On Mon 2008-05-19 09:27, Kent-Andre Mardal wrote: > > søn, 18.05.2008 kl. 22.31 +0200, skrev Jed Brown: > > On Sun 2008-05-18 21:54, Johan Hoffman wrote: > > > > On Sat, May 17, 2008 at 04:40:48PM +0200, Johan Hoffman wrote: > > > > > > > > 1. Solve time may dominate assemble anyway so that's where we should > > > > optimize. > > > > > > Yes, there may be such cases, in particular for simple forms (Laplace > > > equation etc.). For more complex forms with more terms and coefficients, > > > assembly typically dominates, from what I have seen. This is the case for > > > the flow problems of Murtazo for example. > > > > This probably depends if you use are using a projection method. If you are > > solving the saddle point problem, you can forget about assembly time. But > > optimizing the solve is all about constructing a good preconditioner. If > > the > > operator is elliptic then AMG should work well and you don't have to think, > > but > > if it is indefinite all bets are off. I think we can build saddle point > > preconditioners now by writing some funny-looking mixed form files, but that > > could be made easier. > > > > There are some tools for making BlockMatrices and BlockPreconditioners > in dolfin/sandbox/la/poisson (stupid place to put it). The standard > matrices are here glued together to a block matrix in Python and > similarly with the block preconditioners. The backside is that the > Krylov solver then needs to be in Python. I am working on a > Navier-Stokes solver based on this. The preconditioner is optimal for > Stokes, it is a bit unclear what happens when strong convection is > present.
What does optimal mean? Asymptotically optimal is easy since the Schur complement is conditioned independent of mesh refinement. However, there can still be a huge practical difference. Are you all aware of this? http://www.mcc.monash.edu.au/Codes/PetscExt Supposedly PETSc folks are working on a general system for black matrices and associated preconditioners (that plays nicely with DA/DMMG). Jed
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