[petsc-users] Question with preconditioned resid norm and true resid norm

[Song Gao]

Hello,

I am using KSP framework to solve the problem   A \Delta x = b in the
matrix free fashion. where A is the matrix free matrix. I have another
assembled matrix for preconditioning, but I'm NOT using it.  My code is not
working so I'm debugging it.
I run the code with options -ksp_pc_side left -ksp_max_it 10
-ksp_gmres_restart 30 -ksp_monitor_true_residual -pc_type none -ksp_view

I think if pc_type is none, the precondiitoned resid norm should equal to
true resid norm (Am I correct?). But this doesn't happen. So maybe it would
be helpful if I know how preconditioned resid norm and true resid norm are
computed.

Website says true resid norm is just b - A \Delta x.   But how is
preconditioned resid norm computed? Any suggestions? Thank you very much.


  0 KSP preconditioned resid norm 9.619278462343e-03 true resid norm
9.619278462343e-03 ||r(i)||/||b|| 1.000000000000e+00
  1 KSP preconditioned resid norm 9.619210849854e-03 true resid norm
2.552369536916e+06 ||r(i)||/||b|| 2.653389801437e+08
  2 KSP preconditioned resid norm 9.619210847390e-03 true resid norm
2.552458142544e+06 ||r(i)||/||b|| 2.653481913988e+08
  3 KSP preconditioned resid norm 9.619210847385e-03 true resid norm
2.552458343191e+06 ||r(i)||/||b|| 2.653482122576e+08
  4 KSP preconditioned resid norm 9.619210847385e-03 true resid norm
2.552458344014e+06 ||r(i)||/||b|| 2.653482123432e+08
  5 KSP preconditioned resid norm 9.619210847385e-03 true resid norm
2.552458344015e+06 ||r(i)||/||b|| 2.653482123433e+08
.......
Linear solve did not converge due to DIVERGED_ITS iterations 10
KSP Object: 1 MPI processes
  type: gmres
    GMRES: restart=30, using Classical (unmodified) Gram-Schmidt
Orthogonalization with no iterative refinement
    GMRES: happy breakdown tolerance 1e-30
  maximum iterations=10, initial guess is zero
  tolerances:  relative=1e-06, absolute=1e-50, divergence=100000
  left preconditioning
  using PRECONDITIONED norm type for convergence test
PC Object: 1 MPI processes
  type: none
  linear system matrix followed by preconditioner matrix:
  Matrix Object:   1 MPI processes
    type: mffd
    rows=22905, cols=22905
      Matrix-free approximation:
        err=1.49012e-08 (relative error in function evaluation)
        Using wp compute h routine
            Does not compute normU
  Matrix Object:   1 MPI processes
    type: seqbaij
    rows=22905, cols=22905, bs=5
    total: nonzeros=785525, allocated nonzeros=785525
    total number of mallocs used during MatSetValues calls =0
        block size is 5
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