On Thu, Aug 24, 2017 at 2:29 AM, Klaij, Christiaan <c.kl...@marin.nl> wrote:
> Matt, > > Thanks, I can understand the lower condition number of P A, but > what about r? Doesn't that change to P r and if so why can we > assume that ||r|| and ||P r|| have the same order? > r and Pr are the things we can control. We make them whatever we want. Matt > Chris > > > dr. ir. Christiaan Klaij | Senior Researcher | Research & Development > MARIN | T +31 317 49 33 44 <+31%20317%20493%20344> | c.kl...@marin.nl | > www.marin.nl > > [image: LinkedIn] <https://www.linkedin.com/company/marin> [image: > YouTube] <http://www.youtube.com/marinmultimedia> [image: Twitter] > <https://twitter.com/MARIN_nieuws> [image: Facebook] > <https://www.facebook.com/marin.wageningen> > MARIN news: New C-DRONE - for undisturbed wave spectrum measurements > <http://www.marin.nl/web/News/News-items/New-CDRONE-for-undisturbed-wave-spectrum-measurements-1.htm> > > ------------------------------ > *From:* Matthew Knepley <knep...@gmail.com> > *Sent:* Wednesday, August 23, 2017 8:37 AM > *To:* Barry Smith > *Cc:* Klaij, Christiaan; petsc-users@mcs.anl.gov > *Subject:* Re: [petsc-users] Petsc ILU PC Change between 3.6.4 and 3.7.x? > > On Wed, Aug 23, 2017 at 2:30 AM, Barry Smith <bsm...@mcs.anl.gov> wrote: > >> >> Some argue that the preconditioned residual is "closer to" the norm of >> the error than the unpreconditioned norm. I don't have a solid mathematical >> reason to prefer left preconditioning with the preconditioned norm. > > > Because you have || x - x_exact || < k(A) || r || > > where r is the residual and k is the condition number of A. If instead of > A you use P A, which we assume has a lower condition number, then > this bound is improved. > > Thanks, > > Matt > > >> >> Barry >> >> >> >> > On Aug 22, 2017, at 11:27 PM, Klaij, Christiaan <c.kl...@marin.nl> >> wrote: >> > >> > Barry, >> > >> > Thanks for the explanation. >> > >> > We do have some rare cases that give false convergence, but >> > decided to use >> > >> > CALL KSPSetNormType(ksp,KSP_NORM_UNPRECONDITIONED,ierr) >> > >> > so that convergence is always based on the true residual. Our >> > results are much more consistent now. So that could have been >> > your protection against the rare case as well, right? Why do you >> > prefer left preconditioning? >> > >> > Chris >> > >> > >> > >> > dr. ir. Christiaan Klaij | Senior Researcher | Research & Development >> > MARIN | T +31 317 49 33 44 | mailto:c.kl...@marin.nl | >> http://www.marin.nl >> > >> > MARIN news: http://www.marin.nl/web/News/N >> ews-items/BlueWeek-October-911-Rostock.htm >> > >> > ________________________________________ >> > From: Barry Smith <bsm...@mcs.anl.gov> >> > Sent: Tuesday, August 22, 2017 6:25 PM >> > To: Klaij, Christiaan >> > Cc: petsc-users@mcs.anl.gov >> > Subject: Re: [petsc-users] Petsc ILU PC Change between 3.6.4 and 3.7.x? >> > >> >> On Aug 22, 2017, at 6:49 AM, Klaij, Christiaan <c.kl...@marin.nl> >> wrote: >> >> >> >> We also faced this problem in our code. So I've added: >> >> >> >> CALL PetscOptionsSetValue(PETSC_NULL_OBJECT,"-sub_pc_factor_shift >> _type","nonzero",ierr) >> >> >> >> since there seems to be no setter function for this (correct me >> >> if I'm wrong). Then everythings fine again. >> >> >> >> Out of curiosity, what was the reason to change the default >> >> behaviour? >> > >> > The reason we changed this is that we would rather have a failure >> that makes the user aware of a serious problem then to produce "garbage" >> results. In some rare cases the shift can cause a huge jump in the >> preconditioned residual which then decreases rapidly while the true >> residual does not improve. This results in the KSP thinking it has >> converged while in fact it has essentially garbage for an answer. Under the >> previous model, where we shifted by default, users would in this rare case >> think they had reasonable solutions when they did not. >> > >> > For many users, such as yourself, the previous default behavior was >> fine because you didn't have the "rare case" but we decided it was best to >> protect against the rare case even though it would require other users such >> as yourself to add the option. >> > >> > Barry >> >> > > > -- > What most experimenters take for granted before they begin their > experiments is infinitely more interesting than any results to which their > experiments lead. > -- Norbert Wiener > > http://www.caam.rice.edu/~mk51/ > > -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener http://www.caam.rice.edu/~mk51/