On Sat, Jun 6, 2015 at 4:00 PM, Young, Matthew, Adam <[email protected]> wrote:
> Forgive me for being like a child who wanders into the middle of a > movie... > > I've been attempting to follow this conversation from a beginner's level > because I am trying to solve an elliptic PDE with variable coefficients. > Both the operator and the RHS change at each time step and the operator has > off-diagonal terms that become dominant > Yikes. > as the instability of interest grows. > As Matt says, out-of-the-box multigrid will not solve all elliptic problems fast. Is the problem even elliptic if the off diagonals are dominant? Anyway, another way of looking at it is: if the Green's function decays quickly you can exploit that with a local process plus a coarse grid correction. If you have a funny Green's function you need a funny method to deal with it. > I read somewhere that a direct method is the best for this but I'm > intrigued by Justin's comment that GAMG seems to be "the preconditioner to > use for elliptic problems". I don't want to highjack this conversation but > it seems like a good chance to ask for your collective advice on resources > for understanding my problem. Any thoughts? > > --Matt > > -------------------------------------------------------------- > Matthew Young > Graduate Student > Boston University Dept. of Astronomy > -------------------------------------------------------------- > > ------------------------------ > *From:* [email protected] [[email protected]] > on behalf of Justin Chang [[email protected]] > *Sent:* Saturday, June 06, 2015 5:29 AM > *To:* Mark Adams > *Cc:* petsc-users > *Subject:* Re: [petsc-users] Guidance on GAMG preconditioning > > Matt and Mark thank you guys for your responses. > > The reason I brought up GAMG was because it seems to me that this is the > preconditioner to use for elliptic problems. However, I am using CG/Jacobi > for my larger problems and the solver converges (with -ksp_atol and > -ksp_rtol set to 1e-8). Using GAMG I get rough the same wall-clock time, > but significantly fewer solver iterations. > > As I also kind of mentioned in another mail, the ultimate purpose is to > compare how this "correction" methodology using the TAO solver (with > bounded constraints) performs compared to the original methodology using > the KSP solver (without constraints). I have the A for BLMVM and CG/Jacobi > and they are roughly 0.3 and 0.2 respectively (do these sound about > right?). Although the AI is higher for TAO , the ratio of actual FLOPS/s > over the AI*STREAMS BW is smaller, though I am not sure what conclusions to > make of that. This was also partly why I wanted to see what kind of metrics > another KSP solver/preconditioner produces. > > Point being, if I were to draw such comparisons between TAO and KSP, > would I get crucified if people find out I am using CG/Jacobi and not GAMG? > > Thanks, > Justin > > On Fri, Jun 5, 2015 at 2:02 PM, Mark Adams <[email protected]> wrote: > >> >>>> >>> The overwhleming cost of AMG is the Galerkin triple-product RAP. >>> >>> >> That is overstating it a bit. It can be if you have a hard 3D operator >> and coarsening slowly is best. >> >> Rule of thumb is you spend 50% time is the solver and 50% in the setup, >> which is often mostly RAP (in 3D, 2D is much faster). That way you are >> within 2x of optimal and it often works out that way anyway. >> >> Mark >> > >
