dolfin team mailing list archive

["Johan Hoffman" <jhoffman@xxxxxxxxxx>]

> On Sun 2008-05-18 22:55, Johan Hoffman wrote:
>> > 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.
>>
>> Well, this is not what we see. I agree that this is what you would like,
>> but this is not the case now. That is why we are now focusing on the
>> assembly bottleneck.
>
> This just occurred to me.  If you have a Newtonian fluid, then the
> momentum
> equations are block diagonal, but this is not reflected in the matrix
> structure.
> Sure enough, run the stokes demo with -mat_view_draw -draw_pause -1 and
> note
> that the off-diagonal blocks of the momentum equations are cyan which
> means they
> are set, but have value zero.  This almost doubles the number of
> insertions into
> the global matrix.

Good. You are right, this piece of information is not used.

I guess the most general thing is to have ffc delete zero matrix entries
in computing the sparsity pattern. I do not think this is done today?

 Of course, if you really care about speed, you could
> implement the momentum equations matrix-free with a custom preconditioner
> that
> only uses one block (since they are the same).
>
> Also, it seems like a strange design decision for general coupled systems
> for
> the blocks to be separate like this.  (Actually, ordering the unknowns
> this way
> makes some factorizations ``work'' even when the matrix is indefinite.)

 Ok. We should look in to this.

>> We are solving the saddle point problem with an outer fixpoint iteration
>> (or Newton iteration), where the GMRES-AMG splitting can be seen as a
>> preconditioner.
>
> So these solves are a preconditioner for an outer Krylov iteration on the
> Jacobian (which has saddle point structure)?  In that case, this sounds
> similar
> to the artificial compressibility preconditioner in de Niet & Wubs 2007.
> So you
> say that solving the outer Krylov iteration on the Jacobian is faster than
> matrix assembly?  In that case, you could probably use a stale Jacobian
> for
> preconditioning.
>
> What you initially described sounded like a projection method which
> introduces a
> splitting error of $\delta t \eta$ were $\eta$ is viscosity.  Such methods
> are
> quite efficient, but are not always appropriate.

Iterating once is similar to a projection method, but we iterate until
convergence in the outer non linear residual. Of course, after some time
the number of iterations is typically 1, so the method collapses into a
projection type method.

/Johan

>
> Jed
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