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

Lookup NU author(s): Dr John Lloyd, Professor Chris Phillips

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Abstract

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 independent column structure, which we refer to as I2LU. 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.

Publication metadata

Author(s): Pakzad M, Lloyd JL, Phillips C

Publication type: Article

Publication status: Published

Journal: Parallel Computing

Year: 1997

Volume: 23

Issue: 6

Pages: 637-647

Print publication date: 12/05/1998

ISSN (print): 0167-8191

ISSN (electronic): 1872-7336

Publisher: Elsevier BV

URL: http://dx.doi.org/10.1016/S0167-8191(97)00026-4

DOI: 10.1016/S0167-8191(97)00026-4

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