Integration Rule
Add an Integration Rule node () under Global Definitions > Equation Contributions to define a custom numerical quadrature method that you can use in a Weak Contribution feature. A custom integration rule for a mesh element type consists of a set of points, in element coordinates, and corresponding weights. The sum of the weights is expected to equal the volume of the element in element coordinates. Point patterns should be invariant under permutation of the mesh element nodes.
The Settings window contains the following sections:
Interval
Specify the xi1 coordinates of the quadrature points and their corresponding Weights. The weights are expected to sum to 1.
Triangle
Specify the xi1 and xi2 coordinates of the quadrature points and their corresponding Weights. The weights are expected to sum to 1/2.
Quadrilateral
Specify the xi1 and xi2 coordinates of the quadrature points and their corresponding Weights. The weights are expected to sum to 1.
Tetrahedron
Specify the xi1, xi2, and xi3 coordinates of the quadrature points and their corresponding Weights. The weights are expected to sum to 1/6.
Block
Specify the xi1, xi2, and xi3 coordinates of the quadrature points and their corresponding Weights. The weights are expected to sum to 1.
Prism
Specify the xi1, xi2, and xi3 coordinates of the quadrature points and their corresponding Weights. The xi1 and xi2 coordinates refer to the triangular faces while the xi3 coordinate corresponds to the extrusion direction. The weights are expected to sum to 1/2.
Pyramid
Specify the xi1, xi2, and xi3 coordinates of the quadrature points and their corresponding Weights. The xi1 and xi2 coordinates refer to the quadrilateral base while the xi3 coordinate corresponds to the height of the pyramid. The weights are expected to sum to 1/3.