Sparse Matrix Inversion using PETSc

[Dr. Timothy Stitt]

Barry,

The group I am working with are calculating what they call retarded 
Green's Functions of the form:

G_r=(E-H)^(-1)

where (E-H) is a matrix. Apparently they say there is no way to avoid 
this calculation.

Tim.

Barry Smith wrote:
>   Tim,
>
>     A dense matrix with 100,000 rows and columns requires 80 gigabytes to store
> the result. 1,000,000 rows and columns requires 8,000 gigabytes. 
>
>    With this range of sizes I wouldn't even consider iterative solvers and
> would only use direct solvers. I would divide MPI_COMM_WORLD into N 
> subcommunicators of size n each and have each subcommunicator work on a 
> collection of columns of the inverse. For matrix sizes of 5,000 to say 20,000?
> I'd make n be 1 and just use PETSc's native LU solver and use MatMatSolve()
> and not use KSP at all. For larger matrices you may be able to use an n of 2
> to possibly as large as 8?
>
>    Now my numerical analysis training :-) requires me to state the following.
> It is completely insane to compute the EXPLICIT inverse of large sparse matrices
> since they are dense. Please tell me what the inverses are used for and perhaps
> we can come up with an approach the does not require computing them.
>
>    Barry
>
>
>
> On Wed, 15 Aug 2007, Dr. Timothy Stitt wrote:
>
>   
>> Firstly, many thanks to everyone who has replied with information. It has been
>> very useful indeed. Much appreciated.
>>
>> Barry, in this case the sparse matrices would be of ~ order 5000x5000. They
>> could grow in size but this is the sample matrices I am working with right
>> now. We would love a scalable approach so we can deal with more interesting
>> problems and hence larger sparse matrices. Hope that helps.
>>
>> Many thanks again.
>>
>> Tim.
>>
>> Barry Smith wrote:
>>     
>>>   Tim,
>>>
>>>     How large are you matrices?
>>>
>>>    Barry
>>>
>>>
>>> On Wed, 15 Aug 2007, Dr. Timothy Stitt wrote:
>>>
>>>   
>>>       
>>>> Hi all,
>>>>
>>>> I am currently investigating the best way to perform the inversion of a
>>>> large
>>>> sparse matrix and came upon the idea of using PETSc as a framework for
>>>> testing
>>>> various strategies from direct to iterative methods on my sample matrices.
>>>> In
>>>> this setup for an NxN sparse matrix A I would have N rhs's representing
>>>> the
>>>> Identity matrix and then solve for X. I wanted to experiment with both
>>>> parallel and serial strategies ranging from LU Decomposition using
>>>> SuperLU,
>>>> MUMPS etc. to iterative methods using GMRES etc. Am I right in thinking
>>>> that
>>>> all this can be done in PETSc by setting up a core framework and then
>>>> varying
>>>> the solver methods etc?
>>>>
>>>> I have looked over the sample KSP Solver codes although they only seem to
>>>> suggest single vectors for x and b. Can this be changed to accept multiple
>>>> vectors? Can anyone suggest a sample code that maybe demonstrates the sort
>>>> of
>>>> thing I want to achieve...if it is in fact possible.
>>>>
>>>> Thanks in advance for any assistance given,
>>>>
>>>> Regards,
>>>>
>>>> Tim.
>>>>
>>>>
>>>>     
>>>>         
>>>   
>>>       
>>     
>
>