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>
