Your convergence is great, looks like what one should expect (it looks 2nd order to me). What do you think is wrong with it?
If you want something better/faster, it will probably have to be problem-specific solver/algorithm, in which case you have to search for solver/algorithm for your specific problem. Tomasz On Tue, Sep 27, 2016 at 6:53 PM, Gopalakrishnan, Krishnakumar < krishnaku...@imperial.ac.uk> wrote: > Hi Ray, > > > > This looks like linear convergence to me. Anyway, the bottom-line is > that, this is too slow. We need something better – is there any > acceleration routine available? I tried Jonathan’s gist notebook showing > Newton implementation using the ResidualTerm, but couldn’t get past a bunch > of errors from the Python interpreter. > > > > Or could there be a more fundamental problem in our code > formulation/structure itself ? The solutions loo correct, when compared to > a commercial PDE package. > > > > Krishna > > > > *From:* fipy-boun...@nist.gov [mailto:fipy-boun...@nist.gov] *On Behalf > Of *Raymond Smith > *Sent:* Wednesday, September 28, 2016 12:40 AM > *To:* fipy@nist.gov > *Subject:* Re: FiPy sweep convergence bottoms out > > > > I am confused as well now. Comparing with the plots on this Wiki > <https://en.wikipedia.org/wiki/Rate_of_convergence> page which are also > semi-log, it looks to me like Krishna is seeing linear convergence. > > > > On Tue, Sep 27, 2016 at 3:57 PM, Guyer, Jonathan E. Dr. (Fed) < > jonathan.gu...@nist.gov> wrote: > > I don't understand what you mean by "supra-linear trend in the semiology > plot". You show clear 2nd order convergence, which is what I would expect. > > > On Sep 27, 2016, at 4:37 PM, Krishna <krishnaku...@imperial.ac.uk> > wrote: > > > > As you can see, we need supra-linear trend in the semiology plot, such > as to continue with the linear drops achieved in the first few sweeps. > > > > I.e. the solver is effectively bottoming out. Under-relaxation factors, > or solver-changes don't seem to work. > > > > In fact, for certain under-relaxation factors (including 1.0 for 2 of > the variables), it breaks the simulation, and produces NaNs right from the > first sweep. > > > > Krishna > > > > > > > > -------- Original Message -------- > > From: "Gopalakrishnan, Krishnakumar" <krishnaku...@imperial.ac.uk> > > Sent: Tuesday, September 27, 2016 09:02 PM > > To: fipy@nist.gov > > Subject: RE: FiPy sweep convergence bottoms out > > > > Thank you Ray, Thanks for pointing that out. > > > > > > > > Here’s the link to Semilog plot. It takes nearly 22 sweeps to achieve a > tolerance of 10^-4 for \phi_e and \phi_s_neg. > > > > > > > > Furthermore, the time spent in sweeping (within each time-step) > increases as time progresses. > > > > > > > > https://imperialcollegelondon.box.com/s/4ix6pozs1h9syt1r3fbkw2pi05ooicmy > > > > > > > > Krishna > > > > > > > > From: fipy-boun...@nist.gov [mailto:fipy-boun...@nist.gov] On Behalf Of > Raymond Smith > > Sent: Tuesday, September 27, 2016 8:51 PM > > To: fipy@nist.gov > > Subject: Re: FiPy sweep convergence bottoms out > > > > > > > > Hi, Krishna. > > > > It would be more clear to plot the residuals on a semi-log plot (or > equivalently plot the log of residual vs sweep number) to more clearly show > the value of the small residuals, as the plots in that link make it look to > me like the residuals all go to zero. > > > > Ray > > > > > > > > On Tue, Sep 27, 2016 at 12:42 PM, Gopalakrishnan, Krishnakumar < > krishnaku...@imperial.ac.uk> wrote: > > > > > > > > > Hi, > > > > > > > > We are solving a system of 5 coupled non-linear PDEs. > > > > > > > > As shown in this plot of residuals vs. sweep count > https://imperialcollegelondon.box.com/s/9davbq2gq5eani98xuuj2cw9tmz4mbu3 > , our residuals die down very slowly, i.e. the solver bottoms out. The > drop in all the residuals is linear at first, and then asymptotically > bottoms out to a value. > > > > > > > > How do we get our residuals to drop faster, i.e. with lesser sweeps and > faster convergence ? I tried changing solvers and tolerances, but curiously > enough the results remain identical. > > > > > > > > Any pointers on this will be much appreciated. > > > > > > > > > > > > Krishna > > > > > > > > > > > > > > > > > > _______________________________________________ > > fipy mailing list > > fipy@nist.gov > > http://www.ctcms.nist.gov/fipy > > [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ] > > > > > > > > _______________________________________________ > > fipy mailing list > > fipy@nist.gov > > http://www.ctcms.nist.gov/fipy > > [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ] > > > _______________________________________________ > fipy mailing list > fipy@nist.gov > http://www.ctcms.nist.gov/fipy > [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ] > > > > _______________________________________________ > fipy mailing list > fipy@nist.gov > http://www.ctcms.nist.gov/fipy > [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ] > >
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