[petsc-users] any good references on matrix scaling

[Jed Brown]

Umut Tabak <u.tabak at tudelft.nl> writes:

> Dear all,
>
> I am looking for some references for matrix scaling where I would like 
> to improve the conditioning of a block representation such as
>
> A C
> C^T B
>
> where the terms in A and B blocks are of very different orders, such as 
> A is of 1e+8 and B for instance is of order 1e-4 . The ratios can get 
> even worse but not better on the problems I tried.

I recommend non-dimensionalizing (i.e., choosing units) so the system is
better scaled.

> I am trying have an overview for some cheap conditioning approaches for 
> this problem.

Most preconditioners use the diagonal enough to fix the disparate
scales.  If you are using full-space iteration with PCFIELDSPLIT, you'll
likely have to scale the variables first.  You can always use Schur
complement reduction.
-------------- next part --------------
A non-text attachment was scrubbed...
Name: not available
Type: application/pgp-signature
Size: 835 bytes
Desc: not available
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20130912/545c862e/attachment.pgp>