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# [Beowulf] load-balancing parallel direct solver

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Toon Knapen toon.knapen at fft.be
Fri Apr 29 10:56:42 PDT 2005

```Roland Krause wrote:
> Metis - http://www-users.cs.umn.edu/~karypis/metis/parmetis/

Indeed Metis or Zoltan can be used to calculate a distribution. But the
question is how to present the data to metis so that metis returns a
distribution that is well balanced.

For instance, a naive approach is to use a dual-graph where every node
in the graph represents a finite element. The weight of the node is
determined by the number of DOF's of the elements. The edges that
connect the nodes in the metis-graph represent the finite elements that
have common DOF's. The weight of the edge is for instance determined by
the number of common DOF's of both elements. This strategy however is
simple but also provides ill-balanced domains. So actually the
underlying question is: how do you determine the weight on the nodes and
edges in the metis-graph so that it makes groups of elements that are
well-balanced.

toon

>
> Hth
> Roland
> --- Toon Knapen <toon.knapen at fft.be> wrote:
>
>>Hi all,
>>
>>I'm playing around with a parallel direct (schur-complement) solver
>>and
>>now I'm trying to distribute my finite elements over the different
>>processes to obtain a good load-balance (for the local factorization)
>>
>>while minimising the interface between the different FE domains
>>(which
>>determine the schur complement).
>>
>>Do any of you have experience with generating a load-balanced
>>distribution for direct solvers or can provide me with references to
>>papers, I would greatly appreciate it?
>>
>>toon
>>
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