bool SpatialDerivSpecifier::operator<(const SpatialDerivSpecifier& other) const
{
if (type() < other.type()) return true;
if (type() > other.type()) return false;
if (isPartial()) return mi() < other.mi();
if (isNormal()) return normalDerivOrder() < other.normalDerivOrder();
return false;
}
void Legendre::refEval(
const CellType& cellType,
const Array<Point>& pts,
const SpatialDerivSpecifier& sds,
Array<Array<Array<double> > >& result,
int verbosity) const
{
TEUCHOS_TEST_FOR_EXCEPTION(!(sds.isPartial() || sds.isIdentity()),
std::runtime_error,
"cannot evaluate spatial derivative " << sds << " on Legendre basis");
const MultiIndex& deriv = sds.mi();
typedef Array<double> Adouble;
result.resize(1);
result[0].resize(pts.length());
switch(cellType)
{
case PointCell:
result[0] = tuple<Adouble>(tuple(1.0));
return;
case LineCell:
for (int i=0; i<pts.length(); i++)
{
evalOnLine(pts[i], deriv, result[0][i]);
}
return;
case QuadCell:
for (int i=0; i<pts.length(); i++)
{
evalOnQuad(pts[i], deriv, result[0][i]);
}
return;
case BrickCell:
for (int i=0; i<pts.length(); i++)
{
evalOnBrick(pts[i], deriv, result[0][i]);
}
return;
default:
TEUCHOS_TEST_FOR_EXCEPTION(true, std::runtime_error,
"Legendre::refEval() unimplemented for cell type "
<< cellType);
}
}
void EdgeLocalizedBasis::refEval(
const CellType& cellType,
const Array<Point>& pts,
const SpatialDerivSpecifier& sds,
Array<Array<Array<double> > >& result,
int verbosity) const
{
TEUCHOS_TEST_FOR_EXCEPTION(!(sds.isPartial() || sds.isIdentity()),
std::runtime_error,
"cannot evaluate spatial derivative " << sds << " on EdgeLocalizedBasis basis");
const MultiIndex& deriv = sds.mi();
typedef Array<double> Adouble;
result.resize(1);
result[0].resize(pts.length());
int dim = dimension(cellType);
if (dim==0)
{
result[0] = tuple<Adouble>(tuple(1.0));
}
else if (dim==1)
{
for (int i=0; i<pts.length(); i++)
{
evalOnLine(pts[i], deriv, result[0][i]);
}
}
else if (dim==2)
{
for (int i=0; i<pts.length(); i++)
{
evalOnTriangle(pts[i], deriv, result[0][i]);
}
}
else if (dim==3)
{
for (int i=0; i<pts.length(); i++)
{
evalOnTet(pts[i], deriv, result[0][i]);
}
}
}
void RaviartThomas::refEval(
const CellType& cellType,
const Array<Point>& pts,
const SpatialDerivSpecifier& sds,
Array<Array<Array<double> > >& result,
int verbosity) const
{
const MultiIndex& deriv = sds.mi();
switch(cellType) {
case PointCell:
{
TEST_FOR_EXCEPTION(true, RuntimeError, "evaluation of RaviartThomas elements for PointCell not supported");
}
break;
case LineCell:
{
result.resize(1);
result[0].resize(pts.length());
Array<ADReal> tmp;
tmp.resize(2);
for (int i=0;i<pts.length();i++) {
ADReal x = ADReal( pts[i][0] , 0 , 1 );
ADReal one(1.0,1);
result[0][i].resize(2);
tmp[0] = one - x;
tmp[1] = x;
if (deriv.order()==0) {
for (int j=0;j<tmp.length();j++) {
result[0][i][j] = tmp[j].value();
}
}
else {
for (int j=0;j<tmp.length();j++) {
result[0][i][j] = tmp[j].gradient()[deriv.firstOrderDirection()];
}
}
}
}
break;
case TriangleCell:
{
result.resize(2);
result[0].resize(pts.length());
result[1].resize(pts.length());
Array<ADReal> tmp0;
Array<ADReal> tmp1;
tmp0.resize(3);
tmp1.resize(3);
for (int i=0;i<pts.length();i++) {
ADReal x = ADReal(pts[i][0],0,2);
ADReal y = ADReal(pts[i][1],1,2);
ADReal one(1.0,2);
ADReal rt2(std::sqrt(2.0),2);
result[0][i].resize(3);
result[1][i].resize(3);
tmp0[0] = x;
tmp1[0] = y - one;
tmp0[1] = rt2 * x;
tmp1[1] = rt2 * y;
tmp0[2] = x - one;
tmp1[2] = y;
if (deriv.order()==0) {
for (int j=0;j<tmp0.length();j++) {
result[0][i][j] = tmp0[j].value();
result[1][i][j] = tmp1[j].value();
}
}
else {
for (int j=0;j<tmp0.length();j++) {
result[0][i][j] = tmp0[j].gradient()[deriv.firstOrderDirection()];
result[1][i][j] = tmp1[j].gradient()[deriv.firstOrderDirection()];
}
}
}
}
break;
case TetCell:
{
TEST_FOR_EXCEPTION(true, RuntimeError, "evaluation of RaviartThomas elements for TetCell not supported");
}
break;
default:
TEST_FOR_EXCEPTION(true, RuntimeError, "evaluation of RaviartThomas elements unknown cell type");
break;
}
return;
}
