The system i'm trying to solve is of the form 0 = A*y + g(x) 0 = f(x,y) which has the jacobian
| A dg_dx | | df_dy df_dx |
I'm using the schur preconditioner which needs factorization of A and (df_dx - df_dy*inv(A)*dg_dx).
df_dx - df_dy*inv(A)*dg_dx is never formed (and hence never factored) it is dense and way to expensive to ever form. Now approx inverse(df_dx) may be used as a preconditioner for the Schur complement and this means df_dx would be factored.
Please send me the output from running with -snes_view so I can see exactly what Schur complement preconditioner you are forming.
See the attached file.
In affect I think you are correct we want A to not be factored each time because A is a constant matrix that does not change. Is this correct?
Yes, A is constant.
Do you form the big-assed matrix
| A dg_dx | | df_dy df_dx |
explicitly as one big matrix?
Yes.
And each time-step you changes values in the dg_dx, df_dy and df_dx parts with MatSetValues?
Yes,that's correct.
One fix may be to make PCSetUp() smarter and know the matrix has not changed and hence it doesn't have to be refactored (instead of only relying on the flag passed to KSPSetOperators()).
Barry
Since,A is constant it needs to be factorized only once while (df_dx - df_dy*inv(A)*dg_dx) is not constant and needs to be refactorized.
This will be tricky because we don't have a mechanism to pass this information down into PCFIELDSPLIT. Tell me exactly what you want to do that it cannot currently do and I'll what we can do about it.
Currently,the factorization is done for 'both or none'.I wanted the factorization to be done for 'either,both,or none'. I was thinking about having an option say -fieldsplit_xxx_lag_preconditioner <niterations> which will delay the refactorization for field xxx by niterations and if niterations is set to -1 then it will not update the factorization.
Thanks, Shri
Barry
On Mar 14, 2011, at 4:41 PM, Shri wrote:
| A B | |dx| |fx| Jacobian = = | C D | |dy| |fy|
While solving this linear system with a fieldsplit precondioner,is there a way to lag the numerical factorization of the A matrix. The A matrix in my application is constant and is about 3-4 times bigger than the D matrix. The log summary shows that about 90% of the time is spent in the numerical factorization phase. So i would like to do the numerical factorization for A matrix just once and not have it factorized for all the snes iterations. Speaking on the same note, should snes lag_preconditioner functionality be moved to ksp or maybe a -fieldsplit_xxx_lag_preconditioner option?
Thanks, Shri