matrix-free additive schwarz?
P. Aaron Lott
palott at ipst.umd.edu
Sun Mar 4 15:44:18 CST 2007
Hi Matt,
I hope I can explain a bit better what it is I'm looking for, and
also try to understand what I would need to provide to petsc in order
to use its ASM preconditioner. It seems that in essence, for a matrix-
free ASM implementation, I would need to provide either the
restriction operators for each subdomain, or the assembled system
matrix so that petsc's routines could determine the restriction
operators.
Currently, I have a Newton-Krylov spectral element code for solving
the 2D incompressible Navier-Stokes equations. I perform all my
matrix-vector products in a matrix-free framework. I now need a
preconditioner for the subsidiary Advection-Diffusion equation solve,
and I'm wanting to use ASM. I'm hoping to apply this preconditioner
in a matrix free setting as well. My code applies matrix-vector
products element-wise, and then performs an assembly (gather-scatter)
procedure to get the global solution.
If all the subdomains for ASM are extensions of the elements from the
spectral element discretization, then challenge is to construct the
the restriction operators for each element to produce the ASM
subdomains. From your message, it seems like petsc isn't able to
construct these restriction operators unless I provide an assembled
global system matrix. If this is what petsc needs, I could compute
the assembled system matrix (although storing this requires a lot of
memory), and pass it to petsc. I thought though, that it may be
possible to compute the restriction operators without accessing the
assembled system, but rather through local-global maps providing
indirect addressing. If someone has done this before, in a completely
matrix-free setting, the same code could be used, or modified to
obtain the restriction operators for each subdomain. I would be
particularly interested in the second option if it is available
either in petsc, or some package that links with petsc. I suppose the
third option is, as you mentioned, providing my own preconditioner
with PCSHELL, but my original reason for wanting to use petsc, was
for it to provide me with the preconditioner...
Thanks,
-Aaron
On Mar 4, 2007, at 3:41 PM, Matthew Knepley wrote:
> On 3/4/07, P. Aaron Lott <palott at ipst.umd.edu> wrote:
>> Hi,
>>
>> I'm new to petsc, and I've been reading through the petsc manual
>> today trying to figure out if petsc provides a matrix-free
>> implementation of a Newton-Krylov-Schwarz solver. It looks like in
>> terms of the Newton-Krylov part, everything can be done in a matrix-
>> free setting, but I can't tell if there are routines available to
>> allow for a matrix-free Additive Schwarz preconditioner, and if so,
>> what needs to be provided by the user to implement it. I'm very keen
>> on using petsc to provide an additive schwarz preconditioner for my
>> spectral element CFD code, but I need a matrix-free implementation
>> because I don't have access to the global system matrix. Does anyone
>> have experience with applying matrix-free preconditioners in petsc?
>
> Its not quite clear what you want. You can, of course, apply any
> preconditioner
> you want with PCSHELL. We do have an ASM preconditioner, however
> the extra
> support this provides is to
>
> 1) automatically figure out the overlapping domains using the matrix
> nonzero structure
>
> 2) solves the equation restricted to these overlapping partitions
>
> The first job cannot be done without a structure of some sort,
> which we do not
> have in the matrix-free case, and the second depends on the first.
>
> Matt
>
>> Thanks,
>>
>> -Aaron
>>
>>
>>
>> P. Aaron Lott
>> Ph.D. Candidate
>> 4239 Computer and Space Sciences Building
>> University of Maryland
>> College Park, MD 20742-4015
>>
>> palott at ipst.umd.edu
>> http://www.lcv.umd.edu/~palott
>> Office: 301.405.4894
>> Fax: 301.314.0827
>>
>>
>>
>
>
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> and critically is forced to realize that there are scarcely any
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> Drummond Rennie
P. Aaron Lott
Ph.D. Candidate
4239 Computer and Space Sciences Building
University of Maryland
College Park, MD 20742-4015
palott at ipst.umd.edu
http://www.lcv.umd.edu/~palott
Office: 301.405.4894
Fax: 301.314.0827
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