[petsc-users] external solvers

[Umut Tabak]

> Note that shifting changes the matrix so you should always check
> residuals, and wrap it in an iterative method when you are getting the
> wrong solution due to the shift.
>
>   
Dear Jed,
 
Thanks for the swift reply.

I am not sure I understood this, my main problem was due to the badly 
conditioned matrices where the convergence was really too slow for the 
iterative methods, cg especially. Then I just came up with a paper where 
they are comparing some iterative methods and direct solvers from 
HSL(namely, MA57) similar to the ones I have, extracted from commercial 
FE codes where the conditioning of the matrices are on the order of 10e8 
or larger for shell type elements(besides I also need shell type 
elements in my computations for the moment), but my matrices are worser 
in condition numbers in comparison to the ones that they extracted. A 
bit of technical detail.

After I saw these shifting options, -pc_factor_shift_nonzero or 
-pc_factor_shift_positive_definite, in the trouble shooting, I wondered 
why this kind of shift can not be applied to make the systems better 
conditioned, namely, adding on the diagonal

( A +alpha * I )x = b

in that paper they give references to Manteuffel's two papers, when I 
saw that name also in the manual pages, a ring belt so that was the 
story if similar things could be applied or not, I have not checked 
those papers on incomplete cholesky factorization yet though.

This is what I mean, you transform the system to another one, but how to 
recover back to the original problem? On paper I am checking how these 
kinds of tricks might work, but I guess, like applying a preconditioner 
to a matrix, that is not possible. Your explanation above is not clear 
to me yet.

> Is the matrix actually singular or just very ill conditioned?  See the
> -mat_mumps_icntl_* options (look at the MUMPS user's manual for
> details).  SuperLU has a similar option, and both have "iterative
> refinement", which might help.  Finally, depending on your application,
> it may be possible to reformulate your problem to have better
> conditioning.
>
>   
Matrices are pretty badly conditioned. Moreover one is singular but to 
form an operator matrix. I am subtracting another scaled matrix from the 
singular one. As of,

Operator = Sing_Mat - alpha * Another_Mat ; (alpha is large btw, on the 
order of e5)

where Another_Mat is also badly conditioned but in theory this should 
not be singular, can be badly conditioned still though.

Thanks for the pointers.

Best Umut