On Sat, 6 Oct 2018 at 12:42, Matthew Knepley <knep...@gmail.com> wrote:
> On Fri, Oct 5, 2018 at 9:08 PM Mike Wick <michael.wick.1...@gmail.com> > wrote: > >> Hello PETSc team: >> >> I am trying to solve a PDE problem with high-order finite elements. The >> matrix is getting denser and my experience is that MUMPS just outperforms >> iterative solvers. >> > > If the problem is elliptic, there is a lot of evidence that the P1 > preconditioner is descent for the system. Some people > just project the system to P1, invert that with multigrid, and use that as > the PC for Krylov. It should be worth trying. > Matt means project to P1 directly from your high order function space in one step. It is definitely worth trying. For those interested, this approach is first described and discussed (to my knowledge) in this paper: Persson, Per-Olof, and Jaime Peraire. "An efficient low memory implicit DG algorithm for time dependent problems." *44th AIAA Aerospace Sciences Meeting and Exhibit*. 2006. > Moreover, as Jed will tell you, forming matrices for higher order is > counterproductive. You should apply those matrix-free. > I definitely agree with that. Cheers, Dave > > Thanks, > > Matt > > >> For certain problems, MUMPS just fail in the middle for no clear reason. >> I just wander if there is any suggestion to improve the robustness of >> MUMPS? Or in general, any suggestion for interative solver with very >> high-order finite elements? >> >> Thanks! >> >> Mike >> > > > -- > What most experimenters take for granted before they begin their > experiments is infinitely more interesting than any results to which their > experiments lead. > -- Norbert Wiener > > https://www.cse.buffalo.edu/~knepley/ > <http://www.cse.buffalo.edu/~knepley/> >
