[Users] looking for help with CT_MultiLevel

[Slinker, Kyle Patrick]

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
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