Thanks for the answers, Jed, PCPG stands for Preconditioned Conjugate Projected Gradient. Since any FETI literature suggests PCPG, I am planning to go stick with it. My plan is to extend your KSPCG algorithm with optional application of projection space and re-orthogonalizations.
Best regards, On Mon, Dec 29, 2014 at 2:33 AM, Barry Smith <[email protected]> wrote: > > Take a look at KSPFischerGuessCreate() and the material it points to. > From the command line you can run for example > > -ksp_fischer_guess 1,20 > > This method "works" by saving information about Krylov directions and then > projecting those directions out of the NEXT linear solve at the beginning > of the new linear solve (constructing a "better" initial guess), hence it > does not remove these directions out each KSP iteration, just for each new > linear solve. It can be used with the preconditioned conjugate gradient > method. There is a tiny community of people who claim this helps > significantly on their problems, we'd love to hear your experience. > > Barry > > > > On Dec 28, 2014, at 11:24 AM, Alp Kalpalp <[email protected]> wrote: > > > > Thanks for the answers, > > > > Please forgive me, I forgot to say that my stiffness matrix is not > changing during time steps. I could not remember directly but just after a > google search..I just hit this > > > > http://web.stanford.edu/group/frg/publications/recent/FETI-stoch.pdf > > > > please look around eq37 > > > > My problem is not related to this random paper I found. But, I think I > can find several others that shows the enhancing power of orthogonalization > with successive directions when the system's behaviour is not changing > rapidly. In my current sample case a gradually increasing force is applied > to a linear system. > > > > Since I use FETIDP, preconditioned conjugate projected gradient (PCPG) > is crucial in order to select any generalized inverse for the system. > > > > So, any suggestions on how to complete these tasks? > > > > For example anyway of obtaining search direction from KSPCG? > > > > or > > > > how to implement a projection space? > > > > Is it posible or too difficuly to code a variant of a KSPCG that meets > my requirements? > > > > On Sun, Dec 28, 2014 at 7:08 PM, Matthew Knepley <[email protected]> > wrote: > > On Sun, Dec 28, 2014 at 11:02 AM, Umut Tabak <[email protected]> wrote: > > On 12/28/2014 05:54 PM, Alp Kalpalp wrote: > >> Hi, > >> > >> Thank you Mark. > >> > >> Let me clarify my questions; > >> > >> 1-)How to implement or activate a Reorthogonalization procedure for > KSPCG.. > >> As you know, search directions can be found more rapidly (with less > numer of iterations) by using previous successive directions > > Without answering the PETSc related questions, interesting discussion, > > > > indeed, but at the cost of purging the previous directions(which means > explicit orthogonalizations with respect to these vectors also), so I am > not sure if you can gain something with this, cost wise... > > > > This has been proposed many times, but it has never been shown to work. > I have tried every variant I could > > find and it did not work. You can try LGMRES, which is the closest one > to working in my opinion. There is > > definitely no theoretical relation between Krylov directions from > subsequent solves unless the operator is > > identical. > > > > Matt > > > >> 2-) How to implement or activate a projection space over CG. A sample > projection can be; > >> P = I - G*((G'*G)\G'). > >> I need to insert project,scale,precondition,re-scae,re-project steps > during each KSPCG iteration. How can I utilize this? > >> > > Just a side note, I had previous experience on this that these kinds of > practice increase the cost more... > > BR, > > Umut > > > > > > > > -- > > 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 > > > >
