TasGrid::TableGaussPatterson Class Reference

Rule with hard-corded tabulated points and weights. More...

#include <tsgHardCodedTabulatedRules.hpp>

Public Member Functions
	TableGaussPatterson ()
	Constructor, loads the nodes into the internal data structures.
	~TableGaussPatterson ()=default
	Destrutor, cleans all memory.
std::vector< double >	getNodes (int level) const
	Returns the nodes for the level, note that the nodes are nested.
double	getWeight (int level, int point) const
	Return the quadrature weight for level and given point.

Static Public Member Functions
static int	getNumLevels ()
	Return the number of hard-coded levels.

Protected Member Functions
void	loadNodes ()
	Load the nodes into the local data-strutures.
void	loadWeights ()
	Load the weights into the local data-structures.

Detailed Description

Rule with hard-corded tabulated points and weights.

The Gauss-Patterson rule combines nested points with the optimality of the Gauss quadratures. While not as powerful as Gauss-Legendre in one and tow dimensions, the rule wins in polynomial space of exactness with respect to integration for 3 or more dimensions. However, the points and weights are very hard to compute and most algorithms are very ill-conditioned. Thus, it is beneficial to have the points for the first 9 levels hard-coded.

Note that Gauss-Legendre rule combined with a full tensor grid gives highest exactness per number of points with respect to integration in one and two dimensions.

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The documentation for this class was generated from the following file:

• SparseGrids/tsgHardCodedTabulatedRules.hpp