[Users] looking for help with CT_MultiLevel

Slinker, Kyle Patrick kslink at live.unc.edu
Mon Jun 27 12:43:23 CDT 2016

Thanks again for the reply, Eloisa. I think I'm set now.


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

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