/
fespace.cpp
1618 lines (1412 loc) · 39.6 KB
/
fespace.cpp
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// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
// reserved. See file COPYRIGHT for details.
//
// This file is part of the MFEM library. For more information and source code
// availability see http://mfem.org.
//
// MFEM is free software; you can redistribute it and/or modify it under the
// terms of the GNU Lesser General Public License (as published by the Free
// Software Foundation) version 2.1 dated February 1999.
// Implementation of FiniteElementSpace
#include "../mesh/mesh_headers.hpp"
#include "fem.hpp"
#include <cmath>
#include <cstdarg>
#include <limits>
using namespace std;
namespace mfem
{
template <> void Ordering::
DofsToVDofs<Ordering::byNODES>(int ndofs, int vdim, Array<int> &dofs)
{
// static method
int size = dofs.Size();
dofs.SetSize(size*vdim);
for (int vd = 1; vd < vdim; vd++)
{
for (int i = 0; i < size; i++)
{
dofs[i+size*vd] = Map<byNODES>(ndofs, vdim, dofs[i], vd);
}
}
}
template <> void Ordering::
DofsToVDofs<Ordering::byVDIM>(int ndofs, int vdim, Array<int> &dofs)
{
// static method
int size = dofs.Size();
dofs.SetSize(size*vdim);
for (int vd = vdim-1; vd >= 0; vd--)
{
for (int i = 0; i < size; i++)
{
dofs[i+size*vd] = Map<byVDIM>(ndofs, vdim, dofs[i], vd);
}
}
}
int FiniteElementSpace::GetOrder(int i) const
{
int GeomType = mesh->GetElementBaseGeometry(i);
return fec->FiniteElementForGeometry(GeomType)->GetOrder();
}
int FiniteElementSpace::GetFaceOrder(int i) const
{
int GeomType = mesh->GetFaceBaseGeometry(i);
return fec->FiniteElementForGeometry(GeomType)->GetOrder();
}
void FiniteElementSpace::DofsToVDofs (Array<int> &dofs, int ndofs) const
{
if (vdim == 1) { return; }
if (ndofs < 0) { ndofs = this->ndofs; }
if (ordering == Ordering::byNODES)
{
Ordering::DofsToVDofs<Ordering::byNODES>(ndofs, vdim, dofs);
}
else
{
Ordering::DofsToVDofs<Ordering::byVDIM>(ndofs, vdim, dofs);
}
}
void FiniteElementSpace::DofsToVDofs(int vd, Array<int> &dofs, int ndofs) const
{
if (vdim == 1) { return; }
if (ndofs < 0) { ndofs = this->ndofs; }
if (ordering == Ordering::byNODES)
{
for (int i = 0; i < dofs.Size(); i++)
{
dofs[i] = Ordering::Map<Ordering::byNODES>(ndofs, vdim, dofs[i], vd);
}
}
else
{
for (int i = 0; i < dofs.Size(); i++)
{
dofs[i] = Ordering::Map<Ordering::byVDIM>(ndofs, vdim, dofs[i], vd);
}
}
}
int FiniteElementSpace::DofToVDof(int dof, int vd, int ndofs) const
{
if (vdim == 1) { return dof; }
if (ndofs < 0) { ndofs = this->ndofs; }
if (ordering == Ordering::byNODES)
{
return Ordering::Map<Ordering::byNODES>(ndofs, vdim, dof, vd);
}
else
{
return Ordering::Map<Ordering::byVDIM>(ndofs, vdim, dof, vd);
}
}
// static function
void FiniteElementSpace::AdjustVDofs (Array<int> &vdofs)
{
int n = vdofs.Size(), *vdof = vdofs;
for (int i = 0; i < n; i++)
{
int j;
if ((j = vdof[i]) < 0)
{
vdof[i] = -1-j;
}
}
}
void FiniteElementSpace::GetElementVDofs(int i, Array<int> &vdofs) const
{
GetElementDofs(i, vdofs);
DofsToVDofs(vdofs);
}
void FiniteElementSpace::GetBdrElementVDofs(int i, Array<int> &vdofs) const
{
GetBdrElementDofs(i, vdofs);
DofsToVDofs(vdofs);
}
void FiniteElementSpace::GetFaceVDofs(int i, Array<int> &vdofs) const
{
GetFaceDofs(i, vdofs);
DofsToVDofs(vdofs);
}
void FiniteElementSpace::GetEdgeVDofs(int i, Array<int> &vdofs) const
{
GetEdgeDofs(i, vdofs);
DofsToVDofs(vdofs);
}
void FiniteElementSpace::GetVertexVDofs(int i, Array<int> &vdofs) const
{
GetVertexDofs(i, vdofs);
DofsToVDofs(vdofs);
}
void FiniteElementSpace::GetElementInteriorVDofs(int i, Array<int> &vdofs) const
{
GetElementInteriorDofs(i, vdofs);
DofsToVDofs(vdofs);
}
void FiniteElementSpace::GetEdgeInteriorVDofs(int i, Array<int> &vdofs) const
{
GetEdgeInteriorDofs(i, vdofs);
DofsToVDofs(vdofs);
}
void FiniteElementSpace::BuildElementToDofTable() const
{
if (elem_dof) { return; }
Table *el_dof = new Table;
Array<int> dofs;
el_dof -> MakeI (mesh -> GetNE());
for (int i = 0; i < mesh -> GetNE(); i++)
{
GetElementDofs (i, dofs);
el_dof -> AddColumnsInRow (i, dofs.Size());
}
el_dof -> MakeJ();
for (int i = 0; i < mesh -> GetNE(); i++)
{
GetElementDofs (i, dofs);
el_dof -> AddConnections (i, (int *)dofs, dofs.Size());
}
el_dof -> ShiftUpI();
elem_dof = el_dof;
}
void FiniteElementSpace::RebuildElementToDofTable()
{
delete elem_dof;
elem_dof = NULL;
BuildElementToDofTable();
}
void FiniteElementSpace::ReorderElementToDofTable()
{
Array<int> dof_marker(ndofs);
dof_marker = -1;
int *J = elem_dof->GetJ(), nnz = elem_dof->Size_of_connections();
for (int k = 0, dof_counter = 0; k < nnz; k++)
{
const int sdof = J[k]; // signed dof
const int dof = (sdof < 0) ? -1-sdof : sdof;
int new_dof = dof_marker[dof];
if (new_dof < 0)
{
dof_marker[dof] = new_dof = dof_counter++;
}
J[k] = (sdof < 0) ? -1-new_dof : new_dof; // preserve the sign of sdof
}
}
void FiniteElementSpace::BuildDofToArrays()
{
if (dof_elem_array.Size()) { return; }
BuildElementToDofTable();
dof_elem_array.SetSize (ndofs);
dof_ldof_array.SetSize (ndofs);
dof_elem_array = -1;
for (int i = 0; i < mesh -> GetNE(); i++)
{
const int *dofs = elem_dof -> GetRow(i);
const int n = elem_dof -> RowSize(i);
for (int j = 0; j < n; j++)
{
if (dof_elem_array[dofs[j]] < 0)
{
dof_elem_array[dofs[j]] = i;
dof_ldof_array[dofs[j]] = j;
}
}
}
}
static void mark_dofs(const Array<int> &dofs, Array<int> &mark_array)
{
for (int i = 0; i < dofs.Size(); i++)
{
int k = dofs[i];
if (k < 0) { k = -1 - k; }
mark_array[k] = -1;
}
}
void FiniteElementSpace::GetEssentialVDofs(const Array<int> &bdr_attr_is_ess,
Array<int> &ess_vdofs,
int component) const
{
Array<int> vdofs, dofs;
ess_vdofs.SetSize(GetVSize());
ess_vdofs = 0;
for (int i = 0; i < GetNBE(); i++)
{
if (bdr_attr_is_ess[GetBdrAttribute(i)-1])
{
if (component < 0)
{
// Mark all components.
GetBdrElementVDofs(i, vdofs);
mark_dofs(vdofs, ess_vdofs);
}
else
{
GetBdrElementDofs(i, dofs);
for (int d = 0; d < dofs.Size(); d++)
{ dofs[d] = DofToVDof(dofs[d], component); }
mark_dofs(dofs, ess_vdofs);
}
}
}
// mark possible hidden boundary edges in a non-conforming mesh, also
// local DOFs affected by boundary elements on other processors
if (mesh->ncmesh)
{
Array<int> bdr_verts, bdr_edges;
mesh->ncmesh->GetBoundaryClosure(bdr_attr_is_ess, bdr_verts, bdr_edges);
for (int i = 0; i < bdr_verts.Size(); i++)
{
if (component < 0)
{
GetVertexVDofs(bdr_verts[i], vdofs);
mark_dofs(vdofs, ess_vdofs);
}
else
{
GetVertexDofs(bdr_verts[i], dofs);
for (int d = 0; d < dofs.Size(); d++)
{ dofs[d] = DofToVDof(dofs[d], component); }
mark_dofs(dofs, ess_vdofs);
}
}
for (int i = 0; i < bdr_edges.Size(); i++)
{
if (component < 0)
{
GetEdgeVDofs(bdr_edges[i], vdofs);
mark_dofs(vdofs, ess_vdofs);
}
else
{
GetEdgeDofs(bdr_edges[i], dofs);
for (int d = 0; d < dofs.Size(); d++)
{ dofs[d] = DofToVDof(dofs[d], component); }
mark_dofs(dofs, ess_vdofs);
}
}
}
}
void FiniteElementSpace::GetEssentialTrueDofs(const Array<int> &bdr_attr_is_ess,
Array<int> &ess_tdof_list,
int component)
{
Array<int> ess_vdofs, ess_tdofs;
GetEssentialVDofs(bdr_attr_is_ess, ess_vdofs, component);
const SparseMatrix *R = GetConformingRestriction();
if (!R)
{
ess_tdofs.MakeRef(ess_vdofs);
}
else
{
R->BooleanMult(ess_vdofs, ess_tdofs);
}
MarkerToList(ess_tdofs, ess_tdof_list);
}
// static method
void FiniteElementSpace::MarkerToList(const Array<int> &marker,
Array<int> &list)
{
int num_marked = 0;
for (int i = 0; i < marker.Size(); i++)
{
if (marker[i]) { num_marked++; }
}
list.SetSize(0);
list.Reserve(num_marked);
for (int i = 0; i < marker.Size(); i++)
{
if (marker[i]) { list.Append(i); }
}
}
// static method
void FiniteElementSpace::ListToMarker(const Array<int> &list, int marker_size,
Array<int> &marker, int mark_val)
{
marker.SetSize(marker_size);
marker = 0;
for (int i = 0; i < list.Size(); i++)
{
marker[list[i]] = mark_val;
}
}
void FiniteElementSpace::ConvertToConformingVDofs(const Array<int> &dofs,
Array<int> &cdofs)
{
GetConformingProlongation();
if (cP) { cP->BooleanMultTranspose(dofs, cdofs); }
else { dofs.Copy(cdofs); }
}
void FiniteElementSpace::ConvertFromConformingVDofs(const Array<int> &cdofs,
Array<int> &dofs)
{
GetConformingRestriction();
if (cR) { cR->BooleanMultTranspose(cdofs, dofs); }
else { cdofs.Copy(dofs); }
}
SparseMatrix *
FiniteElementSpace::D2C_GlobalRestrictionMatrix (FiniteElementSpace *cfes)
{
int i, j;
Array<int> d_vdofs, c_vdofs;
SparseMatrix *R;
R = new SparseMatrix (cfes -> GetVSize(), GetVSize());
for (i = 0; i < mesh -> GetNE(); i++)
{
this -> GetElementVDofs (i, d_vdofs);
cfes -> GetElementVDofs (i, c_vdofs);
#ifdef MFEM_DEBUG
if (d_vdofs.Size() != c_vdofs.Size())
{
mfem_error ("FiniteElementSpace::D2C_GlobalRestrictionMatrix (...)");
}
#endif
for (j = 0; j < d_vdofs.Size(); j++)
{
R -> Set (c_vdofs[j], d_vdofs[j], 1.0);
}
}
R -> Finalize();
return R;
}
SparseMatrix *
FiniteElementSpace::D2Const_GlobalRestrictionMatrix(FiniteElementSpace *cfes)
{
int i, j;
Array<int> d_dofs, c_dofs;
SparseMatrix *R;
R = new SparseMatrix (cfes -> GetNDofs(), ndofs);
for (i = 0; i < mesh -> GetNE(); i++)
{
this -> GetElementDofs (i, d_dofs);
cfes -> GetElementDofs (i, c_dofs);
#ifdef MFEM_DEBUG
if (c_dofs.Size() != 1)
mfem_error ("FiniteElementSpace::"
"D2Const_GlobalRestrictionMatrix (...)");
#endif
for (j = 0; j < d_dofs.Size(); j++)
{
R -> Set (c_dofs[0], d_dofs[j], 1.0);
}
}
R -> Finalize();
return R;
}
SparseMatrix *
FiniteElementSpace::H2L_GlobalRestrictionMatrix (FiniteElementSpace *lfes)
{
SparseMatrix *R;
DenseMatrix loc_restr;
Array<int> l_dofs, h_dofs;
R = new SparseMatrix (lfes -> GetNDofs(), ndofs);
if (!lfes->GetNE())
{
R->Finalize();
return R;
}
const FiniteElement *h_fe = this -> GetFE (0);
const FiniteElement *l_fe = lfes -> GetFE (0);
IsoparametricTransformation T;
T.SetIdentityTransformation(h_fe->GetGeomType());
h_fe->Project(*l_fe, T, loc_restr);
for (int i = 0; i < mesh -> GetNE(); i++)
{
this -> GetElementDofs (i, h_dofs);
lfes -> GetElementDofs (i, l_dofs);
R -> SetSubMatrix (l_dofs, h_dofs, loc_restr, 1);
}
R -> Finalize();
return R;
}
static void AddDependencies(SparseMatrix& deps, Array<int>& master_dofs,
Array<int>& slave_dofs, DenseMatrix& I)
{
for (int i = 0; i < slave_dofs.Size(); i++)
{
int sdof = slave_dofs[i];
if (!deps.RowSize(sdof)) // not processed yet?
{
for (int j = 0; j < master_dofs.Size(); j++)
{
double coef = I(i, j);
if (std::abs(coef) > 1e-12)
{
int mdof = master_dofs[j];
if (mdof != sdof && mdof != (-1-sdof))
{
deps.Add(sdof, mdof, coef);
}
}
}
}
}
}
static bool DofFinalizable(int dof, const Array<bool>& finalized,
const SparseMatrix& deps)
{
const int* dep = deps.GetRowColumns(dof);
int ndep = deps.RowSize(dof);
// are all constraining DOFs finalized?
for (int i = 0; i < ndep; i++)
{
if (!finalized[dep[i]]) { return false; }
}
return true;
}
/** This is a helper function to get edge (type == 0) or face (type == 1) DOFs.
The function is aware of ghost edges/faces in parallel, for which an empty
DOF list is returned. */
void FiniteElementSpace::GetEdgeFaceDofs(int type, int index, Array<int> &dofs)
const
{
dofs.SetSize(0);
if (type)
{
if (index < mesh->GetNFaces()) { GetFaceDofs(index, dofs); }
}
else
{
if (index < mesh->GetNEdges()) { GetEdgeDofs(index, dofs); }
}
}
void FiniteElementSpace::GetConformingInterpolation() const
{
#ifdef MFEM_USE_MPI
MFEM_VERIFY(dynamic_cast<const ParFiniteElementSpace*>(this) == NULL,
"This method should not be used with a ParFiniteElementSpace!");
#endif
if (cP_is_set) { return; }
cP_is_set = true;
// For each slave DOF, the dependency matrix will contain a row that
// expresses the slave DOF as a linear combination of its immediate master
// DOFs. Rows of independent DOFs will remain empty.
SparseMatrix deps(ndofs);
// collect local edge/face dependencies
for (int type = 0; type <= 1; type++)
{
const NCMesh::NCList &list = type ? mesh->ncmesh->GetFaceList()
/**/ : mesh->ncmesh->GetEdgeList();
if (!list.masters.size()) { continue; }
IsoparametricTransformation T;
if (type) { T.SetFE(&QuadrilateralFE); }
else { T.SetFE(&SegmentFE); }
int geom = type ? Geometry::SQUARE : Geometry::SEGMENT;
const FiniteElement* fe = fec->FiniteElementForGeometry(geom);
if (!fe) { continue; }
Array<int> master_dofs, slave_dofs;
DenseMatrix I(fe->GetDof());
// loop through all master edges/faces, constrain their slave edges/faces
for (unsigned mi = 0; mi < list.masters.size(); mi++)
{
const NCMesh::Master &master = list.masters[mi];
GetEdgeFaceDofs(type, master.index, master_dofs);
if (!master_dofs.Size()) { continue; }
for (int si = master.slaves_begin; si < master.slaves_end; si++)
{
const NCMesh::Slave &slave = list.slaves[si];
GetEdgeFaceDofs(type, slave.index, slave_dofs);
if (!slave_dofs.Size()) { continue; }
slave.OrientedPointMatrix(T.GetPointMat());
fe->GetLocalInterpolation(T, I);
// make each slave DOF dependent on all master DOFs
AddDependencies(deps, master_dofs, slave_dofs, I);
}
}
}
deps.Finalize();
// DOFs that stayed independent are true DOFs
int n_true_dofs = 0;
for (int i = 0; i < ndofs; i++)
{
if (!deps.RowSize(i)) { n_true_dofs++; }
}
// if all dofs are true dofs leave cP and cR NULL
if (n_true_dofs == ndofs)
{
cP = cR = NULL; // will be treated as identities
return;
}
// create the conforming restriction matrix cR
int *cR_J;
{
int *cR_I = new int[n_true_dofs+1];
double *cR_A = new double[n_true_dofs];
cR_J = new int[n_true_dofs];
for (int i = 0; i < n_true_dofs; i++)
{
cR_I[i] = i;
cR_A[i] = 1.0;
}
cR_I[n_true_dofs] = n_true_dofs;
cR = new SparseMatrix(cR_I, cR_J, cR_A, n_true_dofs, ndofs);
}
// create the conforming prolongation matrix cP
cP = new SparseMatrix(ndofs, n_true_dofs);
Array<bool> finalized(ndofs);
finalized = false;
// put identity in the restriction and prolongation matrices for true DOFs
for (int i = 0, true_dof = 0; i < ndofs; i++)
{
if (!deps.RowSize(i))
{
cR_J[true_dof] = i;
cP->Add(i, true_dof++, 1.0);
finalized[i] = true;
}
}
// Now calculate cP rows of slave DOFs as combinations of cP rows of their
// master DOFs. It is possible that some slave DOFs depend on DOFs that are
// themselves slaves. Here we resolve such indirect constraints by first
// calculating rows of the cP matrix for DOFs whose master DOF cP rows are
// already known (in the first iteration these are the true DOFs). In the
// second iteration, slaves of slaves can be 'finalized' (given a row in the
// cP matrix), in the third iteration slaves of slaves of slaves, etc.
bool finished;
int n_finalized = n_true_dofs;
Array<int> cols;
Vector srow;
do
{
finished = true;
for (int dof = 0; dof < ndofs; dof++)
{
if (!finalized[dof] && DofFinalizable(dof, finalized, deps))
{
const int* dep_col = deps.GetRowColumns(dof);
const double* dep_coef = deps.GetRowEntries(dof);
int n_dep = deps.RowSize(dof);
for (int j = 0; j < n_dep; j++)
{
cP->GetRow(dep_col[j], cols, srow);
srow *= dep_coef[j];
cP->AddRow(dof, cols, srow);
}
finalized[dof] = true;
n_finalized++;
finished = false;
}
}
}
while (!finished);
// if everything is consistent (mesh, face orientations, etc.), we should
// be able to finalize all slave DOFs, otherwise it's a serious error
if (n_finalized != ndofs)
{
MFEM_ABORT("Error creating cP matrix.");
}
cP->Finalize();
if (vdim > 1)
{
MakeVDimMatrix(*cP);
MakeVDimMatrix(*cR);
}
}
void FiniteElementSpace::MakeVDimMatrix(SparseMatrix &mat) const
{
if (vdim == 1) { return; }
int height = mat.Height();
int width = mat.Width();
SparseMatrix *vmat = new SparseMatrix(vdim*height, vdim*width);
Array<int> dofs, vdofs;
Vector srow;
for (int i = 0; i < height; i++)
{
mat.GetRow(i, dofs, srow);
for (int vd = 0; vd < vdim; vd++)
{
dofs.Copy(vdofs);
DofsToVDofs(vd, vdofs, width);
vmat->SetRow(DofToVDof(i, vd, height), vdofs, srow);
}
}
vmat->Finalize();
mat.Swap(*vmat);
delete vmat;
}
const SparseMatrix* FiniteElementSpace::GetConformingProlongation() const
{
if (Conforming()) { return NULL; }
if (!cP_is_set) { GetConformingInterpolation(); }
return cP;
}
const SparseMatrix* FiniteElementSpace::GetConformingRestriction() const
{
if (Conforming()) { return NULL; }
if (!cP_is_set) { GetConformingInterpolation(); }
return cR;
}
int FiniteElementSpace::GetNConformingDofs() const
{
const SparseMatrix* P = GetConformingProlongation();
return P ? (P->Width() / vdim) : ndofs;
}
SparseMatrix* FiniteElementSpace::RefinementMatrix(int old_ndofs,
const Table* old_elem_dof)
{
MFEM_VERIFY(mesh->GetLastOperation() == Mesh::REFINE, "");
MFEM_VERIFY(ndofs >= old_ndofs, "Previous space is not coarser.");
Array<int> dofs, old_dofs, old_vdofs;
Vector row;
const CoarseFineTransformations &rtrans = mesh->GetRefinementTransforms();
int geom = mesh->GetElementBaseGeometry(); // assuming the same geom
const FiniteElement *fe = fec->FiniteElementForGeometry(geom);
IsoparametricTransformation isotr;
isotr.SetIdentityTransformation(geom);
int nmat = rtrans.point_matrices.SizeK();
int ldof = fe->GetDof(); // assuming the same FE everywhere
// calculate local interpolation matrices for all refinement types
DenseTensor localP(ldof, ldof, nmat);
for (int i = 0; i < nmat; i++)
{
isotr.GetPointMat() = rtrans.point_matrices(i);
fe->GetLocalInterpolation(isotr, localP(i));
}
SparseMatrix *P = new SparseMatrix(ndofs*vdim, old_ndofs*vdim, ldof);
Array<int> mark(P->Height());
mark = 0;
for (int k = 0; k < mesh->GetNE(); k++)
{
const Embedding &emb = rtrans.embeddings[k];
DenseMatrix &lP = localP(emb.matrix);
elem_dof->GetRow(k, dofs);
old_elem_dof->GetRow(emb.parent, old_dofs);
for (int vd = 0; vd < vdim; vd++)
{
old_dofs.Copy(old_vdofs);
DofsToVDofs(vd, old_vdofs, old_ndofs);
for (int i = 0; i < ldof; i++)
{
int r = DofToVDof(dofs[i], vd);
int m = (r >= 0) ? r : (-1 - r);
if (!mark[m])
{
lP.GetRow(i, row);
P->SetRow(r, old_vdofs, row); // TODO: profiler says this is slow!
mark[m] = 1;
}
}
}
}
MFEM_ASSERT(mark.Sum() == P->Height(), "Not all rows of P set.");
return P;
}
void InvertLinearTrans(IsoparametricTransformation &trans,
const DenseMatrix &invdfdx,
const IntegrationPoint &pt, Vector &x)
{
// invert a linear transform with one Newton step
IntegrationPoint p0;
p0.Set3(0, 0, 0);
trans.Transform(p0, x);
double store[3];
Vector v(store, x.Size());
pt.Get(v, x.Size());
v -= x;
invdfdx.Mult(v, x);
}
void FiniteElementSpace::GetLocalDerefinementMatrices(
int geom, const CoarseFineTransformations &dt, DenseTensor &localR)
{
const FiniteElement *fe = fec->FiniteElementForGeometry(geom);
const IntegrationRule &nodes = fe->GetNodes();
LinearFECollection linfec;
IsoparametricTransformation isotr;
isotr.SetFE(linfec.FiniteElementForGeometry(geom));
int nmat = dt.point_matrices.SizeK();
int ldof = fe->GetDof();
int dim = mesh->Dimension();
DenseMatrix invdfdx(dim);
IntegrationPoint ipt;
Vector pt(&ipt.x, dim), shape(ldof);
// calculate local restriction matrices for all refinement types
localR.SetSize(ldof, ldof, nmat);
for (int i = 0; i < nmat; i++)
{
DenseMatrix &lR = localR(i);
lR = numeric_limits<double>::infinity(); // marks invalid rows
isotr.GetPointMat() = dt.point_matrices(i);
isotr.SetIntPoint(&nodes[0]);
CalcInverse(isotr.Jacobian(), invdfdx);
for (int j = 0; j < nodes.Size(); j++)
{
InvertLinearTrans(isotr, invdfdx, nodes[j], pt);
if (Geometries.CheckPoint(geom, ipt)) // do we need an epsilon here?
{
IntegrationPoint ip;
ip.Set(pt, dim);
fe->CalcShape(ip, shape); // TODO: H(curl), etc.?
MFEM_ASSERT(dynamic_cast<const NodalFiniteElement*>(fe),
"only nodal FEs are implemented");
lR.SetRow(j, shape);
}
}
}
}
SparseMatrix* FiniteElementSpace::DerefinementMatrix(int old_ndofs,
const Table* old_elem_dof)
{
MFEM_VERIFY(Nonconforming(), "Not implemented for conforming meshes.");
MFEM_VERIFY(old_ndofs, "Missing previous (finer) space.");
MFEM_VERIFY(ndofs <= old_ndofs, "Previous space is not finer.");
Array<int> dofs, old_dofs, old_vdofs;
Vector row;
const CoarseFineTransformations &dtrans =
mesh->ncmesh->GetDerefinementTransforms();
int geom = mesh->ncmesh->GetElementGeometry();
int ldof = fec->FiniteElementForGeometry(geom)->GetDof();
DenseTensor localR;
GetLocalDerefinementMatrices(geom, dtrans, localR);
SparseMatrix *R = new SparseMatrix(ndofs*vdim, old_ndofs*vdim, ldof);
Array<int> mark(R->Height());
mark = 0;
for (int k = 0; k < dtrans.embeddings.Size(); k++)
{
const Embedding &emb = dtrans.embeddings[k];
DenseMatrix &lR = localR(emb.matrix);
elem_dof->GetRow(emb.parent, dofs);
old_elem_dof->GetRow(k, old_dofs);
for (int vd = 0; vd < vdim; vd++)
{
old_dofs.Copy(old_vdofs);
DofsToVDofs(vd, old_vdofs, old_ndofs);
for (int i = 0; i < lR.Height(); i++)
{
if (lR(i, 0) == numeric_limits<double>::infinity()) { continue; }
int r = DofToVDof(dofs[i], vd);
int m = (r >= 0) ? r : (-1 - r);
if (!mark[m])
{
lR.GetRow(i, row);
R->SetRow(r, old_vdofs, row);
mark[m] = 1;
}
}
}
}
MFEM_ASSERT(mark.Sum() == R->Height(), "Not all rows of R set.");
return R;
}
FiniteElementSpace::FiniteElementSpace(Mesh *mesh,
const FiniteElementCollection *fec,
int vdim, int ordering)
{
this->mesh = mesh;
this->fec = fec;
this->vdim = vdim;
this->ordering = (Ordering::Type) ordering;
elem_dof = NULL;
sequence = mesh->GetSequence();
const NURBSFECollection *nurbs_fec =
dynamic_cast<const NURBSFECollection *>(fec);
if (nurbs_fec)
{
if (!mesh->NURBSext)
{
mfem_error("FiniteElementSpace::FiniteElementSpace :\n"
" NURBS FE space requires NURBS mesh.");
}
else
{
int Order = nurbs_fec->GetOrder();
if (mesh->NURBSext->GetOrder() == Order)
{
NURBSext = mesh->NURBSext;
own_ext = 0;
}
else
{
NURBSext = new NURBSExtension(mesh->NURBSext, Order);
own_ext = 1;
}
UpdateNURBS();
cP = cR = NULL;
cP_is_set = false;
T = NULL;
own_T = true;
}
}
else
{
NURBSext = NULL;
own_ext = 0;
Construct();
}
BuildElementToDofTable();
}
NURBSExtension *FiniteElementSpace::StealNURBSext()
{
if (NURBSext && !own_ext)
{
mfem_error("FiniteElementSpace::StealNURBSext");
}
own_ext = 0;
return NURBSext;
}
void FiniteElementSpace::UpdateNURBS()
{
nvdofs = 0;
nedofs = 0;
nfdofs = 0;
nbdofs = 0;
fdofs = NULL;
bdofs = NULL;
dynamic_cast<const NURBSFECollection *>(fec)->Reset();
ndofs = NURBSext->GetNDof();