[petsc-users] Nested solves and fgmres residual normalization

[Alexander Lindsay]

Hi all, I've found that having fgmres as an outer solve and the initial
residual scaling that comes with it can cause difficulties for inner solves
as I'm approaching convergence, presumably because I'm running out of
precision. This is the kind of thing I would normally set an absolute
tolerance for, but it feels a little silly to set `-ksp_atol 1e-4` when at
the beginning of solves there is no problem reaching that tolerance. Here
is an example solve history. You can see that the fieldsplit_p_lsc_solve
converges in a single iteration until the very end where it's
clearly struggling to hit the rtol of 1e-5. Is the scaling of the fgmres
residual important to the algorithm? git blame showed that the comment
regarding "scale VEC_VV (the initial residual)" was last hit in 1999 (and
it existed before that time), see line 125 of fgmres.c

0 KSP Residual norm 2.586864431320e-06
  Residual norms for fieldsplit_p_ solve.
  0 KSP Residual norm 4.692593309369e-02
    Residual norms for fieldsplit_p_lsc_ solve.
    0 KSP Residual norm 1.000000000000e+00
    1 KSP Residual norm 4.048060575312e-06
    Residual norms for fieldsplit_p_lsc_ solve.
    0 KSP Residual norm 4.951804839158e+01
    1 KSP Residual norm 9.672178594775e-05
  1 KSP Residual norm 2.076409133334e-02
    Residual norms for fieldsplit_p_lsc_ solve.
    0 KSP Residual norm 1.000000000000e+00
    1 KSP Residual norm 1.346618231753e-06
    Residual norms for fieldsplit_p_lsc_ solve.
    0 KSP Residual norm 8.119436471232e+01
    1 KSP Residual norm 1.233237431511e-04
  2 KSP Residual norm 8.753379232559e-03
    Residual norms for fieldsplit_p_lsc_ solve.
    0 KSP Residual norm 1.000000000000e+00
    1 KSP Residual norm 1.023335686682e-06
    Residual norms for fieldsplit_p_lsc_ solve.
    0 KSP Residual norm 1.095058035930e+02
    1 KSP Residual norm 8.452076098586e-05
  3 KSP Residual norm 1.589938296474e-03
    Residual norms for fieldsplit_p_lsc_ solve.
    0 KSP Residual norm 1.000000000000e+00
    1 KSP Residual norm 7.680981295089e-06
    Residual norms for fieldsplit_p_lsc_ solve.
    0 KSP Residual norm 7.768759831332e+01
    1 KSP Residual norm 5.120395415891e-04
  4 KSP Residual norm 4.191115394200e-04
    Residual norms for fieldsplit_p_lsc_ solve.
    0 KSP Residual norm 1.000000000000e+00
    1 KSP Residual norm 8.815992679344e-07
    Residual norms for fieldsplit_p_lsc_ solve.
    0 KSP Residual norm 5.245482238296e+01
    1 KSP Residual norm 8.672309412797e-05
  5 KSP Residual norm 1.053200310197e-04
    Residual norms for fieldsplit_p_lsc_ solve.
    0 KSP Residual norm 1.000000000000e+00
    1 KSP Residual norm 1.450184043299e-06
    Residual norms for fieldsplit_p_lsc_ solve.
    0 KSP Residual norm 9.058043325461e+01
    1 KSP Residual norm 1.643116692318e-04
  6 KSP Residual norm 2.315708746597e-05
    Residual norms for fieldsplit_p_lsc_ solve.
    0 KSP Residual norm 1.000000000000e+00
    1 KSP Residual norm 1.406236994541e-06
    Residual norms for fieldsplit_p_lsc_ solve.
    0 KSP Residual norm 5.158957906917e+01
    1 KSP Residual norm 8.910977751230e-05
  7 KSP Residual norm 2.378083073391e-06
    Residual norms for fieldsplit_p_lsc_ solve.
    0 KSP Residual norm 1.000000000000e+00
    1 KSP Residual norm 7.981173164359e-06
    Residual norms for fieldsplit_p_lsc_ solve.
    0 KSP Residual norm 7.271546763656e+01
    1 KSP Residual norm 2.211194524633e-04
  8 KSP Residual norm 8.464122393957e-07
    Residual norms for fieldsplit_p_lsc_ solve.
    0 KSP Residual norm 1.000000000000e+00
    1 KSP Residual norm 1.627170127450e-05
    2 KSP Residual norm 1.448537328052e-05
    3 KSP Residual norm 1.309526985856e-05
    4 KSP Residual norm 1.308667010157e-05
    5 KSP Residual norm 1.254021842629e-05
    6 KSP Residual norm 9.490928295823e-06
    Residual norms for fieldsplit_p_lsc_ solve.
    0 KSP Residual norm 7.084510697783e+01
    1 KSP Residual norm 1.444782053473e-04
  9 KSP Residual norm 3.334507715334e-07
Linear fieldsplit_p_ solve converged due to CONVERGED_RTOL iterations 9
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