S.H. Hsieh,
School of Civil Engineering, Purdue University, West Lafayette, IN 47907-1284, U.S.A.

G.H. Paulino and J.F. Abel,
School of civil and Environmental engineering, Cornell University, Ithaca, NY 14853-3501, U.S.A.

Abstract

Recently, several domain partitioning algorithms have been proposed to effect load-balancing among processors in parallel finite element analysis.  The recursive spectral bisection (RSB) algorithm has been shown to be effective.  However, the bisection nature of the RSB results in partitions of an integer power of two, which is too restrictive for computing environments consisting of an arbitrary number of processors.  This paper presents two recursive spectral partitioning algorithms, both of which generalize the RSB algorithm for an arbitrary number of partitions.  These algorithms are based on a graph partitioning approach which includes spectral techniques and graph representation of finite element meshes.  The 'algebraic connectivity vector' is introduced as a parameter to assess the quality of the partitioning results.  Both node-based and element-based partitioning strategies are discussed.  The spectral algorithms are also evaluated and compared for coarse-grained partitioning using different types of structures modeled by 1-D, 2-D and 3-D finite elements.

Key words:  domain decomposition, load balancing, recursive algorithms, partitioning algorithms, parallel finite element analysis, spectral techniques, Lanczos method.

Representative Results:

Parallel analysis of a turbine blade disk

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