/**
* Integrate down the centre of this unknown
* This will not take into account changes
* in the jacobian across the extent of the basis
* function
*/
static
typename UnknownT::NumberT
integrate(
const UnknownT& unknown,
const CoordinatesInterface<DIM,
typename UnknownT::NumberT>& geom,
const int direction)
{
GaussLegendre<UnknownT::ORDER, NumberT> quad;
ValueT integral(0.0);
for (auto interval1D :
unknown.linearIntervals1D(direction)) {
NumberT intervalMin = interval1D.minimum(0);
NumberT intervalMax = interval1D.maximum(0);
auto nodes = quad.nodes(intervalMin, intervalMax);
auto weights = quad.weights(intervalMin, intervalMax);
auto location = unknown.centres();
for (std::size_t j = 0; j < nodes.size(); ++j) {
location[direction] = nodes[j];
integral += weights[j] *
unknown.value(direction, nodes[j]) *
geom.jacobian(direction, nodes[j]);
}
}
return integral;
}
static
std::array<std::array<T, ORDER+1>, DIM>
nodes(const GaussLegendre<ORDER, T>& quad,
const Vector<DIM, T>& mins,
const Vector<DIM, T>& maxs)
{
std::array<std::array<T, ORDER+1>, DIM> allNodes;
for (uint i = 0; i < DIM; ++i) {
assert(maxs[i] > mins[i]);
allNodes[i] = quad.nodes(mins[i], maxs[i]);
}
return allNodes;
}