dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Tue, Nov 08, 2005 at 09:58:46AM +0100, Johan Hoffman wrote:

> This looks very good, I am not worried so much about the overhead. The
> reason I am still interested in the ability of forming linear systems to
> solve in DOLFIN for some problems, is that I do not know if all problems
> can be solved efficiently by using the explicit approach of keeping the
> whole f(u) on the right hand side of the equation as in the fixed point
> iteration you indicate.
> I know you can use damped fixed point to help the problem in case it is
> not suited for pure explicit update, and I know about the short time step
> stabilization for stiff problems. Does this solve all issues? Say for
> example a strong non linearity in f(u), can you still use an explicit
> approach?

When we rewrote the ODE solvers (still in the process) we removed the
adaptive explicit damping for stiff problems. It's a nice approach and
it worked reasonably well but we couldn't make it robust enough to be
an all-purpose solver. We might add it again at some point.

> The alternative is then to use Newton, and I think it is great that the
> Newton solver in the ODE solver is in good shape. For large problems,
> where you cannot store the whole jacobian, does it have the option of
> storing sparse versions, or using a matrix-free representation of the
> jacobian?

The ODE solver always uses a matrix-free approach. Either a user
supplies the action of the Jacobian or it is approximated numerically
by

    Jx = ( f(u + hx) - f(u - hx) ) / 2h

> Is it the PETSc non-linear solver you are using together with the ODE
> solver today?

No, we use PETSc GMRES + hand-coded Newton.

> I think it is great to go for a general discrete solver of ODE/Newton type
> in DOLFIN, where you just feed the right hand side f(u); it is ideal for
> automation. I just wonder if you see any limits to this approach in terms
> of size or type of problems? Or can we skip the whole business with
> forming linear systems of equations Ax=b?

I think we can, but we need to make some more tests. It would be
interesting to see how well the ODE solver handles for example
Navier-Stokes.

/Anders

> I believe you Johan estimated the work for a matrix-free approach based on
> the action of f(u), to be favourable to forming the matrix A and using
> matrix-vector multiplication Ax? In general?