Sundance::FeketeTriangleQuadrature Class Reference

Get abscissas and weights for Fekete point quadrature on triangles. More...

List of all members.

Static Public Member Functions
static void	getPoints (int order, Array< double > &wgt, Array< double > &x, Array< double > &y)
	Reference: T.
static bool	test (int p)
static int	maxOrder ()
static bool	supportsOrder (int order)
static void	evalPKDpolynomials (int order, double x, double y, double *resultPtr)
	Evaluates all basis functions of a Proriol-Koornwinder-Dubiner basis up to the given order at (x,y) in reference (barycentric) coordinates of a triangle; Missing third coordinate z = 1-x-y.
Static Private Member Functions
static void	permute (int m, const Array< double > &q, Array< Array< double > > &qPerm)
static double	exact (int a, int b, int c)
static double	fact (int x)

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Detailed Description

Get abscissas and weights for Fekete point quadrature on triangles.

Definition at line 46 of file SundanceFeketeTriangleQuadrature.hpp.

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Member Function Documentation

void FeketeTriangleQuadrature::evalPKDpolynomials	(	int	order,
		double	x,
		double	y,
		double *	resultPtr
	)		[static]

Evaluates all basis functions of a Proriol-Koornwinder-Dubiner basis up to the given order at (x,y) in reference (barycentric) coordinates of a triangle; Missing third coordinate z = 1-x-y.

Definition at line 183 of file SundanceFeketeTriangleQuadrature.cpp.

References Sundance::pow().

Referenced by Sundance::FeketeQuadrature::computeBasisCoeffs(), and Sundance::FeketeQuadrature::evaluateAllBasisFunctions().

double FeketeTriangleQuadrature::exact	(	int	a,
		int	b,
		int	c
	)		[static, private]

Definition at line 300 of file SundanceFeketeTriangleQuadrature.cpp.

References fact().

Referenced by test().

double FeketeTriangleQuadrature::fact

(

int

x

)

[static, private]

Definition at line 305 of file SundanceFeketeTriangleQuadrature.cpp.

Referenced by exact().

void FeketeTriangleQuadrature::getPoints	(	int	order,
		Array< double > &	wgt,
		Array< double > &	x,
		Array< double > &	y
	)		[static]

Reference: T.

Warburton, An explicit construction of interpolation nodes on the simplex J. Eng. Math. (2006) 56, pp. 247-262

Definition at line 14 of file SundanceFeketeTriangleQuadrature.cpp.

References permute(), SUNDANCE_ERROR, and SUNDANCE_ERROR7.

Referenced by test().

static int Sundance::FeketeTriangleQuadrature::maxOrder

(

)

[inline, static]

Definition at line 54 of file SundanceFeketeTriangleQuadrature.hpp.

void FeketeTriangleQuadrature::permute	(	int	m,
		const Array< double > &	q,
		Array< Array< double > > &	qPerm
	)		[static, private]

Definition at line 224 of file SundanceFeketeTriangleQuadrature.cpp.

References SUNDANCE_ERROR, and SUNDANCE_ERROR7.

Referenced by getPoints().

bool FeketeTriangleQuadrature::supportsOrder

(

int

order

)

[static]

Definition at line 171 of file SundanceFeketeTriangleQuadrature.cpp.

Referenced by Sundance::FeketeQuadratureType::supports().

bool FeketeTriangleQuadrature::test

(

int

p

)

[static]

Definition at line 261 of file SundanceFeketeTriangleQuadrature.cpp.

References exact(), getPoints(), and Sundance::pow().