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