to
// shift the Dirichlet eigenvalues out of the computational range. After
// serial/parallel assembly we extract the corresponding parallel matrices
// A and M.
Vector lambda(pmesh->attributes.Max());
lambda = 1.0;
lambda(0) = lambda(1)*50;
PWConstCoefficient lambda_func(lambda);
Vector mu(pmesh->attributes.Max());
mu = 1.0;
mu(0) = mu(1)*50;
PWConstCoefficient mu_func(mu);
Array<int> ess_bdr(pmesh->bdr_attributes.Max());
ess_bdr = 0;
ess_bdr[0] = 1;
ParBilinearForm *a = new ParBilinearForm(fespace);
a->AddDomainIntegrator(new ElasticityIntegrator(lambda_func, mu_func));
if (myid == 0)
{
cout << "matrix ... " << flush;
}
a->Assemble();
a->EliminateEssentialBCDiag(ess_bdr, 1.0);
a->Finalize();
ParBilinearForm *m = new ParBilinearForm(fespace);
m->AddDomainIntegrator(new VectorMassIntegrator());
m->Assemble();
// shift the eigenvalue corresponding to eliminated dofs to a large value
m->EliminateEssentialBCDiag(ess_bdr, numeric_limits<double>::min());
m->Finalize();
if (myid == 0)
{
cout << "done." << endl;
}
HypreParMatrix *A = a->ParallelAssemble();
HypreParMatrix *M = m->ParallelAssemble();
delete a;
delete m;
// 9. Define and configure the LOBPCG eigensolver and the BoomerAMG
// preconditioner for A to be used within the solver. Set the matrices
// which define the generalized eigenproblem A x = lambda M x.
HypreBoomerAMG * amg = new HypreBoomerAMG(*A);
amg->SetPrintLevel(0);
if (amg_elast)
{
amg->SetElasticityOptions(fespace);
}
else
{
amg->SetSystemsOptions(dim);
}
HypreLOBPCG * lobpcg = new HypreLOBPCG(MPI_COMM_WORLD);
lobpcg->SetNumModes(nev);
lobpcg->SetPreconditioner(*amg);
lobpcg->SetMaxIter(100);
lobpcg->SetTol(1e-8);
lobpcg->SetPrecondUsageMode(1);
lobpcg->SetPrintLevel(1);
lobpcg->SetMassMatrix(*M);
lobpcg->SetOperator(*A);
// 10. Compute the eigenmodes and extract the array of eigenvalues. Define a
// parallel grid function to represent each of the eigenmodes returned by
// the solver.
Array<double> eigenvalues;
lobpcg->Solve();
lobpcg->GetEigenvalues(eigenvalues);
ParGridFunction x(fespace);
// 11. For non-NURBS meshes, make the mesh curved based on the finite element
// space. This means that we define the mesh elements through a fespace
// based transformation of the reference element. This allows us to save
// the displaced mesh as a curved mesh when using high-order finite
// element displacement field. We assume that the initial mesh (read from
// the file) is not higher order curved mesh compared to the chosen FE
// space.
if (!use_nodal_fespace)
{
pmesh->SetNodalFESpace(fespace);
}
// 12. Save the refined mesh and the modes in parallel. This output can be
// viewed later using GLVis: "glvis -np <np> -m mesh -g mode".
{
ostringstream mesh_name, mode_name;
mesh_name << "mesh." << setfill('0') << setw(6) << myid;
ofstream mesh_ofs(mesh_name.str().c_str());
mesh_ofs.precision(8);
pmesh->Print(mesh_ofs);
for (int i=0; i<nev; i++)
{
// convert eigenvector from HypreParVector to ParGridFunction
x = lobpcg->GetEigenvector(i);
mode_name << "mode_" << setfill('0') << setw(2) << i << "."
<< setfill('0') << setw(6) << myid;
ofstream mode_ofs(mode_name.str().c_str());
mode_ofs.precision(8);
x.Save(mode_ofs);
mode_name.str("");
}
}
// 13. Send the above data by socket to a GLVis server. Use the "n" and "b"
// keys in GLVis to visualize the displacements.
if (visualization)
{
char vishost[] = "localhost";
int visport = 19916;
socketstream mode_sock(vishost, visport);
for (int i=0; i<nev; i++)
{
if ( myid == 0 )
{
cout << "Eigenmode " << i+1 << '/' << nev
<< ", Lambda = " << eigenvalues[i] << endl;
}
// convert eigenvector from HypreParVector to ParGridFunction
x = lobpcg->GetEigenvector(i);
mode_sock << "parallel " << num_procs << " " << myid << "\n"
<< "solution\n" << *pmesh << x << flush
<< "window_title 'Eigenmode " << i+1 << '/' << nev
<< ", Lambda = " << eigenvalues[i] << "'" << endl;
char c;
if (myid == 0)
{
cout << "press (q)uit or (c)ontinue --> " << flush;
cin >> c;
}
MPI_Bcast(&c, 1, MPI_CHAR, 0, MPI_COMM_WORLD);
if (c != 'c')
{
break;
}
}
mode_sock.close();
}