gf_integ — General function for obtaining handles to various integrations methods on convexes (used when the elementary matrices are built).
gf_integ(integ_name)
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:
gf_integ('IM_PRODUCT(IM_GAUSS1D(5),IM_GAUSS1D(5))') is the same as:
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.