juliafem / femquad.jl

FEMQuad.jl package contains various of integration schemes for cartesian and tetrahedral domains. The most common integration rules are tabulated and focus is on speed. Each rule has own "label" so we can easily implement several rules with same degree. API is very simple making is easy to utilize package in different FEM projects.

FEMQuad.jl

FEMQuad.jl contains various of integration schemes for cartesian and tetrahedron domains. The most common integration rules are tabulated and focus is on speed.

Usage is straightforward. For example, to integrate function f(x) = 1 + x[1] + x[2] + x[1]*x[2] in a standard rectangular domain [-1,1]^2, 4 point Gauss-Legendre integration rule is needed:

using FEMQuad
f(x) = 1 + x[1] + x[2] + x[1]*x[2]
I = 0.0
for (w, gp) in get_quadrature_points(Val{:GLQUAD4})
    I += w*f(gp)
end

Result can be verified to be 4. w is integration weight, gp is integration point location and GLQUAD4 is the integration rule used. In the same principle we have integration rules for tetrahedrons, hexahedrons and so on. For example, GLTET15 is a 15-point tetrahedron rule.

References

• Wikipedia contributors. "Gaussian quadrature." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 24 Jul. 2017. Web. 29 Jul. 2017.

femquad.jl's Issues

New struct for QuadratureRule

According to @KristofferC (see PR #15 (comment)), it would be better to have own struct defining quadrature rule, something like

struct QuadratureRule{N}
    coords::Vector{NTuple{N, Float64}}
    weights::Vector{Float64}
end

Should we also have some other data in quadrature rule than coordinate points and weights, like dimension, name, integration order or similar..? I agree this is a good idea because the current structure of tuples is a bit complex as we have seen when 1d rules are not following the same "style" like multidimensional rules.

Aware of FastGaussQuadratures.jl?

Did you consider using the FastGaussQuadrature.jl package? https://github.com/ajt60gaibb/FastGaussQuadrature.jl

One of the greatest things about the Julia community is the continuous effort to reuse highly optimized and well-tested packages for fundamental tools such as numerical integration.

Examples are missing

Let's generate some usage examples using Literate.jl.

Deprecate integrate functions

This is also proposed by @KristofferC (see PR #15 (comment)), because there is the same function body with several functions, there should be only one. This is not anyhow mandatory change, but it would be a good place to practice a bit on how to deprecate stuff properly. Maybe @KristofferC can help with this so that everything goes according to the rules of art and science.

Re-register package

@JuliaRegistrator register()

Integration rules for Pyramid needs more rules and tests

I have been testing the rest of the elements so that I symbolically integrate, using Sympy, a complete polynomial up to order n, i.e. p = sum([(x+y+z)**i for i in range(n)]). Now, if integration rule is ok, it should integrate this polynomial without error.

Link not working

The link

https://juliafem.github.io/FEMQuad.jl/latest

at the project description is not working.

Find out integration rules used in ABAQUS for Tet10

It is 4 point rule, but what is the location of integration points and what are weights?