ResultType evaluate(
const ConstGeometricalDataSlice<CoordinateType>& /* testGeomData */,
const ConstGeometricalDataSlice<CoordinateType>& /* trialGeomData */,
const CollectionOf1dSlicesOfConst3dArrays<BasisFunctionType>& testValues,
const CollectionOf1dSlicesOfConst3dArrays<BasisFunctionType>& trialValues,
const CollectionOf2dSlicesOfConstNdArrays<KernelType>& kernelValues) const {
// Assert that there is at least one scalar-valued kernel
assert(kernelValues.size() >= 1);
assert(kernelValues[0].extent(0) == 1);
assert(kernelValues[0].extent(1) == 1);
// Assert that there is at least one test and trial transformation
// and that their dimensions agree
assert(testValues.size() >= 1);
assert(trialValues.size() >= 1);
const size_t transCount = testValues.size();
assert(trialValues.size() == transCount);
if (kernelValues.size() > 1)
assert(kernelValues.size() == transCount);
ResultType result = 0.;
for (size_t transIndex = 0; transIndex < transCount; ++transIndex) {
const size_t transDim = testValues[transIndex].extent(0);
assert(trialValues[transIndex].extent(0) == transDim);
BasisFunctionType dotProduct = 0.;
for (size_t dim = 0; dim < transDim; ++dim)
dotProduct += conjugate(testValues[transIndex](dim)) *
trialValues[transIndex](dim);
if (transCount == 1)
result += dotProduct * kernelValues[0](0, 0);
else
result += dotProduct * kernelValues[transIndex](0, 0);
}
return result;
}
ResultType
evaluate(const ConstGeometricalDataSlice<CoordinateType> &testGeomData,
const ConstGeometricalDataSlice<CoordinateType> &trialGeomData,
const CollectionOf1dSlicesOfConst3dArrays<BasisFunctionType>
&testTransfValues,
const CollectionOf1dSlicesOfConst3dArrays<BasisFunctionType>
&trialTransfValues,
const CollectionOf2dSlicesOfConstNdArrays<KernelType> &kernelValues)
const {
const int dimWorld = 3;
// Assert that there are at least two scalar-valued kernels
assert(kernelValues.size() >= 2);
assert(kernelValues[0].extent(0) == 1);
assert(kernelValues[0].extent(1) == 1);
assert(kernelValues[1].extent(0) == 1);
assert(kernelValues[1].extent(1) == 1);
// Assert that there are at least two test and trial transformations
// (function value and surface div) of correct dimensions
assert(testTransfValues.size() >= 2);
assert(trialTransfValues.size() >= 2);
_1dSliceOfConst3dArray<BasisFunctionType> testValues = testTransfValues[0];
_1dSliceOfConst3dArray<BasisFunctionType> trialValues =
trialTransfValues[0];
_1dSliceOfConst3dArray<BasisFunctionType> testSurfaceDivs =
testTransfValues[1];
_1dSliceOfConst3dArray<BasisFunctionType> trialSurfaceDivs =
trialTransfValues[1];
assert(testValues.extent(0) == 3);
assert(trialValues.extent(0) == 3);
assert(testSurfaceDivs.extent(0) == 1);
assert(trialSurfaceDivs.extent(0) == 1);
// Let K_0(x, y) = kappa * K(x, y) and K_1(x, y) = K(x, y) / kappa.
// Return
// K_0(x, y) u*(x) . v(y) + K_1(x, y) div u*(x) div v(y)
BasisFunctionType sum = 0.;
for (int dim = 0; dim < dimWorld; ++dim)
sum += conjugate(testValues(dim)) * trialValues(dim);
ResultType term_0 = sum * kernelValues[0](0, 0);
ResultType term_1 = (conjugate(testSurfaceDivs(0)) * trialSurfaceDivs(0)) *
kernelValues[1](0, 0);
return term_0 + term_1;
}
ResultType evaluate(
const ConstGeometricalDataSlice<CoordinateType> & /* geomData */,
const CollectionOf1dSlicesOfConst3dArrays<BasisFunctionType> &testValues,
const CollectionOf1dSlicesOfConst3dArrays<BasisFunctionType> &trialValues)
const {
// Assert that there is at least one test and trial transformation
// and that the dimensions of the first pair agree
assert(testValues.size() >= 1);
assert(trialValues.size() >= 1);
assert(testValues[0].extent(0) == trialValues[0].extent(0));
const int transformationDim = testValues[0].extent(0);
BasisFunctionType result = 0.;
for (int dim = 0; dim < transformationDim; ++dim)
result += conjugate(testValues[0](dim)) * trialValues[0](dim);
return result;
}