Re: request for algorithm
- From: spellucci@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (Peter Spellucci)
- Date: Tue, 10 Jan 2006 10:02:43 +0000 (UTC)
In article <slrnds667g.2k2.ndros@xxxxxxxxxxxxxxxxxxxxxxxxxx>,
ndros <ndros@xxxxxxxxxxxxxxx> writes:
>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.
>
>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?
a case there such a scheme is useful (and convergent under additional
assumptions on del_t/del_x) are first order hyperbolic systems
(d/dt) u = A (d/dx)u
with the eigenvalues of the matrix all strictly positive and pairwise different
(clearly nothing elliptic or parabolic)
hth
peter
.
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