[Beowulf] load-balancing parallel direct solver

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 


> Hth
> Roland
> --- Toon Knapen <toon.knapen at fft.be> wrote:
>>Hi all,
>>I'm playing around with a parallel direct (schur-complement) solver
>>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
>>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?
>>Beowulf mailing list, Beowulf at beowulf.org
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