# 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 <literal>k=1,3,…,99</literal>.

• IM_NC(n,k) : Newton-Cotes approximative integration on simplexes, order <literal>k</literal>.

• 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 <literal>k=1,3,5,6,7,8,9,10,13,17,19</literal>.

• IM_QUAD(k) : Gauss methods on quadrilaterons <literal>k=2,3,5, …,17</literal>. Note that IM_GAUSS_PARALLELEPIPED should be prefered for QK fem’s.

• IM_TETRAHEDRON(k) : Gauss methods on tetrahedrons <literal>k=1,2,3,5,6 or 8</literal>.

• IM_SIMPLEX4D(3) : Gauss method on a 4-dimensional simplex.

• IM_STRUCTURED_COMPOSITE(im,k) : Composite method on a grid with <literal>k</literal> 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.