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

[Thomas Witkowski]

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