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Independent columns: A new parallel ILU preconditioner for the PCG method

✍ Scribed by M. Pakzad; J.L. Lloyd; C. Phillips

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 818 KB
Volume: 23
Category: Article
ISSN: 0167-8191
DOI: 10.1016/s0167-8191(97)00026-4

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✦ Synopsis

This paper considers the parallel solution of finite element equations using the preconditioned conjugate gradient method on shared memory multiprocessors. The preconditioner used is an incomplete LU factorization of the stiffness matrix. We have designed a new method for implementing parallel forward and backward substitutions which requires the L and U factors to have an independenr column struchm, which we refer to as I'LU. The algorithm has been implemented on an Encore Multimax and parallel efficiencies up to 80% of the maximum possible theoretical value have been obtained using around 6-8 processors. These figures are shown to be comparable with the efficiencies of an implementation of a similar row-oriented approach, based on level scheduling, tested with the same problems.

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