[petsc-users] any good references on matrix scaling

[Umut Tabak]

On 09/12/2013 08:48 PM, Barry Smith wrote:
>
> http://en.wikipedia.org/wiki/Nondimensionalization
Hi Barry,

For the kind of problems, I am working on, this is a general problem and 
unfortunately, it is not in general possible to get away from this 
property with the scaling on the initial differential equations.

Moreover, the problem is two sided, a structure coupled to a fluid 
domain, where the physics is already inducing different scaling and math 
is obeying that ;-)

This was a problem I discussed here extensively last week. Solving 
directly is not a problem, the challenge is, if possible, to use Schur 
complements and iterative solution techniques, where the source of the 
problem emerged from.

Thanks for the comments anyway.

BR,
Umut
>
>     Barry
>
> On Sep 12, 2013, at 12:04 PM, Umut Tabak <u.tabak at tudelft.nl> wrote:
>
>> 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 am trying have an overview for some cheap conditioning approaches for this problem.
>>
>> Any ideas/references are appreciated.
>>
>> BR,
>> Umut