Jed Brown

A related question here is which of these projections need to be lumped. The diagonal is a fine preconditioner for a consistent L^2 projection, and typically has some quality improvements....

Let's try adding this conservative lumping to `PCJacobi`. Is that something you can do or should we recruit someone else? Should be just a few lines of code (`MatMult`, `VecSum`,...

I'd make it `-pc_jacobi_type conservative" or some similar name, alongside the current options `diagonal,rowmax,rowsum`. See `include/petscpctypes.h` and `src/ksp/pc/impls/jacobi/jacobi.c` (and `src/ksp/f90-mod/petscpc.h` to make it available in Fortran).

I don't trust it (because I haven't used it), but this is the page from Hughes' book (in collapsed comment just above previously linked one).  Here's the description of...

Cool. You had some tests in a profile comparing consistent and lumped for hex elements. Can you do that with quadratic tets and include consistent, diagonal, and this lumping?

Hmm, `src/dm/dt/fe/tests/ex3.c` incorrectly claims to do an "L2 projection", but is really just sampling the dual basis functions. @knepley what's your most convenient test of accuracy of a consistent mass...

Cool that they're that close. I don't a priori have an explanation for that. We could use the projection of diagnostic variables in Ratel as a test of interesting fields...

I think you mean "only been working with hex elements". Note that with `MatSetValuesCOO`, it would be possible to do element-based lumping so long as it was computed before assembly...

Note that returning `const` pointers does not prevent use after free. I don't think we have a good rule for this in PETSc either. It's vaguely "if the caller might...

Good call. Once we figure out drivers, we should also be able to use chipStar (HIP) to run on the Intel GPUs.