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Matt thanks for the response. I'll give those a try. I'm also
interested in try the <font color="#ff0000"><span style="color:
rgb(0, 0, 0);">Cholesky decomposition is there particular
external packages that are required to use it?<br>
<br>
Thanks again.<br>
Luke<br>
</span></font><br>
On 12/10/2010 06:22 PM, Matthew Knepley wrote:
<blockquote
cite="mid:AANLkTikLGoT9WHzaEdk03Xuo02zcaz8H6Q3PLaxVmY83@mail.gmail.com"
type="cite">On Fri, Dec 10, 2010 at 11:03 PM, Luke Bloy <span
dir="ltr"><<a moz-do-not-send="true"
href="mailto:luke.bloy@gmail.com">luke.bloy@gmail.com</a>></span>
wrote:<br>
<div class="gmail_quote">
<blockquote class="gmail_quote" style="margin: 0pt 0pt 0pt
0.8ex; border-left: 1px solid rgb(204, 204, 204);
padding-left: 1ex;">
<div bgcolor="#ffffff" text="#000000"> <br>
Thanks for the response.<br>
<br>
On 12/10/2010 04:18 PM, Jed Brown wrote:
<blockquote type="cite">
<div class="gmail_quote">On Fri, Dec 10, 2010 at 22:15,
Luke Bloy <span dir="ltr"><<a moz-do-not-send="true"
href="mailto:luke.bloy@gmail.com" target="_blank">luke.bloy@gmail.com</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin: 0pt 0pt
0pt 0.8ex; border-left: 1px solid rgb(204, 204, 204);
padding-left: 1ex;"> 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?</blockquote>
</div>
<br>
<div>1. What is the high-level problem you are trying to
solve? There might be a better way.</div>
<div><br>
</div>
</blockquote>
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.<br>
<br>
basically the dynamics can be summarized as <br>
<br>
d_{t+1} = M d_{t} + d_i<br>
<br>
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.<br>
<br>
My current approach is to solve the following system.<br>
<br>
(I-M) d = d_i<br>
<br>
I'm certainly open to any suggestions you might have.<br>
<br>
<blockquote type="cite">
<div>2. If you can afford the memory, a direct solve
probably makes sense.</div>
</blockquote>
<br>
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?<br>
</div>
</blockquote>
<div><br>
</div>
<div>Try -pc_type lu -pc_mat_factor_package <mumps,
superlu_dist> once you have reconfigured using</div>
<div><br>
</div>
<div>
--download-superlu_dist --download-mumps</div>
<div><br>
</div>
<div>They are sparse LU factorization packages that might work.</div>
<div><br>
</div>
<div> Matt</div>
<div> </div>
<blockquote class="gmail_quote" style="margin: 0pt 0pt 0pt
0.8ex; border-left: 1px solid rgb(204, 204, 204);
padding-left: 1ex;">
<div bgcolor="#ffffff" text="#000000"> Thanks<br>
Luke<br>
<br>
</div>
</blockquote>
</div>
<br>
<br clear="all">
<br>
-- <br>
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to
which their experiments lead.<br>
-- Norbert Wiener<br>
</blockquote>
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