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mfem/examples/maxwell-solver/additive_schwarz.cpp
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23 KiB
C++

#include "additive_schwarz.hpp"
// constructor
OverlappingCartesianMeshPartition::OverlappingCartesianMeshPartition(Mesh *mesh_) : mesh(mesh_)
{ // default overlap size is 2 elements
int dim = mesh->Dimension();
int n = pow(mesh->GetNE(), 1.0/(double)dim);
nx = 16;
ny = 1;
nz = 1;
if (nx > n)
{
nx = n;
MFEM_WARNING("Changed partition in the x direction to nx = " << n << endl);
}
if (ny > n)
{
ny = n;
MFEM_WARNING("Changed partition in the y direction to ny = " << n << endl);
}
if (nz > n)
{
nz = n;
MFEM_WARNING("Changed partition in the z direction to nz = " << n << endl);
}
if (dim == 2) nz = 1;
int nxyz[3] = {nx,ny,nz};
nrpatch = nx*ny*nz;
Vector pmin, pmax;
mesh->GetBoundingBox(pmin, pmax);
double h = GetUniformMeshElementSize(mesh);
element_map.resize(nrpatch);
double ppt[dim];
Vector pt(ppt, dim);
int nrelem = mesh->GetNE();
for (int el = 0; el < nrelem; el++)
{
mesh->GetElementTransformation(el)->Transform(
Geometries.GetCenter(mesh->GetElementBaseGeometry(el)), pt);
// Given the center coordinates determine the patches that this element contributes to
Array<int> idx0(dim);
Array<int> idx1(dim);
Array<int> idx2(dim);
vector<Array<int>> idx(3);
if (dim == 2) idx[2].Append(0);
for (int i = 0; i<dim; i++)
{
idx0[i] = (int)floor(nxyz[i]*((pt(i) - pmin[i])/(pmax[i] - pmin[i])));
idx1[i] = (int)floor(nxyz[i]*((pt(i)-2*h - pmin[i])/(pmax[i] - pmin[i])));
idx2[i] = (int)floor(nxyz[i]*((pt(i)-h - pmin[i])/(pmax[i] - pmin[i])));
if (idx0[i] < 0) idx0[i] = 0;
if (idx0[i] >= nxyz[i]) idx0[i] = nxyz[i]-1;
if (idx1[i] < 0) idx1[i] = 0;
if (idx1[i] >= nxyz[i]) idx1[i] = nxyz[i]-1;
if (idx2[i] < 0) idx2[i] = 0;
if (idx2[i] >= nxyz[i]) idx2[i] = nxyz[i]-1;
// convenient to put in one list
idx[i].Append(idx0[i]);
if (idx1[i] != idx0[i]) idx[i].Append(idx1[i]);
if (idx2[i] != idx0[i] && idx2[i] != idx1[i]) idx[i].Append(idx2[i]);
}
// Now loop through all the combinations according to the idx above
// in case of dim = 2 then kk = 0
for (int k=0; k<idx[2].Size(); k++)
{
int kk = idx[2][k];
for (int j=0; j<idx[1].Size(); j++)
{
int jj = idx[1][j];
for (int i=0; i<idx[0].Size(); i++)
{
int ii = idx[0][i];
int ip = kk*nxyz[0]*nxyz[1] + jj*nxyz[0]+ii;
element_map[ip].Append(el);
}
}
}
}
}
// constructor
CartesianMeshPartition::CartesianMeshPartition(Mesh *mesh_) : mesh(mesh_)
{
int dim = mesh->Dimension();
nx = 5;
ny = 1;
nz = 1;
int nxyz[3] = {nx,ny,nz};
nrpatch = nx*ny*nz;
Vector pmin, pmax;
mesh->GetBoundingBox(pmin, pmax);
int nrelem = mesh->GetNE();
int partitioning[nrelem];
// determine the partitioning using the centers of the elements
double ppt[dim];
Vector pt(ppt, dim);
for (int el = 0; el < nrelem; el++)
{
mesh->GetElementTransformation(el)->Transform(
Geometries.GetCenter(mesh->GetElementBaseGeometry(el)), pt);
int part = 0;
for (int i = dim-1; i >= 0; i--)
{
int idx = (int)floor(nxyz[i]*((pt(i) - pmin[i])/(pmax[i] - pmin[i])));
if (idx < 0)
{
idx = 0;
}
if (idx >= nxyz[i])
{
idx = nxyz[i]-1;
}
part = part * nxyz[i] + idx;
}
partitioning[el] = part;
}
element_map.resize(nrpatch);
for (int iel = 0; iel < nrelem; iel++)
{
int ip = partitioning[iel];
element_map[ip].Append(iel);
}
}
STPOverlappingCartesianMeshPartition::STPOverlappingCartesianMeshPartition(Mesh *mesh_) : mesh(mesh_)
{
int dim = mesh->Dimension();
nx = 9;
ny = 1;
nz = 1;
int nxyz[3] = {nx,ny,nz};
// nrpatch = nx*ny*nz;
Vector pmin, pmax;
mesh->GetBoundingBox(pmin, pmax);
int nrelem = mesh->GetNE();
int partitioning[nrelem];
// determine the partitioning using the centers of the elements
double ppt[dim];
Vector pt(ppt, dim);
for (int el = 0; el < nrelem; el++)
{
mesh->GetElementTransformation(el)->Transform(
Geometries.GetCenter(mesh->GetElementBaseGeometry(el)), pt);
int part = 0;
for (int i = dim-1; i >= 0; i--)
{
int idx = (int)floor(nxyz[i]*((pt(i) - pmin[i])/(pmax[i] - pmin[i])));
if (idx < 0)
{
idx = 0;
}
if (idx >= nxyz[i])
{
idx = nxyz[i]-1;
}
part = part * nxyz[i] + idx;
}
partitioning[el] = part;
}
// element_map.resize(nrpatch);
// for (int iel = 0; iel < nrelem; iel++)
// {
// int ip = partitioning[iel];
// element_map[ip].Append(iel);
// }
// // Append the next subdomain to the previous
// for (int ip = 0; ip<nrpatch-1; ip++)
// {
// element_map[ip].Append(element_map[ip+1]);
// }
std::vector<Array<int>> elem_map;
int npatch = nx*ny*nz;
elem_map.resize(npatch);
for (int iel = 0; iel < nrelem; iel++)
{
int ip = partitioning[iel];
elem_map[ip].Append(iel);
}
// Append the next subdomain to the previous
nrpatch = nx*ny*nz-1;
element_map.resize(nrpatch);
for (int ip = 0; ip<nrpatch; ip++)
{
element_map[ip].Append(elem_map[ip]);
element_map[ip].Append(elem_map[ip+1]);
}
}
// constructor
VertexMeshPartition::VertexMeshPartition(Mesh *mesh_) : mesh(mesh_)
{
nrpatch = mesh->GetNV();
element_map.resize(nrpatch);
//every element will contribute to the the patches of its vertices
// loop through the elements
int nrelems = mesh->GetNE();
for (int iel=0; iel<nrelems; ++iel)
{
// get element vertex index
Array<int> vertices;
mesh->GetElementVertices(iel,vertices);
int nrvert = vertices.Size();
// fill in the element contribution lists
for (int iv = 0; iv< nrvert; ++iv)
{
int ip = vertices[iv];
element_map[ip].Append(iel);
}
}
}
MeshPartition::MeshPartition(Mesh* mesh_, int part): mesh(mesh_)
{
partition_kind = part;
if (part == 1)
{
cout << "Non Overlapping Cartesian Partition " << endl;
CartesianMeshPartition partition(mesh);
element_map = partition.element_map;
nx = partition.nx;
ny = partition.ny;
nz = partition.nz;
}
// else if (part == 3 || part == 4)
else if (part == 2)
{
cout << "Overlapping Cartesian Partition " << endl;
OverlappingCartesianMeshPartition partition(mesh);
element_map = partition.element_map;
nx = partition.nx;
ny = partition.ny;
nz = partition.nz;
}
else if (part == 3 || part == 4)
// else if (part == 2)
{
cout << "STP Overlapping Cartesian Partition " << endl;
STPOverlappingCartesianMeshPartition partition(mesh);
element_map = partition.element_map;
nx = partition.nx;
ny = partition.ny;
nz = partition.nz;
}
else
{
cout << "Overlapping Vertex based partition " << endl;
VertexMeshPartition partition(mesh);
element_map = partition.element_map;
partition_kind = 0;
}
nrpatch = element_map.size();
int dim = mesh->Dimension();
patch_mesh.SetSize(nrpatch);
for (int ip = 0; ip<nrpatch; ++ip)
{
int patch_nrelems = element_map[ip].Size();
element_map[ip].SetSize(patch_nrelems);
// need to ensure that a vertex is not added more than once
// and that the ordering of vertices is known for when the element is added
// create a list of for this patch including possible repetitions
// loop through elements in the patch
Array<int> patch_vertices;
for (int iel=0; iel<patch_nrelems; ++iel)
{
// get the vertices list for the element
Array<int> elem_vertices;
int iel_idx = element_map[ip][iel];
mesh->GetElementVertices(iel_idx,elem_vertices);
patch_vertices.Append(elem_vertices);
}
patch_vertices.Sort();
patch_vertices.Unique();
int patch_nrvertices = patch_vertices.Size();
// create the mesh
patch_mesh[ip] = new Mesh(dim,patch_nrvertices,patch_nrelems);
// Add the vertices
for (int iv = 0; iv<patch_nrvertices; ++iv)
{
int vert_idx = patch_vertices[iv];
patch_mesh[ip]->AddVertex(mesh->GetVertex(vert_idx));
}
// Add the elements (for now search through all the vertices in the patch is needed)
for (int iel=0; iel<patch_nrelems; ++iel)
{
// get the vertices list for the element
Array<int> elem_vertices;
int iel_idx = element_map[ip][iel];
mesh->GetElementVertices(iel_idx,elem_vertices);
int nrvert = elem_vertices.Size();
int ind[nrvert];
for (int iv = 0; iv<nrvert; ++iv)
{
ind[iv] = patch_vertices.FindSorted(elem_vertices[iv]);
}
mfem::Element::Type elem_type = mesh->GetElementType(element_map[ip][iel]);
AddElementToMesh(patch_mesh[ip],elem_type,ind);
}
patch_mesh[ip]->FinalizeTopology();
}
}
void MeshPartition::AddElementToMesh(Mesh * mesh,mfem::Element::Type elem_type,
int * ind)
{
switch (elem_type)
{
case Element::QUADRILATERAL:
mesh->AddQuad(ind);
break;
case Element::TRIANGLE :
mesh->AddTri(ind);
break;
case Element::HEXAHEDRON :
mesh->AddHex(ind);
break;
case Element::TETRAHEDRON :
mesh->AddTet(ind);
break;
default:
MFEM_ABORT("Unknown element type");
break;
}
}
void MeshPartition::PrintElementMap()
{
mfem::out << "Element map" << endl;
for (int ip = 0; ip<nrpatch; ++ip)
{
mfem::out << "Patch No: " << ip;
mfem::out << ", element map: " ;
element_map[ip].Print(cout,element_map[ip].Size());
}
}
void SaveMeshPartition(Array<Mesh *> meshes, string mfilename, string sfilename)
{
int nrmeshes = meshes.Size();
for (int ip = 0; ip<nrmeshes; ++ip)
{
cout << "saving mesh no " << ip << endl;
ostringstream mesh_name;
mesh_name << mfilename << setfill('0') << setw(6) << ip;
ofstream mesh_ofs(mesh_name.str().c_str());
mesh_ofs.precision(8);
meshes[ip]->Print(mesh_ofs);
L2_FECollection L2fec(1,meshes[ip]->Dimension());
FiniteElementSpace L2fes(meshes[ip], &L2fec);
GridFunction x(&L2fes);
ConstantCoefficient alpha((double)ip);
x.ProjectCoefficient(alpha);
ostringstream sol_name;
sol_name << sfilename << setfill('0') << setw(6) << ip;
ofstream sol_ofs(sol_name.str().c_str());
x.Save(sol_ofs);
}
}
MeshPartition::~MeshPartition()
{
for (int ip = 0; ip<nrpatch; ++ip)
{
delete patch_mesh[ip];
patch_mesh[ip] = nullptr;
}
patch_mesh.DeleteAll();
}
// constructor
PatchAssembly::PatchAssembly(BilinearForm *bf_, Array<int> & ess_tdofs, int part) : bf(bf_)
{
fespace = bf->FESpace();
Mesh * mesh = fespace->GetMesh();
const FiniteElementCollection *fec = fespace->FEColl();
// list of dofs to distiguish between interior/boundary and essential
Array<int> global_tdofs(fespace->GetTrueVSize());
Array<int> bdr_tdofs(fespace->GetTrueVSize());
global_tdofs = 0;
// Mark boundary dofs and ess_dofs
if (mesh->bdr_attributes.Size())
{
Array<int> ess_bdr(mesh->bdr_attributes.Max());
ess_bdr = 1;
fespace->GetEssentialTrueDofs(ess_bdr, bdr_tdofs);
}
// mark boundary dofs
for (int i = 0; i<bdr_tdofs.Size(); i++) global_tdofs[bdr_tdofs[i]] = 1;
// overwrite flag for essential dofs
for (int i = 0; i<ess_tdofs.Size(); i++) global_tdofs[ess_tdofs[i]] = 0;
MeshPartition * p = new MeshPartition(mesh, part);
// SaveMeshPartition(p->patch_mesh);
nrpatch = p->nrpatch;
patch_fespaces.SetSize(nrpatch);
patch_dof_map.resize(nrpatch);
patch_mat.SetSize(nrpatch);
patch_mat_inv.SetSize(nrpatch);
ess_tdof_list.resize(nrpatch);
ess_int_tdofs.resize(nrpatch);
for (int ip=0; ip<nrpatch; ++ip)
{
// create finite element spaces for each patch
patch_fespaces[ip] = new FiniteElementSpace(p->patch_mesh[ip],fec);
// construct the patch tdof to global tdof map
int nrdof = patch_fespaces[ip]->GetTrueVSize();
patch_dof_map[ip].SetSize(nrdof);
// loop through the elements in the patch
for (int iel = 0; iel<p->element_map[ip].Size(); ++iel)
{
// index in the global mesh
int iel_idx = p->element_map[ip][iel];
// get the dofs of this element
Array<int> patch_elem_dofs;
Array<int> global_elem_dofs;
patch_fespaces[ip]->GetElementDofs(iel,patch_elem_dofs);
fespace->GetElementDofs(iel_idx,global_elem_dofs);
// the sizes have to match
MFEM_VERIFY(patch_elem_dofs.Size() == global_elem_dofs.Size(),
"Size inconsistency");
// loop through the dofs and take into account the signs;
int ndof = patch_elem_dofs.Size();
for (int i = 0; i<ndof; ++i)
{
int pdof_ = patch_elem_dofs[i];
int gdof_ = global_elem_dofs[i];
int pdof = (pdof_ >= 0) ? pdof_ : abs(pdof_) - 1;
int gdof = (gdof_ >= 0) ? gdof_ : abs(gdof_) - 1;
patch_dof_map[ip][pdof] = gdof;
}
}
// Define the patch bilinear form and apply boundary conditions (only the LHS)
Array <int> ess_temp_list;
if (p->patch_mesh[ip]->bdr_attributes.Size())
{
Array<int> ess_bdr(p->patch_mesh[ip]->bdr_attributes.Max());
ess_bdr = 1;
patch_fespaces[ip]->GetEssentialTrueDofs(ess_bdr, ess_temp_list);
}
// Adjust the essential tdof list for each patch
for (int i=0; i<ess_temp_list.Size(); i++)
{
int ldof = ess_temp_list[i];
int tdof = patch_dof_map[ip][ldof];
// check the kind of this tdof
if (!global_tdofs[tdof]) ess_tdof_list[ip].Append(ldof);
}
BilinearForm a(patch_fespaces[ip], bf);
a.Assemble();
OperatorPtr Alocal;
a.FormSystemMatrix(ess_tdof_list[ip],Alocal);
delete patch_fespaces[ip];
patch_mat[ip] = new SparseMatrix((SparseMatrix&)(*Alocal));
patch_mat[ip]->Threshold(0.0);
// Save the inverse
patch_mat_inv[ip] = new KLUSolver;
patch_mat_inv[ip]->SetOperator(*patch_mat[ip]);
}
delete p;
}
void PatchAssembly::print_patch_dof_map()
{
mfem::out << "Patch dof map" << endl;
for (int ip = 0; ip<nrpatch; ++ip)
{
mfem::out << "Patch No: " << ip;
mfem::out << ", dof map: " ;
patch_dof_map[ip].Print(cout,patch_dof_map[ip].Size());
}
}
PatchAssembly::~PatchAssembly()
{
for (int ip=0; ip<nrpatch; ++ip)
{
// delete patch_fespaces[ip]; patch_fespaces[ip]=nullptr;
delete patch_mat_inv[ip];
patch_mat_inv[ip]=nullptr;
delete patch_mat[ip];
patch_mat[ip]=nullptr;
}
patch_fespaces.DeleteAll();
patch_mat.DeleteAll();
patch_mat_inv.DeleteAll();
}
AddSchwarz::AddSchwarz(BilinearForm * bf_, Array<int> & global_ess_tdof_list, int i)
: Solver(bf_->FESpace()->GetTrueVSize(), bf_->FESpace()->GetTrueVSize()),
part(i)
{
p = new PatchAssembly(bf_, global_ess_tdof_list, part);
nrpatch = p->nrpatch;
}
void AddSchwarz::Mult(const Vector &r, Vector &z) const
{
z = 0.0;
Vector rnew(r);
Vector znew(z);
Vector raux(znew.Size());
Vector res_local, sol_local;
for (int iter = 0; iter < maxit; iter++)
{
znew = 0.0;
for (int ip = 0; ip < nrpatch; ip++)
{
Array<int> * dof_map = &p->patch_dof_map[ip];
int ndofs = dof_map->Size();
res_local.SetSize(ndofs);
sol_local.SetSize(ndofs);
rnew.GetSubVector(*dof_map, res_local);
Array<int> ess_bdr_indices = p->ess_tdof_list[ip];
// for the overlapping case
// zero out the entries corresponding to the ess_bdr
p->patch_mat_inv[ip]->Mult(res_local, sol_local);
if (!part) { sol_local.SetSubVector(ess_bdr_indices,0.0); }
znew.AddElementVector(*dof_map,sol_local);
}
// Relaxation parameter
znew *= theta;
z += znew;
// Update residual
if (iter + 1 < maxit)
{
A->Mult(znew, raux);
rnew -= raux;
}
}
}
AddSchwarz::~AddSchwarz()
{
delete p;
}
double GetUniformMeshElementSize(Mesh * mesh)
{
int dim = mesh->Dimension();
int nrelem = mesh->GetNE();
DenseMatrix J(dim);
double hmin, hmax;
hmin = infinity();
hmax = -infinity();
Vector attr(nrelem);
for (int iel=0; iel<nrelem; ++iel)
{
int geom = mesh->GetElementBaseGeometry(iel);
ElementTransformation *T = mesh->GetElementTransformation(iel);
T->SetIntPoint(&Geometries.GetCenter(geom));
Geometries.JacToPerfJac(geom, T->Jacobian(), J);
attr(iel) = J.Det();
attr(iel) = pow(abs(attr(iel)), 1.0/double(dim));
hmin = min(hmin, attr(iel));
hmax = max(hmax, attr(iel));
}
MFEM_VERIFY(abs(hmin-hmax) < 1e-12, "Case not supported yet")
return hmax;
}
Mesh * ExtendMesh(Mesh * mesh, const Array<int> & directions)
{
// extrute on one dimension
// flag = 1 +x, -1 -x, 2 +y, -2 +y , 3 +z, -3, -z
// copy the original mesh;
Mesh * mesh_orig = new Mesh(*mesh);
if (!directions.Size()) return mesh_orig;
int dim = mesh_orig->Dimension();
Mesh * mesh_ext=nullptr;
for (int j=0; j<directions.Size(); j++)
{
int d = directions[j];
MFEM_VERIFY(abs(d)<= dim, "Cannot Extend in dimension " << d << ". Dim = " << dim << endl);
Vector pmin;
Vector pmax;
mesh_orig->GetBoundingBox(pmin,pmax);
// DenseMatrix J(dim);
// double hmin, hmax;
// hmin = infinity();
// hmax = -infinity();
// Vector attr(nrelem);
// // element size
// for (int iel=0; iel<nrelem; ++iel)
// {
// int geom = mesh_orig->GetElementBaseGeometry(iel);
// ElementTransformation *T = mesh_orig->GetElementTransformation(iel);
// T->SetIntPoint(&Geometries.GetCenter(geom));
// Geometries.JacToPerfJac(geom, T->Jacobian(), J);
// attr(iel) = J.Det();
// attr(iel) = pow(abs(attr(iel)), 1.0/double(dim));
// hmin = min(hmin, attr(iel));
// hmax = max(hmax, attr(iel));
// }
// MFEM_VERIFY(hmin==hmax, "Case not supported yet")
double h = GetUniformMeshElementSize(mesh_orig);
double val;
// find the vertices on the specific boundary
switch (d)
{
case 1:
val = pmax[0];
break;
case -1:
val = pmin[0];
h = -h;
break;
case 2:
val = pmax[1];
break;
case -2:
val = pmin[1];
h = -h;
break;
case 3:
val = pmax[2];
break;
case -3:
val = pmin[2];
h = -h;
break;
}
int k = 0;
for (int i = 0; i<mesh_orig->GetNV(); ++i)
{
double * coords = mesh_orig->GetVertex(i);
switch (abs(d))
{
case 1:
if (coords[0] == val) k++;
break;
case 2:
if (coords[1] == val) k++;
break;
case 3:
if (coords[2] == val) k++;
break;
}
}
int nrvertices = mesh_orig->GetNV() + k;
int nrelements = mesh_orig->GetNE() + pow(pow(k,1.0/(dim-1))-1.0,dim-1);
mesh_ext = new Mesh(dim, nrvertices, nrelements);
// Add existing vertices
Array<int> vmap(mesh_orig->GetNV()); vmap = 0;
k = mesh_orig->GetNV();
for (int i=0; i<mesh_orig->GetNV(); ++i)
{
double * vert = mesh_orig->GetVertex(i);
mesh_ext->AddVertex(vert);
switch (abs(d))
{
case 1:
if (vert[0] == val)
{
vmap[i] = k;
k++;
}
break;
case 2:
if (vert[1] == val)
{
vmap[i] = k;
k++;
}
break;
case 3:
if (vert[2] == val)
{
vmap[i] = k;
k++;
}
break;
}
}
// Add existing elements
for (int i=0; i<mesh_orig->GetNE(); ++i)
{
Array<int>ind;
mesh_orig->GetElementVertices(i,ind);
if (dim == 2)
{
mesh_ext->AddQuad(ind);
}
else if (dim == 3)
{
mesh_ext->AddHex(ind);
}
}
// Add new vertices
k = mesh_orig->GetNV();
for (int i=0; i<mesh_orig->GetNV(); ++i)
{
double * vert = mesh_orig->GetVertex(i);
switch (abs(d))
{
case 1:
if (vert[0] == val)
{
double coords[dim];
coords[0] = vert[0] + h;
coords[1] = vert[1];
if (dim == 3) coords[2] = vert[2];
mesh_ext->AddVertex(coords);
}
break;
case 2:
if (vert[1] == val)
{
double coords[dim];
coords[0] = vert[0];
coords[1] = vert[1] + h;
if (dim == 3) coords[2] = vert[2];
mesh_ext->AddVertex(coords);
}
break;
case 3:
if (vert[2] == val)
{
double coords[dim];
coords[0] = vert[0];
coords[1] = vert[1];
coords[2] = vert[2] + h;
mesh_ext->AddVertex(coords);
}
break;
}
}
// loop through boundary elements and extend in the given direction
for (int i=0; i<mesh_orig->GetNBE(); ++i)
{
Array<int> vertices;
mesh_orig->GetBdrElementVertices(i,vertices);
if (dim == 2)
{
int ind[4];
if (vmap[vertices[0]] && vmap[vertices[1]])
{
ind[0] = vmap[vertices[0]];
ind[1] = vmap[vertices[1]];
ind[2] = vertices[1];
ind[3] = vertices[0];
mesh_ext->AddQuad(ind);
}
}
else if (dim == 3)
{
int ind[8];
if (vmap[vertices[0]] && vmap[vertices[1]] && vmap[vertices[2]] && vmap[vertices[3]])
{
ind[0] = vmap[vertices[0]];
ind[1] = vmap[vertices[1]];
ind[2] = vmap[vertices[2]];
ind[3] = vmap[vertices[3]];
ind[4] = vertices[0];
ind[5] = vertices[1];
ind[6] = vertices[2];
ind[7] = vertices[3];
mesh_ext->AddHex(ind);
}
}
}
mesh_ext->FinalizeTopology();
if (j<directions.Size()-1)
{
delete mesh_orig;
mesh_orig = mesh_ext;
}
}
delete mesh_orig;
return mesh_ext;
}