A fast parallel algorithm for solving block-tridiagonal systems of linear equations including the domain decomposition method

•The new parallel algorithm for solving SLAEs with the same block-tridiagonal matrix is proposed.•The dichotomy algorithm allows an effective use of the domain decomposition on a supercomputer.•The band preconditioner can be successfully implemented on supercomputers. In this study, we develop a new...

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Bibliographic Details
Published in:Parallel computing Vol. 39; no. 6-7; pp. 245 - 258
Main Author: Terekhov, Andrew V.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.06.2013
Subjects:
Acoustic solver
Algorithms
Block-tridiagonal matrices
Blocking
Computational efficiency
Domain decomposition method
Domain decomposition methods
Laguerre transform
Linear equations
Mathematical analysis
Parallel dichotomy algorithm
PML absorbing boundary condition
Processors
Spectra
Acoustic solver
Parallel dichotomy algorithm
Block-tridiagonal matrices
Domain decomposition method
PML absorbing boundary condition
Laguerre transform
ISSN:0167-8191, 1872-7336
Online Access:Get full text
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Summary:•The new parallel algorithm for solving SLAEs with the same block-tridiagonal matrix is proposed.•The dichotomy algorithm allows an effective use of the domain decomposition on a supercomputer.•The band preconditioner can be successfully implemented on supercomputers. In this study, we develop a new parallel algorithm for solving systems of linear algebraic equations with the same block-tridiagonal matrix but with different right-hand sides. The method is a generalization of the parallel dichotomy algorithm for solving systems of linear equations with tridiagonal matrices [1]. Using this approach, we propose a parallel realization of the domain decomposition method (the Schur complement method). The calculation of acoustic wave fields using the spectral-difference technique improves the efficiency of the parallel algorithms. A near-linear dependence of the speedup with the number of processors is attained using both several and several thousands of processors. This study is innovative because the parallel algorithm developed for solving block-tridiagonal systems of equations is an effective and simple set of procedures for solving engineering tasks on a supercomputer.
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ISSN:0167-8191
1872-7336
DOI:10.1016/j.parco.2013.03.003