Skip to content

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.

License

Notifications You must be signed in to change notification settings

JuliaFEM/FEMQuad.jl

Folders and files

NameName
Last commit message
Last commit date

Latest commit

 

History

75 Commits
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Repository files navigation

FEMQuad.jl

ci docs-stable docs-latest

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.

About

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.

Topics

Resources

License

Stars

Watchers

Forks

Packages

No packages published

Languages