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

Subject: Re: [Boost-users] multi-array and pdes
From: petros (pmamales_at_[hidden])
Date: 2011-10-30 12:28:03

Hi Larry,
ADI is well suited for problems with sacial and temporal vatiation of the 
PDE cofficients.
Among experts it is indeed considered somewhat of a "hack" (not really 
though, only not universal solver)
and other more elaborate solvers are preferred.
Having said all this, it is the industry standard for its speed and ability 
to tackle a large variety of problems.
ADE is a very new method advocated by DD and -to be honest- the fact that 
noone has picked it up makes me cautius
(he-as of now- is the only one supporting it).
Would I ever implement it? Sure, after ADI though because of the 
standard-ness and because once you have one you have
enough infra for the other.
Now on the error level you report, it does not make much sense. After all it 
is a 2nd order scheme, stabilized for time evolution with 2nd
order RK.
Are you sure that
a) took the BCs into account properly?
b) you propagated the BCs as well?
c) have you experimented with various values of theta?
d) have you experimented with different time step size?
HTH
P-
ps: thx for the update. these days I am deep in multithreading LES (for the 
purpose of PDE solving) and providing with proper memory
alignment for mkl to be called.

-----Original Message----- 
From: Larry Evans
Sent: Saturday, October 29, 2011 4:36 PM
To: boost-users_at_[hidden]
Subject: Re: [Boost-users] multi-array and pdes

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

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