Through fenics I am solving some 3D simulations of problems with 1 Million+ dofs, some of them with direct solver, others with iterative ones. I am pretty sure that some of my problems are failing to be solved with direct solvers due to the assembled Matrix bandwidth.
Since I have a pretty good computer (128 GB ram) my goal is to solve everything with direct solvers to save some time. Do you guys know if is there a way Fenics to perform some kind of smart node numbering with the imported mesh (like reverse cuthill-mckee, or some other …)?
Using direct solvers on 3D problems is not scalable. Additionally, I’m very skeptical of your assumption that a direct solver will offer the best time-to-solution within a reasonable tolerance. See this paper, for example.
I am definitely not sure about this assumption. I said that purely based on my premature iterative solver setup results and on my advisor experience (not so contemporary) with the matter.
Anyway, I will try using ‘Boost’ to improve my node numbering. I will also definitely read your paper, hope to keep in contact with you if I miss something in it.