On 10/4/24 08:10, 'yy.wayne' via deal.II User Group wrote:
I've considered multigrid preconditioners as the iterations are relatively
constant, but isn't it suits diffusion problems more,
as mentioned here (A former discussion
<https://groups.google.com/g/dealii/c/det9e4HWGrk/m/q0oj-yQlBAAJ#:~:text=-%20lumping%20of%20mass%20matrices%0A-%20AMG/GMG%20for%20laplace-like%20operators%0A-%20ILU/Jacobi%20for%20mass%20matrix-like%20operators%0A-%20spectrally-equivalent%20matrices%20to%20approximate%20Schur%20complements%0A-%20and%20more>)?
Multigrid works well for diffusion problems. It doesn't work well for
advection problems.
But if your matrix really is M + dt^2 K (i.e., with dt^2 instead of dt), then
you must be solving a problem with second time derivatives -- say the wave
equation. That's not a diffusion problem either.
I assume multigrid works well for M+dt^2K type problem, but it's expensive for
such 'easy' problem(when dt is small). The only drawback
for jacobi preconditioner is the iteration number scales with problem size ...
Well, that's the trade-off you have. Your simple method takes too many
iterations. You need to invest in a more complicated method that perhaps per
iteration is more expensive, but at least results in a smaller number of
iterations. The total time to solution is (time per iteration) * (number of
iterations). Your current approach results in (cheap) * (growing number)
whereas multigrid might be (expensive) * (constant). At some point, the latter
will be better than the former.
Best
W.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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