Re: request for algorithm

Hi,

> Hi everybody, I am really desperate on this and would certainly appreciate
> any recommendations/suggestions. I am looking for practical problems
> that can be solved by means of N-dimensional iterative algorithms,
> N>=3 (e.g. 3D space domain, 2D space domain+time domain, 3D space
> domain+time domain etc), where in each iteration one computes the value
> at a point U(x,y,z,...) with the aid of "previous" points. For instance,
> U(x-1,y,z,...), U(x,y-1,z,...), U(x-1,y,z-1,...), U(x,y-2,z-3,...) are
> all welcome, but e.g. U(x+1,y,z,...), U(x-1,y+1,z,...) are not. Any
> algorithm name/URL/physical problem will do, I am willing to delve into
> the details myself.

I could eventually understand why you don't want to have a forward
reference in time (you would have to solve a system of equations). But
I can't really understand why you don't want to depend on the points
U(x+1,y,t), U(x,y+1,t) for instance...

What is the problem you are faced to, exactly?


> For instance, I have been looking into time/space discretizations of
> initial value problems/boundary value problems, such as the Poisson
> equation, but when using only previous points convergence gives me
> a rough time. I really don't mind reduced accuracy of the one-sided
> discretization compared to a central alternative one, as long as the
> algorithm ensures convergence. Any ideas?

As already pointed out by Peter, such scheme can only work with
particular equation, that has a flow of information coming from the
points x-k, y-m, t-l with k,m,l >0.

This can't be the case e.g. for elliptic equation like the Poisson
equation, because by nature the flow of information comes from every
direction (hence, you need value at x+k,y+m). Of course, you can always
use an explicit discretization in time (e.g. the value at time t is
computed with the values at previous times t-l), but you will need
value of U(x+k, y+m, t)

HTH,
Loic.

.

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