Adding mesh adaptation

[taupalosaurus]

This issue is a summary of a discussion during a meeting at IC on march 22nd. The goal of the issue is to present the roadmap we came up with, and open it to discussion.

The idea is to use Pragmatic library [https://github.com/meshadaptation/pragmatic] which will be plugged into PETSc DMPlex. First, a very limited prototype will be implemented so the workflow can be tested, then a more complete version will be developed. A major issue in implementing mesh adaptation will be the solution transfer procedure (for adaptive restarts as well as time-dependant simulations), from the "old" mesh to the "new" one. Should it be done at a topologic level in PETSc/DMPlex ? This might be simpler for standard P1 Lagrange elements, but would become difficult for more complex elements spaces, given that DMPlex objects have no notion of degrees of freedom. So it seems better to implement the interpolation procedure in Firedrake.

The adopted roadmap was summarised in the picture attached at the end of this issue. The main points were :

• Preliminary step: look at Dolfin's adap/refine API and see what can be reused.
• First steps: simplified version, restricted to 2D simplicial meshes, in serial.
  • make sure we can compute/generate a metric tensor space in Firedrake
  • write a first adaptation code in Firedrake, even if it is very limited. From a user point of view, there should be a single function that takes a metric and a mesh as input and gives a mesh (and additional information ?) as output. This should involve development in PETSc/DMPlex, as well as in Firedrake to set up the interface. It should be noted at this point that DM objects in Firedrake don't know the vertices coordinates for now.
  • Once an adapted mesh can be generated, a good way to make sure it is valid is to have Firedrake solve an equation on it
  • A first version of the interpolation procedure could use the already existing point evaluation of Firedrake
  • A full adaptation loop can then be considered and tested for steady-state problems: solve the equations, generate metric field, adapt the mesh, transfer the solution the the adapted mesh, and solve the equations on the new mesh starting from the interpolated solution...
• Next steps: from the simple prototype, several aspects will need to be completed:
  • An interpolation procedure that works for all the types of elements and function spaces supported must be written, and it would be better if it were generic. The use of elements such as Discontinuous Galerkin ones may make us consider supermeshing [http://amcg.ese.ic.ac.uk/~pef/thesis.pdf]
  • The purely mesh adaptation procedure has to be parallelized, which should be fairly easy from a Firedrake point of view, but requires some work in PETSc DMPLex. Notably, we need to think carefully about adaptation operations on halos (notably removing vertices/elements and swaps)
  • A strategy for extruded meshes has to be devised. Adapting the 2D surface then extruding it seems reasonable, but moving from 3D to 2D DMs should be considered with care.

[debunge]

Could anyone tell me please, what is current status of mesh adaptation in firedrake?

[taupalosaurus]

There is currently a PR open that implements some of the above: https://github.com/firedrakeproject/firedrake/pull/1063 (works on "regular" (non extruded) meshes with limited CG solution transfer capabilities, for now in serial). The PR mainly awaits rework of the parallel part to land.