Loading...
Searching...
No Matches
Dune::QuadratureType Namespace Reference
dune-geometry » Quadrature

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 , 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 `TensorProductQuadratureRule`. In this case the 1D rules eventually need higher order to compensate occurring weight functions(i.e. simplices).

GaussJacobi_1_0 | Gauss-Jacobi rules with . -1D Gauss-Jacobi rule with parameters -Is used to construct efficient simplex quadrature rules of higher order
GaussJacobi_2_0 | Gauss-Legendre rules with . -1D Gauss-Jacobi rule with parameters -Is used to construct efficient simplex quadrature rules of higher order

GaussJacobi_n_0

Gauss-Legendre rules with .

-1D: Gauss-Jacobi rule with parameters -higher dimension: For the 2D/3D case efficient rules for certain geometries may be used if available. Higher dimensional quadrature rules are constructed via `TensorProductQuadratureRule`. In this case the 1D rules respect eventually occurring 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.
size |