[petsc-users] optimizing repeated calls to KSPsolve?

[Luke Bloy]

Matt thanks for the response.  I'll give those a try. I'm also 
interested in try the Cholesky decomposition is there particular 
external packages that are required to use it?

Thanks again.
Luke

On 12/10/2010 06:22 PM, Matthew Knepley wrote:
> On Fri, Dec 10, 2010 at 11:03 PM, Luke Bloy <luke.bloy at gmail.com 
> <mailto:luke.bloy at gmail.com>> wrote:
>
>
>     Thanks for the response.
>
>     On 12/10/2010 04:18 PM, Jed Brown wrote:
>>     On Fri, Dec 10, 2010 at 22:15, Luke Bloy <luke.bloy at gmail.com
>>     <mailto:luke.bloy at gmail.com>> wrote:
>>
>>         My problem is that i have a large number (~500,000)  of b
>>         vectors that I would like to find solutions for. My plan is
>>         to call KSPsolve repeatedly with each b. However I wonder if
>>         there are any solvers or approaches that might benefit from
>>         the fact that my A matrix does not change. Are there any
>>         decompositions that might still be sparse that would offer a
>>         speed up?
>>
>>
>>     1. What is the high-level problem you are trying to solve?  There
>>     might be a better way.
>>
>     I'm solving a diffusion problem. essentially I have 2,000,000
>     possible states for my system to be in. The system evolves based
>     on a markov matrix M, which describes the probability the system
>     moves from one state to another. This matrix is extremely sparse
>     on the < 100,000,000 nonzero elements. The problem is to pump
>     mass/energy into the system at certain states. What I'm interested
>     in is the steady state behavior of the system.
>
>     basically the dynamics can be summarized as
>
>     d_{t+1} = M d_{t} + d_i
>
>     Where d_t is the state vector at time t and d_i shows the states I
>     am pumping energy into. I want to find d_t as t goes to infinity.
>
>     My current approach is to solve the following system.
>
>     (I-M) d = d_i
>
>     I'm certainly open to any suggestions you might have.
>
>>     2. If you can afford the memory, a direct solve probably makes sense.
>
>     My understanding is the inverses would generally be dense. I
>     certainly don't have any memory to hold a 2 million by 2 million
>     dense matrix, I have about 40G to play with. So perhaps a
>     decomposition might work? Which might you suggest?
>
>
> Try -pc_type lu -pc_mat_factor_package <mumps, superlu_dist> once you 
> have reconfigured using
>
>   --download-superlu_dist --download-mumps
>
> They are sparse LU factorization packages that might work.
>
>    Matt
>
>     Thanks
>     Luke
>
>
>
>
> -- 
> What most experimenters take for granted before they begin their 
> experiments is infinitely more interesting than any results to which 
> their experiments lead.
> -- Norbert Wiener
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