gf_integ

Synopsis

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.