juliafem / mortar2d.jl

Mortar2D.jl is a Julia package to calculate discrete projections between non-conforming finite element meshes. The resulting "mortar matrices" can be used to tie non-conforming finite elements meshes together in an optimal way.

Mortar2D.jl

Mortar2D.jl is a Julia package to calculate discrete projections between non-conforming finite element meshes. The resulting "mortar matrices" can be used to tie non-conforming finite element meshes together which are meshed separately to construct bigger models.

Using mortar methods in mesh tie problems results variationally consistent solution. Mathematically, goal is to solve mixed problem with primary field variable and Lagrange multipliers, which have a physical meaning (e.g. contact pressure if unknown field is displacement). The problem arising is a typical saddle point problem with zeros on diagonal.

Installing and testing package

Installing package goes same way like other packages in julia, i.e.

julia> Pkg.add("Mortar2D")

Testing package can be done using Pkg.test, i.e.

julia> Pkg.test("Mortar2D")

Probably the easiest way to test the functionality of package is to use JuliaBox.

Usage example

Let us calculate projection matrices D and M for the following problem:

Problem setup:

Xs = Dict(1 => [0.0, 1.0], 2 => [5/4, 1.0], 3 => [2.0, 1.0])
Xm = Dict(4 => [0.0, 1.0], 5 => [1.0, 1.0], 6 => [2.0, 1.0])
coords = merge(Xm , Xs)
Es = Dict(1 => [1, 2], 2 => [2, 3])
Em = Dict(3 => [4, 5], 4 => [5, 6])
elements = merge(Es, Em)
element_types = Dict(1 => :Seg2, 2 => :Seg2, 3 => :Seg2, 4 => :Seg2)
slave_element_ids = [1, 2]
master_element_ids = [3, 4]

Calculate projection matrices D and M

s, m, D, M = calculate_mortar_assembly(
    elements, element_types, coords,
    slave_element_ids, master_element_ids)

According to theory, the interface should transfer constant without any error. Let's test that:

u_m = ones(3)
u_s = D[s,s] \ (M[s,m]*um)

# output

3-element Array{Float64,1}:
 1.0
 1.0
 1.0

The rest of the story can be read from the documentation. There's also brief review to the theory behind non-conforming finite element meshes.

mortar2d.jl's Issues

Implement bi-orthogonal basis

Info about upcoming removal of packages in the General registry

As described in https://discourse.julialang.org/t/ann-plans-for-removing-packages-that-do-not-yet-support-1-0-from-the-general-registry/ we are planning on removing packages that do not support 1.0 from the General registry. This package has been detected to not support 1.0 and is thus slated to be removed. The removal of packages from the registry will happen approximately a month after this issue is open.

To transition to the new Pkg system using Project.toml, see https://github.com/JuliaRegistries/Registrator.jl#transitioning-from-require-to-projecttoml.
To then tag a new version of the package, see https://github.com/JuliaRegistries/Registrator.jl#via-the-github-app.

If you believe this package has erroneously been detected as not supporting 1.0 or have any other questions, don't hesitate to discuss it here or in the thread linked at the top of this post.

Re-register package

@JuliaRegistrator register()

Error tagging new release

Cannot tag a new version "v0.1.0" preceding all existing versions.
cc: @ahojukka5