Examples of academic usage

[ChrisRackauckas]

I am interested in using this in a more academic case, and in previous discussions it sounds like that's a development target. So I was wondering if there could be examples showing how to do it. Essentially, I would not want any of the physics related parts of the FEM, just the ability to discretize equations. For example, for the Heat Equation

u_t = u_xx + f(t,u)

is there a step-by-step for how to:

a) Discretize space (into a tetrahedral mesh)
b) Assemble the stiffness matrix
c) Get back a vector for the values at elements and the matrices for the assembled operators so I can then solve the equation in my own ways?

[ahojukka5]

Hi. I have written some examples to our web page juliafem.org, describing assemble procedure. We are in a middle of process of separating core functionality to own package FEMBase.jl which serves as a basis for implementing own physical models. That's where I'm next putting focus on + improving documentation, so it can be expected to see results in near future.

For that a), if I understand you correctly, we have no plans to implement any kind of meshing functionality. It is assumed that mesh already exists and is done e.g. using SALOME (we have AsterReader.jl) or ABAQUS. For purely academic problems, maybe some unit_square or unit_cube would be good.

[ChrisRackauckas]

Is the format for the mesh documented anywhere?

For purely academic problems, maybe some unit_square or unit_cube would be good.

Yes, for sure. Or at least spawn it out as a package with the intention to mesh some basic shapes.

[ChrisRackauckas]

x

[ahojukka5]

The mesh format is undocumented, but the object can be located here:

Here, mesh.nodes contains location of vertices and mesh.elements connectivity. mesh.element_types define the topology type, e.g. :Tet10, :Tet4, :Tri3, :Tri6 and so on. Nodes / element can be grouped to sets, so one can easily define properties to the group of set. Say, you have set called :BODY1 and you want to set some property to them, you can call

elements = create_elements(mesh, "BODY1")
update!(elements, "my attribute", 1.0)

[TeroFrondelius]

@ahojukka5 does PDAssembler.jl answer this issue?

[ahojukka5]

Well..

• Here we discretize simple unit square ready for calculation,
• Here we assemble stiffness matrix of heat equation,
• Here we assemble the boundary terms of heat equation,
• Here we return linear system which can be used in other solution workflows.

So I think we answer to all questions?

[ahojukka5]

Well yeah of course step-by-step howto is missing like always :)