A class storing tables with (position, weight) pairs for line Lobatto integration rules. More...

Collaboration diagram for GmLobattoIntegrationTables:

Static Public Member Functions
static const QVector< QPair< double, double > > *	lineRuleTable (int rule)
	Returns the table storing (position, weight) pairs for the given line Lobatto rule. Rule SHOULD be in the interval 1 to 11. Returns NULL for any unknown rule.

static int	lineRuleDegree (int rule)
	Returns the integration degree for the given line Lobatto rule (The polynomial degree for which this rule is exact). Returns an undefined value for invalid rules.

static bool	initTables ()
	Initialization function for the set of integration rule tables. Must be called once.

Static Private Member Functions
static void	initLineTable ()
	Implementation of the First 11 Integral Weights-Points using the Gauss-Lobatto-Legendre Quadrature. More...

static double	jacobi (double eps, int p, double alpha, double beta)
	Jacobi Polynomial generator. 'p' is the order.

static double	dJacobi (double eps, int order, double alpha, double beta)
	First derive of Jacobi Polynomial.

static double	rootChevyshev (int indexRoot, int orderPol)
	Calculate of OrderPol-Roots of Chevyshev polynomials.

static void	rootJacobi (int order, double alpha, double beta, GmVector &zeros)
	Roots of Jacobi Polynomials using Chevyshev roots. Fills the zeros vector.

static void	quadPoints (int Q, GmMatrix &Quad)
	Integral Weights-Points Generator for Lobatto rules of any order Q > 0. Fills the Quad matrix(Qx2) with ppositions and weights.

Static Private Attributes
static QVector< QPair< double, double > >	_lineTable [11]
	The static table storing (position, weight) pairs for the first 11 line Lobatto rules.

Detailed Description

A class storing tables with (position, weight) pairs for line Lobatto integration rules.

Member Function Documentation

void GmLobattoIntegrationTables::initLineTable ( )

staticprivate

Implementation of the First 11 Integral Weights-Points using the Gauss-Lobatto-Legendre Quadrature.

Reference: Pavel Solin, Higher-Order Finite Element Methods Karniadakis Sherwin, Spectral/hp Elements Methods for Computational Fluid Dynamics

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