How do I use FastGaussQuadrature.jl to compute the integral of a 2d triangle element and 3d tetrahedron element

[stevengj]

@00krishna

However, for solving 2 and 3 dimensional elements, I imagine I need to use a package like FastGaussQuadrature.jl.

FastGaussQuadrature constructs 1d quadrature rules. Of course, you can integrate over a 2d or 3d region by doing nested integrals (either with QuadGK or via tensor products of quadrature rules), or you can use a multi-dimensional integration package like HCubature.jl. See also

2D integration over non-rectangular domain using cubature

Hello everyone, I have a very basic question. I’m looking for the most efficient way to perform the following very classical integral: [image] For now I’m using hquadrature of the cubature package in two steps. This works, but I’m not sure whether this is the most efficient way. More generally, I would like to know, how to perform multidimensional integration over non-rectangular domains. It seems cubature does not allow bounds to be functions. Am I correct? Many thanks in advance Olivi…

If you want a fixed-order quadrature rule for a 2d triangle or 3d tetrahedron, see e.g. the SimplexQuad.jl package, or FEMQuad.jl, or the quadrature routines in NESSie.jl or …