[Dune] Applying an ISTL InverseOperator to multiple right-hand sides

[Carsten Gräser]

Dear Bard,

Am 02.05.2010 22:28, schrieb Bård Skaflestad:
> Dear Christian,
> 
> Thank you for your comments.  I'm simply trying to solve multiple linear systems with the exact same coefficient matrix.  The right-hand sides may be calculated independently.  On the other hand, calculating the right-hand side values in our case amounts (almost) to a complete matrix assembly (one pass over the grid's codim=0 entities for each right-hand side, and with a fairly expensive calculation for each entity).  Thus, my desire to assemble all components at the same time and have the solver automagically DTRT[tm] when presented with the resulting matrix system.
> 
> Still, you are right of course, that operating on multiple vectors within a Krylov method is probably not particularly well defined.  I'll restructure our solver to follow the
> 
>     krylov-method
>       preconditioner
>         foreach rhs

with this approach you will compute one step size for all right hand sides
in the Krylov step. This might lead to suboptimal convergence compared to
the approach where you solve the systems independently with optimal step size
for each system.

E.g. for a Laplace equation on [0,1]^2 with a (geometric) MG you can save
up to one third of the iteration steps by choosing the optimal step size
(normally between 1.0 and 1.2) compared to 1.0.

If you really want to solve the systems all at once you might want to
consider using a BCRSMatrix<ScaledIdentityMatrix<K,m> >.
However I don't know if the AMG works with it.

Best regards
Carsten


-- 
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Carsten Gräser           | phone: +49-30 / 838-75349
Freie Universität Berlin | fax  : +49-30 / 838-54977
Institut für Mathematik  | email: graeser at math.fu-berlin.de
Arnimallee 6             |
14195 Berlin, Germany    | URL  : http://page.mi.fu-berlin.de/graeser
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