Re: GSoc Mentor for IBVP for PDEs 1D

[c.]

On 27 Feb 2014, at 05:13, prao <address@hidden> wrote:
> Hi all,
> 
> I'm a PhD student in computational fluid dynamics and interested in
> implementing initial-boundary value problems for parabolic and elliptic
> equations. In my field, we use a lot of numerical analysis and PDEs (C++, C,
> Matlab, Python, etc).


Hi Pooja,

Great to hear from you. It's always good to have new contributors. 

If you haven't done so already, please read carefully this section: 
<http://wiki.octave.org/GSoC_Project_Ideas#Steps_Toward_a_Successful_Application>
to find out what is expected from GSoC applicants. 

> I have gone through the suggested material (paper and
> wiki book and using Matlab pdepe function) and have a few ideas and
> questions.
> There was no particular mentor listed for this project, so I am
> not sure who to point my questions to (or if this is even the right place).
> I will put them out there anyway, but I apologise in advance for any
> inconvenience.


This is exactly the right place to ask! 

I hope I will be able to answer your questions and, and if I am failing 
in some part I hope someone else may jump into the conversation.

> 1. Are we trying to do just the single equation 1D or are we also trying to
> do the system of 1D?

As you say yourself below you are free to adapt the project description 
according
to your specific interests and skill set, but I think, as it stands now,
the project is aimed at developing Matlab compatible solvers.

The solvers currently available in Matlab for this kind of problems are

pdepe: http://www.mathworks.it/it/help/matlab/ref/pdepe.html

which is specifically meant for elliptic/parabolic equations,

and the bvp* class of functions, including the solvers

bvp4c: http://www.mathworks.it/it/help/matlab/ref/bvp4c.html

and 

bvp5c: http://www.mathworks.it/it/help/matlab/ref/bvp5c.html

plus a set of utility and helper functions. 

All those solvers work for systems of equations, so definitely you should aim
at systems.


> 2. What coordinate system to use?

For pdepe, look at equation (1-4) on the pdepe website for the ansatz of the 
equation
you should be aiming to solve.

As for bvp* they actually solves systems of first-order equations with 
two-point conditions,
so the concept of "coordinates" is even more foggy there.

> 3. If not selected for GSoC, can I still work on the project (if no one is
> assigned to it)? 

Definitely yes! 

Actually, we encourage GSoC applicants to show their skills in the selection
period by taking on some small Octave project and/or contribute bugfixes or 
patches.

So you are welcome to start right now.

> I know the scope of the project is flexible but was hoping to get some idea
> about the expectation from this project.

As I said this project was intended to be about Matlab compatible functions.

One special word of caution when aiming at compatibility is that you should
make sure to only look at public information (such as web documentation and 
published scientific papers) and make sure that all the code you contribute is
either your own or is licensed under a GPLv3 compatible license.


> I have a few more questions about
> the numerical integration methods but maybe they fall more into the category
> of "implementation part" and hence, apart of the the other half of the
> application. 
> Looking forward to being part of this community!

Again welcome, looking for your contributions!

c.