Hi Dan,
This is tired, albeit very loosely with the user's choice of PDE solution
library/tool.
I come from a MATLAB background, and solving a complicated system of non-linear
PDEs is my first ever python project-motivated because of FiPys excellent and
easy interface to high quality solvers, it's reputation and no analogous FV
toolbox exists for Matlab (atleast to our knowledge). I am learning python
concurrently while implementing our problem-specific concepts in FiPy.
When I am tackling a new technical concept to implement, such as Aitken under
relaxation, I look at MATLAB central, which hosts user-submissions of nifty
functions, handy scripts etc.. Usually I find something which helps to get
started, and I can edit their code to adapt to my problem in typically a few
hours, rather than coding the equations from scratch.
Since python to be a very distributed ecosystem, this question for some kind of
a starter code, may not fit well in a general/computational math
stackexchange post , nor in this mailing list. fipy's details are certainly
required to implement an Aitken type dynamic under relaxation. , I.e. one needs
access to the internal and residual matrices, in order to apply text book
formulae, and then split the relaxation vectors into individual scalars for use
in the 'underrelaxation' parameter for each sweep method. The first two sweeps
must be static/initial 'underrelaxation' so that we can apply the formula.
The details of how to implement such a scheme in FiPy are quite hazy to me. I
suspect that for a least squares dynamic under relaxation, one works similarly
require access to such internal matrices. I was wondering if something like
this has been attempted before in the knowledge of the general FiPy community.
Best Regards,
Krishna
Original Message
From: Daniel Wheeler
Sent: Tuesday, September 6, 2016 11:01 AM
To: Multiple recipients of list
Subject: Re: Dynamic under-relaxation factors for FiPy sweep
>On Mon, Aug 29, 2016 at 2:40 PM, Gopalakrishnan, Krishnakumar
> wrote:
>>
>> I am trying to sweep for 8 field variables in FiPy, until all their residues
>> die down to appreciably small values.
>>
>>
>>
>> Currently, the convergence of this iterative loop is very slow. I have fixed
>> under-relaxation implemented right now, but looking for implementing a
>> dynamic under-relaxation factor for each of these 8 variables – something
>> like an Aitken’s or least-squares method should be helpful.
>>
>>
>>
>> Is there any helpful resource that the users of FiPy may be able to point me
>> to ?
>
>I don't think there are any FiPy specific resources on that. Your
>issue is with the algorithm or theory rather than how to implement it
>in Python / FiPy, right?
>
>--
>Daniel Wheeler
>
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