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List:       beowulf
Subject:    parallel linear solvers
From:       Emil Briggs briggs () tick ! physics ! ncsu ! edu
Date:       1999-10-26 12:50:00
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>
>The matrices I am looking at are coming mainly from finte differences
>and finite elements. But I would be interested in any experiences
>with any kind of matrices.
> 

OK. For this type of problem you have to consider the computational 
workload of the algorithm. Typically something of the type

      W = (prefactor) x pow(N, M)

     where N represents the problem size and M is some exponent
     greater than or equal to one.


   For finite difference problems M=1 for multigrid iterative methods
   and for large enough N it's always the most efficient choice. The
   prefactor though is important and for smaller N a direct method
   may be faster depending on the sizes of the prefactors for the
   different methods. 

   Multigrid iterative methods work well on clusters but the 
   programming is nontrivial. I think that you're more likely
   to find canned routines for direct methods. If you want to
   look at some multigrid based stuff for three-dimensional
   finite difference problems I can send you some code that you
   can take a look at.


Emil
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