[petsc-users] direct solver question

[Barry Smith]

On Aug 7, 2012, at 1:59 PM, Matthew Knepley <knepley at gmail.com> wrote:

> On Tue, Aug 7, 2012 at 1:53 PM, Tabrez Ali <stali at geology.wisc.edu> wrote:
> Matt
> 
> So if I want to use a direct solver I should really use (2) instead of (3).
> 
> To guarantee robustness, yes.

   Note also the  -pc_factor_shift_type nonzero   if this truly is needed then that means A != LU but instead A + dI = LU for some d > 0 which means the LU factorization is not for A and hence a single solve of the LU will not solver for A and it needs to iterate hence you need the GMRES.

   Barry

> 
>    Matt
>  
> Tabrez
> 
> On 08/07/2012 01:05 PM, Matthew Knepley wrote:
>> On Tue, Aug 7, 2012 at 12:48 PM, Tabrez Ali <stali at geology.wisc.edu> wrote:
>> Barry
>> 
>> So which one of the two gives the correct solution? And yes the condition number is high.
>> 
>> Actually I am trying to solve a trivial quasi-static problem with the following flags
>> 
>> (1) -ksp_type gmres -pc_type asm
>> (2) -ksp_type gmres -pc_type lu -pc_factor_shift_type nonzero
>> (3) -ksp_type preonly -pc_type lu -pc_factor_shift_type nonzero
>> 
>> This does no iterative refinement, so you are stuck with the initial accuracy of the LU
>> factorization, which can be bad for an ill-conditioned matrix.
>> 
>>    Matt
>>  
>> The results at t=0 for all three cases are equivalent.
>> 
>> For the time dependent part (linear system is solved again), results from (1) and (2) are the same. But (3) gives a very different answer.
>> 
>> I also solve the same quasi-static problem using a different code (does not use PETSc) and the results obtained are similar to (1) and (2).
>> 
>> So basically I am trying to understand why '-ksp_type preonly' gives me a (potentially) wrong solution.
>> 
>> Thanks
>> Tabrez
>> 
>> 
>> 
>> On 08/07/2012 12:01 PM, Barry Smith wrote:
>> On Aug 7, 2012, at 12:06 PM, Tabrez Ali<stali at geology.wisc.edu>  wrote:
>> 
>> Hello list
>> 
>> By any chance is using
>> 
>> -ksp_type gmres -pc_type lu
>> 
>> similar to
>> 
>> -ksp_type preonly -pc_type lu?
>> 
>> Should the results be equivalent?
>> 
>> T
>>     The should be similar but will not be identical necessarily, in particular when the matrix is ill conditioned they can be very different and in fact GMRES may iterate a few times.
>> 
>>     Barry
>> 
>> 
>> 
>> -- 
>> No one trusts a model except the one who wrote it; Everyone trusts an observation except the one who made it- Harlow Shapley
>> 
>> 
>> 
>> 
>> -- 
>> What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.
>> -- Norbert Wiener
> 
> 
> 
> 
> -- 
> What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.
> -- Norbert Wiener