Hi Jed This problem was external flow, transonic Euler, (M=0.85), conserved variables. As I stated in my email, the additive schwartz method + (block) ILU on the subdomains works extremely well for this problem. The real problem I am interested in however, is preconditioning for the RANS equations. For the most part, ASM+ILU works fine for these problems as well, but I am investigating other methods that may potentially increase robustness/reduce memory/reduce computational cost.
Since the solver I'm using is a structured multiblock solver that uses multigrid for the primal problem, I can use geometric multigrid, provided I construct the restriction and prolongation operators myself. I guess geometric multigrid is the best approach here. Thank you Gaetan On Mon, Apr 29, 2013 at 9:40 AM, Jed Brown <jedbrown at mcs.anl.gov> wrote: > Gaetan Kenway <gaetank at gmail.com> writes: > > > Hello > > > > I am the process of trying out some of the multigrid functionality in > PETSc > > and not having much luck. The simple system I am trying to solve is > adjoint > > system of equations resulting from the finite volume discretization of > the > > Euler equation on a 147,456 cell mesh resulting in a linear system of > > equations of size 5*147,456=737280. All of the test are done on a single > > processor and use petsc-3.2-p7. > > Is this steady-state Euler? Exterior or recirculating flow? > Conservative variables? What Mach number? > > The heuristics used in algebraic multigrid do not work for hyperbolic > systems like Euler. There has been some research, but the multigrid > efficiency that we enjoy for elliptic problems continues to elude us. > > For low Mach number, we can build preconditioners based on splitting, > reducing to an elliptic solve in the pressure space (changing variables > in the preconditioner if you use conservative variables for the full > problem). Otherwise, we're currently stuck with geometric multigrid if > we want significant coarse-grid acceleration. With finite volume > methods, this is done by agglomeration, leading to large cells with many > faces, but that exactly preserve the conservation statement of the > fine-grid problem. > > The implementation effort required for such methods is why it's still > popular to use one-level domain decomposition. > -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20130429/820887a2/attachment.html>
