Sundance::FeketeTriangleQuadrature Class Reference

List of all members.

Static Public Member Functions

static void getPoints (int order, Array< double > &wgt, Array< double > &x, Array< double > &y)
static bool test (int p)
static int maxOrder ()
static bool supportsOrder (int order)
static void evalPKDpolynomials (int order, double x, double y, double *resultPtr)
static void computeBasisCoeffs (const int order, Array< double > &basisCoeffs)

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)

Detailed Description

Get abscissas and weights for Fekete point quadrature on triangles

Definition at line 46 of file SundanceFeketeTriangleQuadrature.hpp.

Member Function Documentation

void FeketeTriangleQuadrature::computeBasisCoeffs ( const int  order,
Array< double > &  basisCoeffs 
) [static]

Here we calculate coefficients for Proriol-Koornwinder-Dubiner polynomials so that they form a Lagrange basis at given (Fekete quadrature) points in the triangle

Definition at line 199 of file SundanceFeketeTriangleQuadrature.cpp.

References dgetrf_(), dgetri_(), evalPKDpolynomials(), and getPoints().

Referenced by Sundance::FeketeQuadrature::evaluateAllBasisFunctions().

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 265 of file SundanceFeketeTriangleQuadrature.cpp.

References Sundance::pow().

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

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

Definition at line 382 of file SundanceFeketeTriangleQuadrature.cpp.

References fact().

Referenced by test().

double FeketeTriangleQuadrature::fact ( int  x  )  [static, private]

Definition at line 387 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 30 of file SundanceFeketeTriangleQuadrature.cpp.

References permute(), and SUNDANCE_ERROR.

Referenced by computeBasisCoeffs(), and 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 306 of file SundanceFeketeTriangleQuadrature.cpp.


Referenced by getPoints().

bool FeketeTriangleQuadrature::supportsOrder ( int  order  )  [static]

bool FeketeTriangleQuadrature::test ( int  p  )  [static]

Definition at line 343 of file SundanceFeketeTriangleQuadrature.cpp.

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

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