From: Paul <paul@abelian.demon.co.uk>
Subject: Re: Question on relaxation method
Date: Tue, 01 Aug 2000 08:23:34 +0100
Newsgroups: sci.math.num-analysis
Summary: [missing]

I wrote
> ...I list those regions in which cell value movements are
> still occuring. Then I work only on these regions, ignoring
> the others. From time to time I rescan the whole grid and
> reconstruct the list of active regions.

Thanks for the replies, apparently this was referred to as
subset solving in

  S. J. Polak, C. Den Heijer,
  W. H. A. Schilders and P. A. Markowich,
  Semiconductor Device Modelling from the Numerical
  Point of View, IJNME, Vol. 24, pp. 763-838, 1987

Peter Spellucci wrote:

> sounds like reinventing multigrid (in a somewhat preliminary
> and crude way). look a the multigrid tutorial of briggs&higham
> (SIAM) for a explanantion of that.

Thanks, I've found

  A Multigrid Tutorial
  William L. Briggs
  ISBN 0-89871-221-1

which could be a great help. I'm using what may be multigrid -
I start by fully relaxing a coarse grid, then double the number
of cells in each dimension, repeating the process until I reach
the desired resolution. The subset solving is applied within
each coarseness.

Also I use a variable grid size across the field, coarser in
regions away from the areas of interest. 

From  what I can see it appears multigrid and subset solving are
independant and complimentary improvements to relaxation.
--
Paul Nicholson,
Manchester, UK.
--