> > So you could reorder your equations and see a block diagonal matrix with >> 576 blocks. right? >> > > I not sure I understand the question correctly. For each mesh vertex, we > have a 576x576 diagonal matrix. The unknowns are ordered in this way: > v0, v2.., v575 for vertex 1, and another 576 variables for mesh vertex 2, > and so on. >
My question is,mathematically, or algebraically, is this preconditioner equivalent to 576 Laplacian PCs? I see that it is not because you coarsen the number of variables per node. So your interpolation operators couple your equations. I think that other than the coupling from eigen estimates and Krylov methods, and the coupling from your variable coursening that you have independent scalar Laplacian PCs. 10 levels is a lot. I am guessing you do like 5 levels of variable coarsening and 5 levels of (normal) vertex coarsening with some sort of AMG method. This is a very different regime that problems that I am used to. And it would still be interesting to see the flop counters to get a sense of the underlying performance differences between the normal and the all-at-once PtAp.
