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Thread Subject:
Poisson problem in a rectangle

Subject: Poisson problem in a rectangle

From: carlos lopez

Date: 29 Mar, 2010 23:42:21

Message: 1 of 2

Hello:
I have tried some standard finite difference solvers and they are painfully slow. I switched to some standard spectral method but still no good balancing between accuracy and CPU time.
I wonder if there exist some way to take advantage of special features of the problem:
.- rectangular domain
.- smooth forcing term, which can be evaluated exactly in any location (i.e. no need to be restricted to a regular grid)
.- requested output is not the Poisson solution, but its gradient.
Is there any code/theory which takes advantage of this special case? I know this question is near to be off-topic, but any cue will be welcome.
Regards
Carlos

Subject: Poisson problem in a rectangle

From: Bruno Luong

Date: 30 Mar, 2010 07:09:04

Message: 2 of 2

"carlos lopez" <clv2clv_00000000_@adinet.com.uy> wrote in message <hordst$31h$1@fred.mathworks.com>...
> Hello:
> I have tried some standard finite difference solvers and they are painfully slow. I switched to some standard spectral method but still no good balancing between accuracy and CPU time.
> I wonder if there exist some way to take advantage of special features of the problem:
> .- rectangular domain
> .- smooth forcing term, which can be evaluated exactly in any location (i.e. no need to be restricted to a regular grid)
> .- requested output is not the Poisson solution, but its gradient.
> Is there any code/theory which takes advantage of this special case? I know this question is near to be off-topic, but any cue will be welcome.
> Regards
> Carlos

Not sure what is "standard spectral method", but for rectangular domain, you can solve in Fourier domain (since Fourier functions are spectral functions of laplacian operator). This takes almost as fast as calling an fft2.

Bruno

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