Thanks for the reply, Eloisa. I wasn't thinking of solving the elliptic equation in terms of the stationary state of a parabolic equation as you described in your paper. But, I see now how Gauss-Seidel for the elliptic equation can be derived from finite differencing the parabolic equation. Now that I think I'm on the same page in those terms, let me see if I can rephrase the issue I'm seeing.
I tried a couple times to write something, but the best explanation I came up with is an example. I attached a short PDF walking through it. Thanks again for your help. Kyle On 06/22/2016 03:41 PM, Eloisa Bentivegna wrote: > On 22/06/16 16:42, Slinker, Kyle Patrick wrote: >> I have been working with CT_MultiLevel in an attempt to solve the >> non-conformally-flat constraint equations and I'm wondering if there is >> an error in the thorn. Where I'm potentially seeing an issue is in >> CT_SolvePsiEquation.cc and CT_SolveErrorEquation.cc in the definitions >> of dtime (for both files this is line 33 in the Brahe release). >> >> First of all, having 0.5 in this definition means that the coefficient >> for the central point in the finite difference is hard-coded to a second >> order stencil. When using fourth order, this coefficient should be 0.4, >> I believe. This effectively changes the SOR omega. >> >> More importantly, I don't think it accounts for ct_cxx, ct_cyy, or >> ct_czz. So the central point in the finite difference is not getting >> multiplied by whatever coefficient the user is setting. >> >> Am I misunderstanding how the thorn works or are these really problems? >> I've attached what I believe is a way to fix them. Thanks for your help. > Dear Kyle, > > thanks for the comments. I am not sure I understand your points though: > in CT_MultiLevel, fd_order is used to control the approximation order of > spatial derivatives, while dtime appears in the way the "time" > derivative is discretized. These two are in principle independent. > > Can you clarify which derivative you believe is wrong? > > Thanks, > Eloisa > _______________________________________________ > Users mailing list > Users@einsteintoolkit.org > http://lists.einsteintoolkit.org/mailman/listinfo/users >
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