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) |
Definition at line 46 of file SundanceFeketeTriangleQuadrature.hpp.
| 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] |
| 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.
References SUNDANCE_ERROR.
Referenced by getPoints().
| bool FeketeTriangleQuadrature::supportsOrder | ( | int | order | ) | [static] |
Definition at line 187 of file SundanceFeketeTriangleQuadrature.cpp.
Referenced by Sundance::FeketeQuadratureType::supports().
| bool FeketeTriangleQuadrature::test | ( | int | p | ) | [static] |
Definition at line 343 of file SundanceFeketeTriangleQuadrature.cpp.
References exact(), getPoints(), and Sundance::pow().