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

Parallel normalized implicit preconditioned conjugate gradient methods for solving biharmonic equations on symmetric multiprocessor systems

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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A new class of inner-outer iterative procedures in conjunction with conjugate gradient-type schemes based on normalized approximate factorization procedures for solving sparse linear systems of irregular structure, which are derived from the finite element method of biharmonic equations in three space variables, is introduced. Normalized implicit preconditioned conjugate gradient-type methods are presented, for the efficient solution of linear sparse systems. Applications of the method on a three-dimensional biharmonic problem are discussed and numerical results are given. The parallel implementation on symmetric multiprocessor systems of the forward and backward substitution for the decomposition factors is also investigated.

Keywords:  Biharmonic equations; Finite element method; Approximate factorization procedures; Preconditioning; Parallel computations

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