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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| Vydáno v: | Parallel computing Ročník 39; číslo 6-7; s. 245 - 258 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier B.V
01.06.2013
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| ISSN: | 0167-8191, 1872-7336 |
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| Abstract | •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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| AbstractList | 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. •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. |
| Author | Terekhov, Andrew V. |
| Author_xml | – sequence: 1 givenname: Andrew V. surname: Terekhov fullname: Terekhov, Andrew V. email: andrew.terekhov@mail.ru organization: Institute of Computational Mathematics and Mathematical Geophysics, 630090 Novosibirsk, Russia |
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| Keywords | Acoustic solver Parallel dichotomy algorithm Block-tridiagonal matrices Domain decomposition method PML absorbing boundary condition Laguerre transform |
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| Snippet | •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... 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... |
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| SubjectTerms | 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 |
| Title | A fast parallel algorithm for solving block-tridiagonal systems of linear equations including the domain decomposition method |
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