[petsc-users] Richardson with direct solver does not converge in preconditioned residual norm

[Thomas Witkowski]

Shouldn't be, but it seems that is is close to singular in computer 
arithmetic. I would like to understand we it's so. The matrix is a 2x2 
block matrix with no coupling between the main blocks. I know that this 
does not make much sense but its for tests only and I would like to add 
some couplings later. Both blocks are nonsingular and easy solvable with 
direct solvers. But when adding both together, the condition number rise 
to something around 10^23. Is it only a question of scaling both 
matrices to the same order?

Thomas

Am 02.02.2012 15:32, schrieb Jed Brown:
> Is this problem singular?
>
> On Thu, Feb 2, 2012 at 13:47, Thomas Witkowski 
> <thomas.witkowski at tu-dresden.de 
> <mailto:thomas.witkowski at tu-dresden.de>> wrote:
>
>     For some tests I use richardson iterations with direct solver for
>     preconditioning (if everything is fine, richardson should be
>     replaces by preonly).
>
>      -ksp_type richardson -pc_type lu -pc_factor_mat_solver_package
>     mumps -ksp_monitor -ksp_monitor_true_residual -ksp_max_it 10
>
>     For some matrices I see that it converges fine in true residual
>     norm but not in the preconditioned one:
>
>      0 KSP Residual norm 1.540366130785e+05
>      0 KSP preconditioned resid norm 1.540366130785e+05 true resid
>     norm 4.257656834616e+04 ||r(i)||/||b|| 1.000000000000e+00
>      1 KSP Residual norm 1.355077212761e+05
>      1 KSP preconditioned resid norm 1.355077212761e+05 true resid
>     norm 1.468758291284e-11 ||r(i)||/||b|| 3.449686877867e-16
>      2 KSP Residual norm 3.775360693480e+05
>      2 KSP preconditioned resid norm 3.775360693480e+05 true resid
>     norm 5.008860262312e-12 ||r(i)||/||b|| 1.176435879376e-16
>      3 KSP Residual norm 1.714431257209e+05
>      3 KSP preconditioned resid norm 1.714431257209e+05 true resid
>     norm 5.365631839419e-12 ||r(i)||/||b|| 1.260231166541e-16
>      4 KSP Residual norm 7.164219897555e+04
>      4 KSP preconditioned resid norm 7.164219897555e+04 true resid
>     norm 5.582291603774e-12 ||r(i)||/||b|| 1.311118256030e-16
>      5 KSP Residual norm 2.480147180914e+05
>      5 KSP preconditioned resid norm 2.480147180914e+05 true resid
>     norm 5.464714292269e-12 ||r(i)||/||b|| 1.283502758569e-16
>      6 KSP Residual norm 1.749548383255e+05
>      6 KSP preconditioned resid norm 1.749548383255e+05 true resid
>     norm 6.601924132117e-12 ||r(i)||/||b|| 1.550600339239e-16
>      7 KSP Residual norm 1.873773824295e+05
>      7 KSP preconditioned resid norm 1.873773824295e+05 true resid
>     norm 6.368611865551e-12 ||r(i)||/||b|| 1.495802060366e-16
>      8 KSP Residual norm 2.610223461339e+05
>      8 KSP preconditioned resid norm 2.610223461339e+05 true resid
>     norm 8.365362648969e-12 ||r(i)||/||b|| 1.964780858090e-16
>      9 KSP Residual norm 2.459609758347e+05
>      9 KSP preconditioned resid norm 2.459609758347e+05 true resid
>     norm 8.427381039077e-12 ||r(i)||/||b|| 1.979347177668e-16
>      10 KSP Residual norm 1.611793769272e+05
>      10 KSP preconditioned resid norm 1.611793769272e+05 true resid
>     norm 8.325158481093e-12 ||r(i)||/||b|| 1.955338066095e-16
>
>
>     Would could be the reason for?
>
>     Thomas
>
>

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20120203/27ac997c/attachment.htm>