Meshing

Underworld can precondition a Stokes solve with geometric multigrid built from a real hierarchy of meshes, rather than with the algebraic multigrid it falls back to. What the difference is, how to build a mesh that has a hierarchy, and when the choice is worth making.

There are three ways to put resolution where a calculation needs it: rebuild the mesh, subdivide it, or move its nodes. The third conserves the node budget and leaves the connectivity, the parallel partition and the multigrid hierarchy untouched — nothing is created or destroyed, only relocated. How that redistribution works in Underworld3, what it is worth in numbers, and where its ceiling is.

It can be difficult to figure out where you are in an unstructured mesh of triangles or tetrahedra; worse when the mesh is distributed in parallel. We have to solve this problem for particle-in-cell type codes such as Underworld3. This is how we do it.

Underworld is built around the idea of active Lagrangian tracer particles that carry history and composition information as the material deforms. How do we combine this information with our symbolic mathematical framework ?

One of the less glamorous but important problems in a finite element framework is this: how does the user assign values to a field variable, and how does the framework ensure that PETSc sees those values correctly, in parallel, without the user needing to keep track themselves?

Generating Voronoi diagrams and interpolating / smoothing with spline tensions are among a list of new features in Stripy 2.0