dolfin team mailing list archive

[Jed Brown <jed@xxxxxxxx>]

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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