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Distributed finite element normalized approximate inverse preconditioning

CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES 2006年第2期16卷 69-82页

作者： Gravvanis, G. A. Giannoutakis, K. M. Democritus Univ Thrace Sch Engn Dept Elect & Comp Engn Xanthi 67100 Greece

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.

关键词： finite element method sparse linear systems normalized approximate factorization procedures normalized approximate inverses preconditioning parallel preconditioned conjugate gradient methods parallel computations distributed computations

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normalized explicit finite element approximate inverse preconditioning

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COMPUTERS & STRUCTURES 2004年第28期82卷 2377-2388页

作者： Gravvanis, GA Giannoutakis, KM Hellen Open Univ Dept Comp Sci GR-11362 Athens Greece Univ Athens Dept Informat & Telecommun GR-15784 Athens Greece

normalized explicit approximate inverse matrix techniques for computing explicitly various families of normalized approximate inverses based on normalized approximate factorization procedures for solving sparse linear systems, which are derived from the finite difference and finite element discretization of partial differential equations are presented. normalized explicit preconditioned conjugate gradient-type schemes in conjunction with normalized approximate inverse matrix techniques are presented for the efficient solution of linear and non-linear systems. Theoretical estimates on the rate of convergence and computational complexity of the normalized explicit preconditioned conjugate gradient method are also presented. Applications of the proposed methods on characteristic linear and non-linear problems are discussed and numerical results are given. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： initial/boundary value problems finite element method finite difference method non-linear systems sparse linear systems normalized approximate factorization procedures normalized approximate inverse finite element matrix techniques preconditioning conjugate gradient schemes rate of convergence and computational complexity parallel iterative methods parallel computations

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normalized explicit approximate inverse preconditioning for solving 3D boundary value problems on uniprocessor and distributed systems

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2006年第1期65卷 84-110页

作者： Gravvanis, GA Giannoutakis, KM Univ Athens Dept Informat & Telecommun GR-15784 Athens Greece

normalized explicit approximate inverse matrix techniques, based on normalized approximate factorization procedures, for solving sparse linear systems resulting from the finite difference discretization of partial differential equations in three space variables are introduced. normalized explicit preconditioned conjugate gradient schemes in conjunction with normalized approximate inverse matrix techniques are presented for solving sparse linear systems. The convergence analysis with theoretical estimates on the rate of convergence and computational complexity of the normalized explicit preconditioned conjugate gradient method are also derived. A Parallel normalized Explicit Preconditioned Conjugate Gradient method for distributed memory systems, using message passing inter-face (MPI) Communication library, is also given along with theoretical estimates on speedups, efficiency and computational complexity. Application of the proposed method on a three-dimensional boundary value problem is discussed and numerical results are given for uniprocessor and multicomputer systems. Copyright (c) 2005 John Wiley & Sons, Ltd.

关键词： sparse linear systems normalized approximate factorization procedures normalized approximate inverse matrix techniques preconditioning conjugate gradient schemes rate of convergence and computational complexity parallel preconditioned conjugate gradient methods parallel computations distributed computations

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ON THE RATE OF CONVERGENCE AND COMPLEXITY OF normalized IMPLICIT PRECONDITIONING FOR SOLVING FINITE DIFFERENCE EQUATIONS IN THREE SPACE VARIABLES

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INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS 2004年第2期1卷 367-386页

作者： Gravvanis, George A. Giannoutakis, Konstantinos M. Hellen Open Univ Dept Comp Sci Patras Greece Univ Athens Dept Informat & Telecommun GR-15784 Athens Greece

normalized approximate factorization procedures for solving sparse linear systems, which are derived from the finite difference method of partial differential equations in three space variables, are presented. normalized implicit preconditioned conjugate gradient-type schemes in conjunction with normalized approximate factorization procedures are presented for the efficient solution of sparse linear systems. The convergence analysis with theoretical estimates on the rate of convergence and computational complexity of the normalized implicit preconditioned conjugate gradient method are also given. Application of the proposed method on characteristic three dimensional boundary value problems is discussed and numerical results are given.

关键词： Sparse linear systems normalized approximate factorization procedures preconditioning conjugate gradient schemes rate of convergence and computational complexity

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normalized explicit finite element approximate inverse preconditioning

Normalized explicit finite element approximate inverse preco...

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2nd MIT Conference on Computational Fluid and Solid Mechanics

作者： Gravvanis, GA Giannoutakis, KM Hellen Open Univ Dept Comp Sci GR-11362 Athens Greece Univ Athens Dept Informat & Telecommun GR-15784 Athens Greece

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