Is there any interest in creating a FEM Julia organization?

[chakravala]

@PetrKryslUCSD

A fully general mesh framework needs to support, in addition to the basic cube -like and simplex -like shapes with the minimum number of vertices, analogous shapes with higher numbers of vertices (mid-edge, interior, and such), and also shapes with variable number of vertices (Voronoi-type polyhedra and so on).

@BLI

add attribute (internal) independent variables to spatial (external) variables. For such problems, higher dimensional grids than 3D may be needed.

CAD in Julia?

A very good universal API for points, vertices, faces, edges, spheres, circles, lines, areas, volumes, etc can be phrased in terms of geometric algebra and homological algebra… So I recommend using the number system I am developing in the Grassmann package as an underlying type for the geometry. Then we can build the specific geometry types by storing the geometric numbers from Grassmann in that struct. To see what I’m talking about, have a look at this presentation where conformal geometric al…

As I have mentioned in the other threads before here, the Grassmann.jl differential geometric algebriac number system would be well suited to this, since it naturally supports homological algebra with simplices and faces and edges and points and lattices and so on. It also generalizes to any number of dimensions and works with projective geometry. Also, it supports multivariable differential operators and differential forms.

Simplicial homology

That is to say, I have not created a mesh geometry framework with it yet… but I believe it would be beneficial to use this universal mathematical language as a foundational building block for such things… since it is a universal language that can be used for automatic differentiation and geometry simultaneously.