KOKKOS_INLINE_FUNCTION
void OrthPolynomial<1>::generate( /**/ outputViewType output,
const inputViewType input,
const ordinal_type p ) {
typedef outputViewType::value_type value_type;
typedef Sacado::Fad::SFad<value_type,2> fad_type;
constexpr ordinal_type maxCard = (maxOrder+1)*(maxOrder+2)/2;
const ordinal_type
npts = input.dimension(0),
card = output.dimension(0);
// use stack buffer
fad_type inBuf[maxNumPts][2], outBuf[maxCard][maxNumPts];
Kokkos::View<fad_type**, Kokkos::Impl::ActiveExecutionMemorySpace> in(&inBuf[0][0], npts, 2);
Kokkos::View<fad_type***,Kokkos::Impl::ActiveExecutionMemorySpace> out(&outBuf[0][0][0], card, npts);
for (ordinal_type i=0;i<npts;++i)
for (ordinal_type j=0;j<2;++j) {
in(i,j) = Sacado::Fad::SFad<value_type,2>( input(i,j) );
in(i,j).diff(j,2);
}
OrthPolynomial<0>::generate<maxOrder,maxNumPts>(out, in, p);
for (ordinal_type i=0;i<card;++i)
for (ordinal_type j=0;j<npts;++j)
for (ordinal_type k=0;k<2;++k)
output(i,j,k) = out(i,j).dx(k);
}
KOKKOS_INLINE_FUNCTION
void
Basis_Constant_FEM::Serial<opType>::
getValues( /**/ outputViewType output,
const inputViewType input ) {
switch (opType) {
case OPERATOR_VALUE : {
output(0) = 1.0;
break;
}
case OPERATOR_MAX : {
const ordinal_type jend = output.dimension(1);
const ordinal_type iend = output.dimension(0);
for (ordinal_type j=0;j<jend;++j)
for (ordinal_type i=0;i<iend;++i)
output(i, j) = 0.0;
break;
}
default: {
INTREPID2_TEST_FOR_ABORT( opType != OPERATOR_VALUE &&
opType != OPERATOR_MAX,
">>> ERROR: (Intrepid2::Basis_Constant_FEM::Serial::getValues) operator is not supported");
}
}
}
KOKKOS_INLINE_FUNCTION
void operator()(const size_type iter) const {
size_type cl = 0, bf = 0, pt = 0;
size_type outputRank(_output.rank()), rightRank(_rightInput.rank());
if (_hasField)
Util::unrollIndex( cl, bf, pt,
_output.dimension(0),
_output.dimension(1),
_output.dimension(2),
iter );
else
Util::unrollIndex( cl, pt,
_output.dimension(0),
_output.dimension(1),
iter );
auto result = ( _hasField ? Kokkos::subview(_output, cl, bf, pt, Kokkos::ALL(), Kokkos::ALL()) :
/**/ Kokkos::subview(_output, cl, pt, Kokkos::ALL(), Kokkos::ALL()));
const auto right = ( outputRank == rightRank ? ( _hasField ? Kokkos::subview(_rightInput, cl, bf, pt, Kokkos::ALL(), Kokkos::ALL()) :
/**/ Kokkos::subview(_rightInput, cl, pt, Kokkos::ALL(), Kokkos::ALL()) ) :
/**/ ( _hasField ? Kokkos::subview(_rightInput, bf, pt, Kokkos::ALL(), Kokkos::ALL()) :
/**/ Kokkos::subview(_rightInput, pt, Kokkos::ALL(), Kokkos::ALL()) ) );
const auto left = (_leftInput.dimension(1) == 1) ? Kokkos::subview(_leftInput, cl, 0) :
/**/ Kokkos::subview(_leftInput, cl, pt);
const size_type iend = result.dimension(0);
const size_type jend = result.dimension(1);
const auto val = left();
if (_reciprocal)
for(size_type i = 0; i < iend; ++i)
for(size_type j = 0; j < jend; ++j)
result(i, j) = right(i, j)/val;
else
for(size_type i = 0; i < iend; ++i)
for(size_type j = 0; j < jend; ++j)
result(i, j) = right(i, j)*val;
}
KOKKOS_INLINE_FUNCTION
void operator()(const size_type iter) const {
size_type cl, bf, pt;
size_type leftRank(_leftInput.rank()), rightRank(_rightInput.rank());
if (_hasField)
unrollIndex( cl, bf, pt,
_output.dimension(0),
_output.dimension(1),
_output.dimension(2),
iter );
else
unrollIndex( cl, pt,
_output.dimension(0),
_output.dimension(1),
iter);
auto result = ( _hasField ? Kokkos::subview(_output, cl, bf, pt) :
/**/ Kokkos::subview(_output, cl, pt));
const auto left = (_leftInput.dimension(1) == 1) ? Kokkos::subview(_leftInput, cl, 0, Kokkos::ALL(), Kokkos::ALL()) :
/**/ Kokkos::subview(_leftInput, cl, pt, Kokkos::ALL(), Kokkos::ALL());
const auto right = (rightRank == leftRank + int(_hasField)) ?
( _hasField ? Kokkos::subview(_rightInput, cl, bf, pt, Kokkos::ALL(), Kokkos::ALL()) :
/**/ Kokkos::subview(_rightInput, cl, pt, Kokkos::ALL(), Kokkos::ALL())) :
( _hasField ? Kokkos::subview(_rightInput, bf, pt, Kokkos::ALL(), Kokkos::ALL()) :
/**/ Kokkos::subview(_rightInput, pt, Kokkos::ALL(), Kokkos::ALL()));
const size_type iend = left.dimension(0);
const size_type jend = left.dimension(1);
value_type tmp(0);
for(size_type i = 0; i < iend; ++i)
for(size_type j = 0; j < jend; ++j)
tmp += left(i, j)*right(i, j);
result() = tmp;
}
KOKKOS_INLINE_FUNCTION
void
Basis_HGRAD_TRI_C2_FEM::Serial<opType>::
getValues( /**/ outputViewType output,
const inputViewType input ) {
switch (opType) {
case OPERATOR_VALUE: {
const auto x = input(0);
const auto y = input(1);
// output is a rank-2 array with dimensions (basisCardinality_, dim0)
output(0) = (x + y - 1.0)*(2.0*x + 2.0*y - 1.0);
output(1) = x*(2.0*x - 1.0);
output(2) = y*(2.0*y - 1.0);
output(3) = -4.0*x*(x + y - 1.0);
output(4) = 4.0*x*y;
output(5) = -4.0*y*(x + y - 1.0);
break;
}
case OPERATOR_D1:
case OPERATOR_GRAD: {
const auto x = input(0);
const auto y = input(1);
// output is a rank-3 array with dimensions (basisCardinality_, dim0, spaceDim)
output(0, 0) = 4.0*x + 4.0*y - 3.0;
output(0, 1) = 4.0*x + 4.0*y - 3.0;
output(1, 0) = 4.0*x - 1.0;
output(1, 1) = 0.0;
output(2, 0) = 0.0;
output(2, 1) = 4.0*y - 1.0;
output(3, 0) = -4.0*(2.0*x + y - 1.0);
output(3, 1) = -4.0*x;
output(4, 0) = 4.0*y;
output(4, 1) = 4.0*x;
output(5, 0) = -4.0*y;
output(5, 1) = -4.0*(x + 2.0*y - 1.0);
break;
}
case OPERATOR_CURL: {
const auto x = input(0);
const auto y = input(1);
// CURL(u) = (u_y, -u_x), is rotated GRAD
output(0, 1) =-(4.0*x + 4.0*y - 3.0);
output(0, 0) = 4.0*x + 4.0*y - 3.0;
output(1, 1) =-(4.0*x - 1.0);
output(1, 0) = 0.0;
output(2, 1) = 0.0;
output(2, 0) = 4.0*y - 1.0;
output(3, 1) = 4.0*(2.0*x + y - 1.0);
output(3, 0) = -4.0*x;
output(4, 1) = -4.0*y;
output(4, 0) = 4.0*x;
output(5, 1) = 4.0*y;
output(5, 0) = -4.0*(x + 2.0*y - 1.0);
break;
}
case OPERATOR_D2: {
// output is a rank-3 array with dimensions (basisCardinality_, dim0, DkCardinality)
// D2 -> (2,0) -> dx^2.
output(0, 0) = 4.0;
output(1, 0) = 4.0;
output(2, 0) = 0.0;
output(3, 0) =-8.0;
output(4, 0) = 0.0;
output(5, 0) = 0.0;
// D2 -> (1,1) -> dx dy
output(0, 1) = 4.0;
output(1, 1) = 0.0;
output(2, 1) = 0.0;
output(3, 1) =-4.0;
output(4, 1) = 4.0;
output(5, 1) =-4.0;
// D2 -> (0,2) -> dy^2
output(0, 2) = 4.0;
output(1, 2) = 0.0;
output(2, 2) = 4.0;
output(3, 2) = 0.0;
output(4, 2) = 0.0;
output(5, 2) =-8.0;
break;
}
case OPERATOR_MAX: {
const ordinal_type jend = output.dimension(1);
const ordinal_type iend = output.dimension(0);
for (ordinal_type j=0;j<jend;++j)
for (ordinal_type i=0;i<iend;++i)
output(i, j) = 0.0;
break;
}
default: {
INTREPID2_TEST_FOR_ABORT( opType != OPERATOR_VALUE &&
opType != OPERATOR_GRAD &&
opType != OPERATOR_CURL &&
opType != OPERATOR_D1 &&
opType != OPERATOR_D2 &&
opType != OPERATOR_MAX,
">>> ERROR: (Intrepid2::Basis_HGRAD_TRI_C2_FEM::Serial::getValues) operator is not supported");
}
}
}
KOKKOS_INLINE_FUNCTION
void
Basis_HGRAD_HEX_C1_FEM::Serial<opType>::
getValues( /**/ outputViewType output,
const inputViewType input ) {
switch (opType) {
case OPERATOR_VALUE : {
const auto x = input(0);
const auto y = input(1);
const auto z = input(2);
// output is a rank-2 array with dimensions (basisCardinality_, dim0)
output(0) = (1.0 - x)*(1.0 - y)*(1.0 - z)/8.0;
output(1) = (1.0 + x)*(1.0 - y)*(1.0 - z)/8.0;
output(2) = (1.0 + x)*(1.0 + y)*(1.0 - z)/8.0;
output(3) = (1.0 - x)*(1.0 + y)*(1.0 - z)/8.0;
output(4) = (1.0 - x)*(1.0 - y)*(1.0 + z)/8.0;
output(5) = (1.0 + x)*(1.0 - y)*(1.0 + z)/8.0;
output(6) = (1.0 + x)*(1.0 + y)*(1.0 + z)/8.0;
output(7) = (1.0 - x)*(1.0 + y)*(1.0 + z)/8.0;
break;
}
case OPERATOR_GRAD : {
const auto x = input(0);
const auto y = input(1);
const auto z = input(2);
// output is a rank-3 array with dimensions (basisCardinality_, dim0, spaceDim)
output(0, 0) = -(1.0 - y)*(1.0 - z)/8.0;
output(0, 1) = -(1.0 - x)*(1.0 - z)/8.0;
output(0, 2) = -(1.0 - x)*(1.0 - y)/8.0;
output(1, 0) = (1.0 - y)*(1.0 - z)/8.0;
output(1, 1) = -(1.0 + x)*(1.0 - z)/8.0;
output(1, 2) = -(1.0 + x)*(1.0 - y)/8.0;
output(2, 0) = (1.0 + y)*(1.0 - z)/8.0;
output(2, 1) = (1.0 + x)*(1.0 - z)/8.0;
output(2, 2) = -(1.0 + x)*(1.0 + y)/8.0;
output(3, 0) = -(1.0 + y)*(1.0 - z)/8.0;
output(3, 1) = (1.0 - x)*(1.0 - z)/8.0;
output(3, 2) = -(1.0 - x)*(1.0 + y)/8.0;
output(4, 0) = -(1.0 - y)*(1.0 + z)/8.0;
output(4, 1) = -(1.0 - x)*(1.0 + z)/8.0;
output(4, 2) = (1.0 - x)*(1.0 - y)/8.0;
output(5, 0) = (1.0 - y)*(1.0 + z)/8.0;
output(5, 1) = -(1.0 + x)*(1.0 + z)/8.0;
output(5, 2) = (1.0 + x)*(1.0 - y)/8.0;
output(6, 0) = (1.0 + y)*(1.0 + z)/8.0;
output(6, 1) = (1.0 + x)*(1.0 + z)/8.0;
output(6, 2) = (1.0 + x)*(1.0 + y)/8.0;
output(7, 0) = -(1.0 + y)*(1.0 + z)/8.0;
output(7, 1) = (1.0 - x)*(1.0 + z)/8.0;
output(7, 2) = (1.0 - x)*(1.0 + y)/8.0;
break;
}
case OPERATOR_D2 : {
const auto x = input(0);
const auto y = input(1);
const auto z = input(2);
// output is a rank-3 array with dimensions (basisCardinality_, dim0, D2Cardinality = 6)
output(0, 0) = 0.0; // {2, 0, 0}
output(0, 1) = (1.0 - z)/8.0; // {1, 1, 0}
output(0, 2) = (1.0 - y)/8.0; // {1, 0, 1}
output(0, 3) = 0.0; // {0, 2, 0}
output(0, 4) = (1.0 - x)/8.0; // {0, 1, 1}
output(0, 5) = 0.0; // {0, 0, 2}
output(1, 0) = 0.0; // {2, 0, 0}
output(1, 1) = -(1.0 - z)/8.0; // {1, 1, 0}
output(1, 2) = -(1.0 - y)/8.0; // {1, 0, 1}
output(1, 3) = 0.0; // {0, 2, 0}
output(1, 4) = (1.0 + x)/8.0; // {0, 1, 1}
output(1, 5) = 0.0; // {0, 0, 2}
output(2, 0) = 0.0; // {2, 0, 0}
output(2, 1) = (1.0 - z)/8.0; // {1, 1, 0}
output(2, 2) = -(1.0 + y)/8.0; // {1, 0, 1}
output(2, 3) = 0.0; // {0, 2, 0}
output(2, 4) = -(1.0 + x)/8.0; // {0, 1, 1}
output(2, 5) = 0.0; // {0, 0, 2}
output(3, 0) = 0.0; // {2, 0, 0}
output(3, 1) = -(1.0 - z)/8.0; // {1, 1, 0}
output(3, 2) = (1.0 + y)/8.0; // {1, 0, 1}
output(3, 3) = 0.0; // {0, 2, 0}
output(3, 4) = -(1.0 - x)/8.0; // {0, 1, 1}
output(3, 5) = 0.0; // {0, 0, 2}
output(4, 0) = 0.0; // {2, 0, 0}
output(4, 1) = (1.0 + z)/8.0; // {1, 1, 0}
output(4, 2) = -(1.0 - y)/8.0; // {1, 0, 1}
output(4, 3) = 0.0; // {0, 2, 0}
output(4, 4) = -(1.0 - x)/8.0; // {0, 1, 1}
output(4, 5) = 0.0; // {0, 0, 2}
output(5, 0) = 0.0; // {2, 0, 0}
output(5, 1) = -(1.0 + z)/8.0; // {1, 1, 0}
output(5, 2) = (1.0 - y)/8.0; // {1, 0, 1}
output(5, 3) = 0.0; // {0, 2, 0}
output(5, 4) = -(1.0 + x)/8.0; // {0, 1, 1}
output(5, 5) = 0.0; // {0, 0, 2}
output(6, 0) = 0.0; // {2, 0, 0}
output(6, 1) = (1.0 + z)/8.0; // {1, 1, 0}
output(6, 2) = (1.0 + y)/8.0; // {1, 0, 1}
output(6, 3) = 0.0; // {0, 2, 0}
output(6, 4) = (1.0 + x)/8.0; // {0, 1, 1}
output(6, 5) = 0.0; // {0, 0, 2}
output(7, 0) = 0.0; // {2, 0, 0}
output(7, 1) = -(1.0 + z)/8.0; // {1, 1, 0}
output(7, 2) = -(1.0 + y)/8.0; // {1, 0, 1}
output(7, 3) = 0.0; // {0, 2, 0}
output(7, 4) = (1.0 - x)/8.0; // {0, 1, 1}
output(7, 5) = 0.0; // {0, 0, 2}
break;
}
case OPERATOR_MAX : {
const ordinal_type jend = output.dimension(1);
const ordinal_type iend = output.dimension(0);
for (ordinal_type j=0;j<jend;++j)
for (ordinal_type i=0;i<iend;++i)
output(i, j) = 0.0;
break;
}
default: {
INTREPID2_TEST_FOR_ABORT( opType != OPERATOR_VALUE &&
opType != OPERATOR_GRAD &&
opType != OPERATOR_CURL &&
opType != OPERATOR_D2 &&
opType != OPERATOR_MAX,
">>> ERROR: (Intrepid2::Basis_HGRAD_HEX_C1_FEM::Serial::getValues) operator is not supported");
}
}
}
KOKKOS_INLINE_FUNCTION
void
Basis_HGRAD_QUAD_C1_FEM::Serial<opType>::
getValues( outputViewType output,
const inputViewType input ) {
switch (opType) {
case OPERATOR_VALUE : {
const auto x = input(0);
const auto y = input(1);
// output with dimensions (basisCardinality_)
output(0) = (1.0 - x)*(1.0 - y)/4.0;
output(1) = (1.0 + x)*(1.0 - y)/4.0;
output(2) = (1.0 + x)*(1.0 + y)/4.0;
output(3) = (1.0 - x)*(1.0 + y)/4.0;
break;
}
case OPERATOR_GRAD : {
const auto x = input(0);
const auto y = input(1);
// output with dimensions (basisCardinality_, spaceDim)
output(0, 0) = -(1.0 - y)/4.0;
output(0, 1) = -(1.0 - x)/4.0;
output(1, 0) = (1.0 - y)/4.0;
output(1, 1) = -(1.0 + x)/4.0;
output(2, 0) = (1.0 + y)/4.0;
output(2, 1) = (1.0 + x)/4.0;
output(3, 0) = -(1.0 + y)/4.0;
output(3, 1) = (1.0 - x)/4.0;
break;
}
case OPERATOR_CURL : {
const auto x = input(0);
const auto y = input(1);
// output with dimensions (basisCardinality_, spaceDim)
output(0, 0) = -(1.0 - x)/4.0;
output(0, 1) = (1.0 - y)/4.0;
output(1, 0) = -(1.0 + x)/4.0;
output(1, 1) = -(1.0 - y)/4.0;
output(2, 0) = (1.0 + x)/4.0;
output(2, 1) = -(1.0 + y)/4.0;
output(3, 0) = (1.0 - x)/4.0;
output(3, 1) = (1.0 + y)/4.0;
break;
}
case OPERATOR_D2 : {
// output with dimensions (basisCardinality_, D2Cardinality=3)
output(0, 0) = 0.0;
output(0, 1) = 0.25;
output(0, 2) = 0.0;
output(1, 0) = 0.0;
output(1, 1) = -0.25;
output(1, 2) = 0.0;
output(2, 0) = 0.0;
output(2, 1) = 0.25;
output(2, 2) = 0.0;
output(3, 0) = 0.0;
output(3, 1) = -0.25;
output(3, 2) = 0.0;
break;
}
case OPERATOR_MAX : {
const ordinal_type jend = output.dimension(1);
const ordinal_type iend = output.dimension(0);
for (ordinal_type j=0;j<jend;++j)
for (ordinal_type i=0;i<iend;++i)
output(i, j) = 0.0;
break;
}
default: {
INTREPID2_TEST_FOR_ABORT( opType != OPERATOR_VALUE &&
opType != OPERATOR_GRAD &&
opType != OPERATOR_CURL &&
opType != OPERATOR_D2 &&
opType != OPERATOR_MAX,
">>> ERROR: (Intrepid2::Basis_HGRAD_QUAD_C1_FEM::Serial::getValues) operator is not supported");
}
}
}