Dune::QuadratureType Namespace Reference

Defines an enum for currently available quadrature rules. More...

Enumerations
enum	Enum {   GaussLegendre = 0 , GaussJacobi_1_0 = 1 , GaussJacobi_2_0 = 2 , GaussJacobi_n_0 = 3 ,   GaussLobatto = 4 , GaussRadauLeft = 5 , GaussRadauRight = 6 , size }

Detailed Description

Defines an enum for currently available quadrature rules.

Enumeration Type Documentation

Enum

enum Dune::QuadratureType::Enum

Enumerator
GaussLegendre	Gauss-Legendre rules (default) -1D: Gauss-Jacobi rule with parameters \f$\alpha = \beta =0 \f$, i.e. for integrals with a constant weight function. The quadrature points do not include interval endpoints. Polynomials of order 2n - 1 can be integrated exactly. -higher dimension: For the 2D/3D case efficient rules for certain geometries may be used if available. Higher dimensional quadrature rules are constructed via \p TensorProductQuadratureRule. In this case the 1D rules eventually need higher order to compensate occuring weight functions(i.e. simplices).
GaussJacobi_1_0	Gauss-Jacobi rules with \(\alpha =1\). -1D Gauss-Jacobi rule with parameters \f$\alpha =1,\ \beta =0 \f$ -Is used to construct efficient simplex quadrature rules of higher order
GaussJacobi_2_0	Gauss-Legendre rules with \(\alpha =2\). -1D Gauss-Jacobi rule with parameters \f$\alpha =2,\ \beta =0 \f$ -Is used to construct efficient simplex quadrature rules of higher order
GaussJacobi_n_0	Gauss-Legendre rules with \(\alpha =n\). -1D: Gauss-Jacobi rule with parameters \f$\alpha = n,\ \beta =0 \f$ -higher dimension: For the 2D/3D case efficient rules for certain geometries may be used if available. Higher dimensional quadrature rules are constructed via \p TensorProductQuadratureRule. In this case the 1D rules respect eventually occuring weight functions(i.e. simplices). -The rules for high dimension or order are computed at run time and only floating point number types are supported.(LAPACK is needed for this case) -Most efficient quadrature type for simplices. \note For details please use the book "Approximate Calculation of Multiple Integrals" by A.H. Stroud published in 1971.
GaussLobatto	Gauss-Lobatto rules. 1D: Gauss-Lobatto rules for a constant weight function. These are optimal rules under the constraint that both interval endpoints are quadrature points. Polynomials of order 2n - 3 can be integrated exactly.
GaussRadauLeft	Gauss-Radau rules including the left endpoint. 1D: Gauss-Radau rules for a constant weight function. These are optimal rules under the constraint that the left endpoint of the integration interval is a quadrature point. Polynomials of order 2n - 2 can be integrated exactly.
GaussRadauRight	Gauss-Radau rules including the right endpoint. 1D: Gauss-Radau rules for a constant weight function. These are optimal rules under the constraint that the right endpoint of the integration interval is a quadrature point. Polynomials of order 2n - 2 can be integrated exactly. The right Gauss-Radau rules are the just the mirrored left Gauss-Radau rules.