Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Normalized implicit preconditioned methods based on normalized finite element approximate factorization procedures

George A. Gravvanis*, Konstantinos M. Giannoutakis
Department of Electrical and Computer Engineering, School of Engineering, Democritus University of Thrace, GR 67100 Xanthi, Greece

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Normalized implicit preconditioned conjugate gradient-type schemes based on finite element normalized approximate factorization procedures for solving sparse linear systems, which are derived from the finite element method of partial differential equations in three space variables, are presented. Theoretical estimates on the rate of convergence and computational complexity of the normalized implicit preconditioned conjugate gradient method are also given. The application of the proposed method on a characteristic three-dimensional boundary value problem is discussed and numerical results are given.

Keywords:  Finite element systems; Normalized approximate factorization procedures; Preconditioning; Conjugate gradient schemes; Rate of convergence and computational complexity

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