gf_integ

General object for obtaining handles to various integrations methods on convexes (used when the elementary matrices are built).

# Calling Sequence

    I = gf_integ(string method)

## Description

General constructor for integ objects.

General object for obtaining handles to various integrations methods on convexes (used when the elementary matrices are built).

## Command list

- `I = gf_integ(string method)`

  Here is a list of some integration methods defined in getfem++ (see the description of finite element and integration methods for a complete reference): - IM_EXACT_SIMPLEX(n) : Exact integration on simplices (works only with linear geometric transformations and PK fem's). - IM_PRODUCT(A,B) : Product of two integration methods. - IM_EXACT_PARALLELEPIPED(n) : Exact integration on parallelepipeds. - IM_EXACT_PRISM(n) : Exact integration on prisms. - IM_GAUSS1D(k) : Gauss method on the segment, order `k=1,3,...,99`. - IM_NC(n,k) : Newton-Cotes approximative integration on simplexes, order `k`. - IM_NC_PARALLELEPIPED(n,k) : Product of Newton-Cotes integration on parallelepipeds. - IM_NC_PRISM(n,k) : Product of Newton-Cotes integration on prisms. - IM_GAUSS_PARALLELEPIPED(n,k) : Product of Gauss1D integration on parallelepipeds. - IM_TRIANGLE(k) : Gauss methods on triangles `k=1,3,5,6,7,8,9,10,13,17,19`. - IM_QUAD(k) : Gauss methods on quadrilaterons `k=2,3,5, ...,17`. Note that IM_GAUSS_PARALLELEPIPED should be prefered for QK fem's. - IM_TETRAHEDRON(k) : Gauss methods on tetrahedrons `k=1,2,3,5,6 or 8`. - IM_SIMPLEX4D(3) : Gauss method on a 4-dimensional simplex. - IM_STRUCTURED_COMPOSITE(im,k) : Composite method on a grid with `k` divisions. - IM_HCT_COMPOSITE(im) : Composite integration suited to the HCT composite finite element. Example: - I = gf_integ('IM_PRODUCT(IM_GAUSS1D(5),IM_GAUSS1D(5))') is the same as: - I = gf_integ('IM_GAUSS_PARALLELEPIPED(2,5)') Note that 'exact integration' should be avoided in general, since they only apply to linear geometric transformations, are quite slow, and subject to numerical stability problems for high degree fem's.

## See Also

- getfem types

## Authors

Y. Collette