[petsc-users] optimizing repeated calls to KSPsolve?

[Matthew Knepley]

On Fri, Dec 10, 2010 at 11:03 PM, Luke Bloy <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> 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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