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 -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20101211/d3351d67/attachment-0001.htm>
