[petsc-users] [KSP] true norm residual

[domenico.borzacchiello at univ-st-etienne.fr]

Hi,
When I solve a linear system and monitor the true norm residual I got
somethig like this (rtol is set to 1e-6) :


  Residual norms for stokes_ solve.
  0 KSP preconditioned resid norm 1.270103385648e+00 true resid norm
2.319288792500e+06 ||r(i)||/||b|| 1.667494921925e-01
  1 KSP preconditioned resid norm 5.669390085343e-01 true resid norm
1.031308013796e+06 ||r(i)||/||b|| 7.414776812212e-02
  2 KSP preconditioned resid norm 2.347505837595e-01 true resid norm
5.772588330636e+05 ||r(i)||/||b|| 4.150307524801e-02
  3 KSP preconditioned resid norm 1.374434713779e-01 true resid norm
2.045693242518e+05 ||r(i)||/||b|| 1.470788417874e-02
  4 KSP preconditioned resid norm 4.177447095627e-02 true resid norm
1.127811207483e+05 ||r(i)||/||b|| 8.108604100745e-03
  5 KSP preconditioned resid norm 1.979676092561e-02 true resid norm
1.175236295643e+05 ||r(i)||/||b|| 8.449575410292e-03
  6 KSP preconditioned resid norm 7.297213488366e-03 true resid norm
1.135209489825e+05 ||r(i)||/||b|| 8.161795399204e-03
  7 KSP preconditioned resid norm 3.043016937820e-03 true resid norm
1.156795165002e+05 ||r(i)||/||b|| 8.316989542594e-03
  8 KSP preconditioned resid norm 1.655126721698e-03 true resid norm
1.141320219921e+05 ||r(i)||/||b|| 8.205729606261e-03
  9 KSP preconditioned resid norm 4.928188158108e-04 true resid norm
1.143795580962e+05 ||r(i)||/||b|| 8.223526665338e-03
 10 KSP preconditioned resid norm 2.038487964289e-04 true resid norm
1.141943101596e+05 ||r(i)||/||b|| 8.210207927522e-03
 11 KSP preconditioned resid norm 1.116161343513e-04 true resid norm
1.142236376429e+05 ||r(i)||/||b|| 8.212316480350e-03

Linear solve converged due to CONVERGED_RTOL iterations 11.


I'd be thankful if I could get some clarification on a few things:

- the unpreconditioned norm doesn't converge but if I visualize my
solution it looks ok

- the solver says that the solution has converged due to RTOL but it doesn't
  seem that r(11)/r(0) is less than 1e-6

I use GMRES with MG Preconditioning and GMRES+PCSHELL as smoother. The
PCSHELL at each level also implies a pre-solve scaling of the solution and
rhs vectors but these are also unscaled in a post-solve step.


thanks,
Domenico