[petsc-users] Richardson with multiplicative MG vs. full MG

[John Fettig]

I am a little confused about what Richardson means.  If you use
multiplicative V-cycle multigrid with Richardson KSP (and no
convergence monitor), it sets the applyrichardson operator to
PCApplyRichardson_MG, which appears to just run V-cycles until
convergence.  As far as I can tell, it doesn't ever update according
to the documented

x^{n+1} = x^{n} + scale*B(b - A x^{n})

If on the other hand you use full MG, it does update according to the
above formula.  This also happens if you set a convergence monitor.

I can see how multiplicative V-cycle with Richardson is simply using
multigrid as a solver.  What I don't understand is how full MG with
Richardson is using multigrid as a solver, because it is using the
update formula above in between cycles..  Shouldn't there be a
applyrichardson for full multigrid as well?  If not, why?

Thanks,
John