Re: [Boost-users] multi-array and pdes

Subject: Re: [Boost-users] multi-array and pdes
From: Larry Evans (cppljevans_at_[hidden])
Date: 2011-10-29 16:36:01

On 05/24/11 00:58, pmamales_at_[hidden] wrote:
> Hi Larry,
> 
> Thank you very much for your extended response.
> I am not sure, will have to think about it, altough this seems right.
> In appreciation of your effort to help me, let me give you some color:
> Say I am trying to sove a 3d problem using splitting methods. Lets say that the original
> system f reference is xyz.
> One alays ends up to a system of equations in the vectorized reprezentation of the grid (very much like the
> array where the elements of the ma are stored). 
> Then, when trying to solve the problem in the x direction (while in fortran storage scheme),
> I obtain a nice tridiagonal system of equations which I can solve very efficiently (using Thomas algorithm which is O(N) ).
> When I go to the second dimension, the tridiagonal system is hidden (in the original vector). However, in the rotsted yzx system it is there!!
[snip]
Hi Petros,

Based on your mention of tridiagonal system and some private emails to
me, you're using the ADI method.

However, Daniel Duffy, author of:

http://www.amazon.com/Finite-Difference-Methods-Financial-Engineering/dp/0470858826

expressed some doubts about ADI in this blog:

  http://www.datasimfinancial.com/forum/viewtopic.php?t=416

I'm a novice about PDE; so, I'd appreciate insight about why ADI seems
the better solution for your problem.

-regards,
Larry