void DGFiniteElement<D>::
CalcGradientMatrix (FlatMatrix<> gmat) const
{
IntegrationRule ir (this->ElementType(), 2*order);
Vector<> shape(ndof);
MatrixFixWidth<D> dshape(ndof);
Vector<> norms(ndof);
gmat = 0.0;
norms = 0.0;
for (int i = 0; i < ir.Size(); i++)
{
this -> CalcShape (ir[i], shape);
this -> CalcDShape (ir[i], dshape);
for (int j = 0; j < ndof; j++)
for (int k = 0; k < ndof; k++)
for (int l = 0; l < D; l++)
gmat(k*D+l, j) += ir[i].Weight() * dshape(j,l) * shape(k);
for (int j = 0; j < norms.Size(); j++)
norms(j) += ir[i].Weight() * sqr (shape(j));
}
for (int j = 0; j < ndof; j++)
gmat.Rows(D*j, D*(j+1)) /= norms(j);
}
void ScalarFiniteElement<D> ::
CalcShape (const IntegrationRule & ir,
SliceMatrix<> shape) const
{
for (int i = 0; i < ir.Size(); i++)
CalcShape (ir[i], shape.Col(i));
}
virtual void Do(LocalHeap & lh)
{
cout << "solve conservation equation" << endl;
// prepare ...
const L2HighOrderFESpace & fes =
dynamic_cast<const L2HighOrderFESpace&> (*gfu->GetFESpace());
int ne = ma->GetNE();
int nf = ma->GetNFacets();
elementdata.SetSize (ne);
facetdata.SetSize (nf);
ConstantCoefficientFunction one(1);
MassIntegrator<D> bfi(&one);
for (int i = 0; i < ne; i++)
{
HeapReset hr(lh);
const DGFiniteElement<D> & fel = dynamic_cast<const DGFiniteElement<D>&> (fes.GetFE (i, lh));
const IntegrationRule ir(fel.ElementType(), 2*fel.Order());
const_cast<DGFiniteElement<D>&> (fel).PrecomputeShapes (ir);
const_cast<DGFiniteElement<D>&> (fel).PrecomputeTrace ();
MappedIntegrationRule<D,D> mir(ir, ma->GetTrafo (i, 0, lh), lh);
elementdata[i] = new ElementData (fel.GetNDof(), ir.Size());
ElementData & edi = *elementdata[i];
cfflow -> Evaluate (mir, FlatMatrix<> (edi.flowip));
for (int j = 0; j < ir.Size(); j++)
{
Vec<D> flow = mir[j].GetJacobianInverse() * edi.flowip.Row(j);
flow *= ir[j].Weight() * mir[j].GetMeasure();
edi.flowip.Row(j) = flow;
}
FlatMatrix<> mass(fel.GetNDof(), lh);
bfi.CalcElementMatrix (fel, ma->GetTrafo(i, 0, lh), mass, lh);
CalcInverse (mass, edi.invmass);
}
Array<int> elnums, fnums, vnums;
for (int i = 0; i < nf; i++)
{
HeapReset hr(lh);
const DGFiniteElement<D-1> & felfacet =
dynamic_cast<const DGFiniteElement<D-1>&> (fes.GetFacetFE (i, lh));
IntegrationRule ir (felfacet.ElementType(), 2*felfacet.Order());
const_cast<DGFiniteElement<D-1>&> (felfacet).PrecomputeShapes (ir);
facetdata[i] = new FacetData (ir.Size());
FacetData & fai = *facetdata[i];
ma->GetFacetElements (i, elnums);
fai.elnr[1] = -1;
for (int j = 0; j < elnums.Size(); j++)
{
fai.elnr[j] = elnums[j];
ma->GetElFacets (elnums[j], fnums);
for (int k = 0; k < fnums.Size(); k++)
if (fnums[k] == i) fai.facetnr[j] = k;
}
ELEMENT_TYPE eltype = ma->GetElType(elnums[0]);
ma->GetElVertices (elnums[0], vnums);
Facet2ElementTrafo transform(eltype, vnums);
FlatVec<D> normal_ref = ElementTopology::GetNormals(eltype) [fai.facetnr[0]];
int nip = ir.Size();
// transform facet coordinates to element coordinates
IntegrationRule & irt = transform(fai.facetnr[0], ir, lh);
MappedIntegrationRule<D,D> mir(irt, ma->GetTrafo(elnums[0], 0, lh), lh);
FlatMatrixFixWidth<D> flowir(nip, lh);
cfflow -> Evaluate (mir, flowir);
for (int j = 0; j < nip; j++)
{
Vec<D> normal = Trans (mir[j].GetJacobianInverse()) * normal_ref;
fai.flown(j) = InnerProduct (normal, flowir.Row(j));
fai.flown(j) *= ir[j].Weight() * mir[j].GetJacobiDet();
}
}
FlatVector<> vecu = gfu->GetVector().FVDouble();
Vector<> conv(vecu.Size());
Vector<> w(vecu.Size());
Vector<> hu(vecu.Size());
#pragma omp parallel
{
LocalHeap lh2 = lh.Split();
for (double t = 0; t < tend; t += dt)
{
#pragma omp single
cout << "\rt = " << setw(6) << t << flush;
CalcConvection (vecu, conv, lh2);
SolveM (conv, w, lh2);
#pragma omp single
{
hu = vecu + (0.5*dt) * w;
}
CalcConvection (hu, conv, lh2);
SolveM (conv, w, lh2);
#pragma omp single
{
vecu += dt * w;
/*
cout << " time T/F/M [us] = "
<< 1e6 * timer_element.GetTime()/timer_element.GetCounts()/vecu.Size() << " / "
<< 1e6 * timer_facet.GetTime()/timer_facet.GetCounts()/vecu.Size() << " / "
<< 1e6 * timer_mass.GetTime()/timer_mass.GetCounts()/vecu.Size()
<< "\r";
*/
Ng_Redraw();
}
}
}
}
void CalcConvection (FlatVector<double> vecu, FlatVector<double> conv,
LocalHeap & lh)
{
const L2HighOrderFESpace & fes =
dynamic_cast<const L2HighOrderFESpace&> (*gfu->GetFESpace());
#pragma omp single
timer_element.Start();
int ne = ma->GetNE();
#pragma omp for
for (int i = 0; i < ne; i++)
{
HeapReset hr(lh);
const ScalarFiniteElement<D> & fel =
static_cast<const ScalarFiniteElement<D>&> (fes.GetFE (i, lh));
const IntegrationRule ir(fel.ElementType(), 2*fel.Order());
FlatMatrixFixWidth<D> flowip = elementdata[i]->flowip;
/*
// use this for time-dependent flow
MappedIntegrationRule<D,D> mir(ir, ma->GetTrafo (i, 0, lh), lh);
FlatMatrixFixWidth<D> flowip(mir.Size(), lh);
cfflow -> Evaluate (mir, flowip);
for (int j = 0; j < ir.Size(); j++)
{
Vec<D> flow = mir[j].GetJacobianInverse() * flowip.Row(j);
flow *= mir[j].GetWeight();
flowip.Row(j) = flow;
}
*/
IntRange dn = fes.GetElementDofs (i);
int nipt = ir.Size();
FlatVector<> elui(nipt, lh);
FlatMatrixFixWidth<D> flowui (nipt, lh);
fel.Evaluate (ir, vecu.Range (dn), elui);
flowui = flowip;
for (int k = 0; k < nipt; k++)
flowui.Row(k) *= elui(k);
fel.EvaluateGradTrans (ir, flowui, conv.Range(dn));
}
#pragma omp single
{
timer_element.Stop();
timer_facet.Start();
}
int nf = ma->GetNFacets();
#pragma omp for
for (int i = 0; i < nf; i++)
{
HeapReset hr(lh);
const FacetData & fai = *facetdata[i];
if (fai.elnr[1] != -1)
{
const DGFiniteElement<D> & fel1 =
static_cast<const DGFiniteElement<D>&> (fes.GetFE (fai.elnr[0], lh));
const DGFiniteElement<D> & fel2 =
static_cast<const DGFiniteElement<D>&> (fes.GetFE (fai.elnr[1], lh));
const DGFiniteElement<D-1> & felfacet =
static_cast<const DGFiniteElement<D-1>&> (fes.GetFacetFE (i, lh));
IntRange dn1 = fes.GetElementDofs (fai.elnr[0]);
IntRange dn2 = fes.GetElementDofs (fai.elnr[1]);
int ndoffacet = felfacet.GetNDof();
int ndof1 = fel1.GetNDof();
int ndof2 = fel2.GetNDof();
FlatVector<> aelu1(ndof1, lh), aelu2(ndof2, lh);
FlatVector<> trace1(ndoffacet, lh), trace2(ndoffacet, lh);
fel1.GetTrace (fai.facetnr[0], vecu.Range (dn1), trace1);
fel2.GetTrace (fai.facetnr[1], vecu.Range (dn2), trace2);
IntegrationRule ir(felfacet.ElementType(), 2*felfacet.Order());
int nip = ir.Size();
FlatVector<> flown = fai.flown;
FlatVector<> tracei1(nip, lh), tracei2(nip, lh);
FlatVector<> tracei(nip, lh);
felfacet.Evaluate (ir, trace1, tracei1);
felfacet.Evaluate (ir, trace2, tracei2);
for (int j = 0; j < nip; j++)
tracei(j) = flown(j) * ( (flown(j) > 0) ? tracei1(j) : tracei2(j) );
felfacet.EvaluateTrans (ir, tracei, trace1);
fel1.GetTraceTrans (fai.facetnr[0], trace1, aelu1);
fel2.GetTraceTrans (fai.facetnr[1], trace1, aelu2);
#pragma omp critical (addres)
{
conv.Range (dn1) -= aelu1;
conv.Range (dn2) += aelu2;
}
}
else
{
const DGFiniteElement<D> & fel1 =
dynamic_cast<const DGFiniteElement<D>&> (fes.GetFE (fai.elnr[0], lh));
const DGFiniteElement<D-1> & felfacet =
dynamic_cast<const DGFiniteElement<D-1>&> (fes.GetFacetFE (i, lh));
IntRange dn1 = fes.GetElementDofs (fai.elnr[0]);
int ndoffacet = felfacet.GetNDof();
int ndof1 = fel1.GetNDof();
FlatVector<> elu1(ndof1, lh);
FlatVector<> trace1(ndoffacet, lh);
fel1.GetTrace (fai.facetnr[0], vecu.Range (dn1), trace1);
IntegrationRule ir(felfacet.ElementType(), 2*felfacet.Order());
int nip = ir.Size();
FlatVector<> flown = fai.flown;
FlatVector<> tracei1(nip, lh), tracei(nip, lh);
felfacet.Evaluate (ir, trace1, tracei1);
for (int j = 0; j < nip; j++)
tracei(j) = flown(j) * ( (flown(j) > 0) ? tracei1(j) : 0 );
felfacet.EvaluateTrans (ir, tracei, trace1);
fel1.GetTraceTrans (fai.facetnr[0], trace1, elu1);
#pragma omp critical (addres)
{
conv.Range (dn1) -= elu1;
}
}
}
#pragma omp single
timer_facet.Stop();
}