Wikipedia explains it concisely and clearly http://en.wikipedia.org/wiki/Boundary_value_problem Also, to get a brief idea about Finite difference Method - http://www.stanford.edu/~fringer/teaching/numerical_methods_02/handouts/lect... . This is a good link to start with. Pages 7 -10 explain the method. On Mon, Feb 3, 2014 at 1:37 AM, Karsten Ahnert < karsten.ahnert@googlemail.com> wrote:
On 02/02/2014 09:01 PM, Utsav Tiwary wrote:
Currently I am working on a semester long project to learn various numerical methods like Gauss Elimination, Gauss Jacobi, Gauss Seidel methods etc. to learn how to do the computations using MPI(Message Passing Interface). Later I will be learning how to solve boundary value problem using finite difference method using the same tool - MPI. The idea is to develop a library which could make use of parallel programming to achieve the objective of solving boundary value problems. I would love to hear suggestions regarding the same.
What exactly do you mean by boundary value problems? And how are finite difference are related to this problem?
On Mon, Feb 3, 2014 at 1:24 AM, Karsten Ahnert < karsten.ahnert@googlemail.com> wrote:
On 02/02/2014 04:08 PM, Utsav Tiwary wrote:
Thankyou for showing interest in the idea Mr. Ahnert. I would like to know what pre-requisite knowledge do you expect any candidate to have prior
to
starting to work on this project ?
I have added a description of the implicit routines project idea and basic requirements for possible candidates at
https://svn.boost.org/trac/boost/wiki/SoC2014
It would also be good to have a basic idea how odeint works internally.
If you are asking about the boundary value problem I need to know more about the idea and the methods to see wether I could mentor such a project. So a working description would be very useful.
On Sun, Feb 2, 2014 at 8:20 PM, Karsten Ahnert < karsten.ahnert@googlemail.com> wrote:
On 02/02/2014 12:00 PM, Christopher Kormanyos wrote:
> And we also would like to mentor a GSOC project about implicit > methods in odeint. There are extremely important to solve PDEs.
* Is the idea ripe enough for formulation?
Yes, we had several GSOC project proposals about implicit ODE solvers last year but none of them had been accepted. Is this a problem for applications this year?
* Is there a committed mentor?
Might the potential mentor formally add the project to the list here:
I would volunteer to mentor this project. Of course, I will add the description to the ideas page.
On Saturday, February 1, 2014 9:31 PM, Larry Evans < cppljevans@suddenlink.net> wrote:
On 02/01/14 13:19, Karsten Ahnert wrote: > On 02/01/2014 03:47 PM, Utsav Tiwary wrote: >> Does it involve the use of parallel programming ? If not, is doing
it a
>> good idea ? > > There was a GSOC last year about parallelization of odeint with MPI and > OpenMP [1]. I think it was successful, although the code has not yet > been merged into the odeint trunk. Parallelization with GPUs already > works with the help of Thrust, VexCL or ViennaCL. > > odeint is a library devoted to solve the initial value problem of ODEs. > I think building shooting methods for boundary value problems on top of > odeint would be a good idea. And we also would like to mentor a GSOC > project about implicit methods in odeint. There are extremely important > to solve PDEs. > Back in June, 2011, petros posted a question to the user's list about multi-array and pdes:
http://thread.gmane.org/gmane.comp.lib.boost.user/68017
Later, he posted a question about rotating the arrays axes:
http://article.gmane.org/gmane.comp.lib.boost.user/68718/match=multi_array+r...
to help solve a pde using ADI (Alternating Direction Implicit):
http://article.gmane.org/gmane.comp.lib.boost.user/71096
In response, I prototyped a method using ADI and mentioned it here:
http://article.gmane.org/gmane.comp.lib.boost.user/71047
HTH.
-regards,
Larry
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