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