Thanks again for the reply, Eloisa. I think I'm set now. Kyle
On 06/24/2016 04:19 PM, Eloisa Bentivegna wrote: > On 23/06/16 22:06, Slinker, Kyle Patrick wrote: >> 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. > Dear Kyle, > > I've followed your reasoning, but I don't see where equation (2) comes > from. To the best of my knowledge, one is not free to construct an > iterative process by deforming the differencing stencils at will. The > existing recipes (like Gauss-Seidel) are carefully crafted to have > specific properties; you can, for instance, read on the Numerical > Recipes book (equation 20.5.4 and following, in the third edition) what > dtime needs to be set to for a stable evolution. This has to do with the > stability of the Forward-Time-Centered-Space representation of the equation. > > Notice, however, that what dtime is set to in CT_MultiLevel is only the > largest admissible value. One is free to decrease this number (although > that would require more iterations to relax to the same state); your > suggestion for the coefficient, for instance, would also work. And you > are right to point out that a change in dtime is equivalent to a change > in the SOR omega (which, however, also cannot be chosen arbitrarily). > > I hope this clarifies the issue! > > Eloisa > _______________________________________________ Users mailing list Users@einsteintoolkit.org http://lists.einsteintoolkit.org/mailman/listinfo/users