Open Access

ARTICLE

Distributed Finite Element Normalized Approximate Inverse Preconditioning

by G.A. Gravvanis¹, K.M. Giannoutakis¹

1 Department of Electrical and Computer Engineering, School of Engineering, Democritus University of Thrace, 12 Vas. Sofias street, GR 67100 Xanthi, Greece; Email: {ggravvan, kgiannou}@ee.duth.gr

Computer Modeling in Engineering & Sciences 2006, 16(2), 69-82. https://doi.org/10.3970/cmes.2006.016.069

Abstract

A new class of normalized explicit optimized approximate inverse finite element matrix techniques, based on normalized finite element approximate factorization procedures, for solving sparse linear systems resulting from the finite element discretization of partial differential equations in three space variables are introduced. A new parallel normalized explicit preconditioned conjugate gradient square method in conjunction with normalized approximate inverse finite element matrix techniques for solving efficiently sparse finite element linear systems on distributed memory systems is also presented along with theoretical estimates on speedups and efficiency. The performance on a distributed memory machine, using Message Passing Interface (MPI) communication library, is also investigated. Applications on characteristic non-linear initial / boundary value problems in three dimensions are discussed and numerical results are given.

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