inline typename DefaultLocalAssemblerForOperatorsOnSurfacesUtilities<
BasisFunctionType>::CoordinateType
DefaultLocalAssemblerForOperatorsOnSurfacesUtilities<BasisFunctionType>::
elementSizeSquared(int elementIndex,
const RawGridGeometry<CoordinateType> &rawGeometry) {
// This implementation could be optimised
CoordinateType maxEdgeLengthSquared = 0.;
const arma::Mat<int> &cornerIndices = rawGeometry.elementCornerIndices();
const arma::Mat<CoordinateType> &vertices = rawGeometry.vertices();
arma::Col<CoordinateType> edge;
if (cornerIndices(cornerIndices.n_rows - 1, elementIndex) == -1) {
// Triangular element
const int cornerCount = 3;
for (int i = 0; i < cornerCount; ++i) {
edge = vertices.col(cornerIndices((i + 1) % cornerCount, elementIndex)) -
vertices.col(cornerIndices(i, elementIndex));
CoordinateType edgeLengthSquared = arma::dot(edge, edge);
maxEdgeLengthSquared = std::max(maxEdgeLengthSquared, edgeLengthSquared);
}
} else {
// Quadrilateral element. We assume it is convex.
edge = vertices.col(cornerIndices(2, elementIndex)) -
vertices.col(cornerIndices(0, elementIndex));
maxEdgeLengthSquared = arma::dot(edge, edge);
edge = vertices.col(cornerIndices(3, elementIndex)) -
vertices.col(cornerIndices(1, elementIndex));
CoordinateType edgeLengthSquared = arma::dot(edge, edge);
maxEdgeLengthSquared = std::max(maxEdgeLengthSquared, edgeLengthSquared);
}
return maxEdgeLengthSquared;
}
inline Vector<typename DefaultLocalAssemblerForOperatorsOnSurfacesUtilities<
BasisFunctionType>::CoordinateType>
DefaultLocalAssemblerForOperatorsOnSurfacesUtilities<BasisFunctionType>::
elementCenter(int elementIndex,
const RawGridGeometry<CoordinateType> &rawGeometry) {
const Matrix<int> &cornerIndices = rawGeometry.elementCornerIndices();
const Matrix<CoordinateType> &vertices = rawGeometry.vertices();
const int maxCornerCount = cornerIndices.rows();
// each element has at least one corner
Vector<CoordinateType> center(vertices.col(cornerIndices(0, elementIndex)));
int i = 1;
for (; i < maxCornerCount; ++i) {
int cornerIndex = cornerIndices(i, elementIndex);
if (cornerIndex == -1)
break;
center += vertices.col(cornerIndex);
}
// now i contains the number of corners of the specified element
center /= i;
return center;
}
void DefaultLocalAssemblerForOperatorsOnSurfacesUtilities<BasisFunctionType>::
checkConsistencyOfGeometryAndShapesets(
const RawGridGeometry<CoordinateType> &rawGeometry,
const std::vector<const Shapeset<BasisFunctionType> *> &shapesets) {
if (rawGeometry.vertices().n_rows != 3)
throw std::invalid_argument(
"DefaultLocalAssemblerForOperatorsOnSurfacesUtilities::"
"checkConsistencyOfGeometryAndShapesets(): "
"vertex coordinates must be three-dimensional");
const size_t elementCount = rawGeometry.elementCornerIndices().n_cols;
if (rawGeometry.elementCornerIndices().n_rows < 3 ||
4 < rawGeometry.elementCornerIndices().n_rows)
throw std::invalid_argument(
"DefaultLocalAssemblerForOperatorsOnSurfacesUtilities::"
"checkConsistencyOfGeometryAndShapesets(): "
"Elements must have either 3 or 4 corners");
if (!rawGeometry.auxData().is_empty() &&
rawGeometry.auxData().n_cols != elementCount)
throw std::invalid_argument(
"DefaultLocalAssemblerForOperatorsOnSurfacesUtilities::"
"checkConsistencyOfGeometryAndShapesets(): "
"number of columns of auxData must match that of "
"elementCornerIndices");
if (shapesets.size() != elementCount)
throw std::invalid_argument(
"DefaultLocalAssemblerForOperatorsOnSurfacesUtilities::"
"checkConsistencyOfGeometryAndShapesets(): "
"size of shapesets must match the number of columns of "
"elementCornerIndices");
}
void DefaultLocalAssemblerForOperatorsOnSurfacesUtilities<BasisFunctionType>::
precalculateElementSizesAndCentersForSingleGrid(
const RawGridGeometry<CoordinateType> &rawGeometry,
std::vector<CoordinateType> &elementSizesSquared,
arma::Mat<CoordinateType> &elementCenters,
CoordinateType &averageElementSize) {
const size_t elementCount = rawGeometry.elementCount();
const int worldDim = rawGeometry.worldDimension();
averageElementSize = 0.; // We will store here temporarily
// the sum of element sizes
elementSizesSquared.resize(elementCount);
for (int e = 0; e < elementCount; ++e) {
elementSizesSquared[e] = elementSizeSquared(e, rawGeometry);
averageElementSize += sqrt(elementSizesSquared[e]);
}
averageElementSize /= elementCount;
elementCenters.set_size(worldDim, elementCount);
for (int e = 0; e < elementCount; ++e)
elementCenters.col(e) = elementCenter(e, rawGeometry);
}
