Parallel Preconditioned Conjugate Gradient Square Method Based on Normalized Approximate Inverses | Zendy

George A. Gravvanis | Zendy; Konstantinos M. Giannoutakis | Zendy

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Parallel Preconditioned Conjugate Gradient Square Method Based on Normalized Approximate Inverses

Author(s) -

George A. Gravvanis,

Konstantinos M. Giannoutakis

Publication year - 2005

Publication title -

scientific programming

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.269

H-Index - 36

eISSN - 1875-919X

pISSN - 1058-9244

DOI - 10.1155/2005/508607

Subject(s) - conjugate gradient method , mimd , discretization , message passing interface , distributed memory , inverse , matrix (chemical analysis) , linear system , mathematics , conjugate residual method , computer science , boundary value problem , derivation of the conjugate gradient method , square (algebra) , sparse matrix , boundary (topology) , incomplete lu factorization , algorithm , parallel computing , shared memory , message passing , matrix decomposition , mathematical analysis , geometry , gradient descent , eigenvalues and eigenvectors , materials science , composite material , quantum mechanics , machine learning , artificial neural network , gaussian , physics

A new class of 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. A new parallel normalized explicit preconditioned conjugate gradient square method in conjunction with normalized approximate inverse matrix techniques for solving efficiently sparse linear systems on distributed memory systems, using Message Passing Interface (MPI) communication library, is also presented along with theoretical estimates on speedups and efficiency. The implementation and performance on a distributed memory MIMD machine, using Message Passing Interface (MPI) is also investigated. Applications on characteristic initial/boundary value problems in three dimensions are discussed and numerical results are given

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