Parallel multigrid technique: Reduction to independent problems
The unsatisfactory operation of a parallel multigrid algorithm is caused by two reasons: the imbalanced load of processors and the intensive exchanges of data between them. The further development of the parallel universal multigrid technique based on the reduction of a difference initial boundary v...
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| Vydáno v: | Mathematical models and computer simulations Ročník 9; číslo 1; s. 120 - 126 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Moscow
Pleiades Publishing
01.01.2017
Springer Nature B.V |
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| ISSN: | 2070-0482, 2070-0490 |
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| Abstract | The unsatisfactory operation of a parallel multigrid algorithm is caused by two reasons: the imbalanced load of processors and the intensive exchanges of data between them. The further development of the parallel universal multigrid technique based on the reduction of a difference initial boundary value problem to a set of independent problems is considered. The universal multigrid technique is a single-grid algorithm, which uses the fundamental multigrid principle to minimize the number of problem-dependent components. The use of the same grid for the calculation of a correction eliminates all the difficulties produced by imbalanced loads and intensive exchanges on coarse grids. It has been shown that it is possible to decrease the volume of stored data and the time of computation and to attain nearly absolute parallelism in some cases. The results of some computational experiments with the difference six-order approximation pattern are presented. |
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| AbstractList | The unsatisfactory operation of a parallel multigrid algorithm is caused by two reasons: the imbalanced load of processors and the intensive exchanges of data between them. The further development of the parallel universal multigrid technique based on the reduction of a difference initial boundary value problem to a set of independent problems is considered. The universal multigrid technique is a single-grid algorithm, which uses the fundamental multigrid principle to minimize the number of problem-dependent components. The use of the same grid for the calculation of a correction eliminates all the difficulties produced by imbalanced loads and intensive exchanges on coarse grids. It has been shown that it is possible to decrease the volume of stored data and the time of computation and to attain nearly absolute parallelism in some cases. The results of some computational experiments with the difference six-order approximation pattern are presented. |
| Author | Martynenko, S. I. Yanovskiy, L. S. Volokhov, V. M. |
| Author_xml | – sequence: 1 givenname: S. I. surname: Martynenko fullname: Martynenko, S. I. organization: Institute of Problems of Chemical Physics, Russian Academy of Sciences – sequence: 2 givenname: V. M. surname: Volokhov fullname: Volokhov, V. M. email: vvm@icp.ac.ru organization: Institute of Problems of Chemical Physics, Russian Academy of Sciences – sequence: 3 givenname: L. S. surname: Yanovskiy fullname: Yanovskiy, L. S. organization: Institute of Problems of Chemical Physics, Russian Academy of Sciences |
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| Cites_doi | 10.1016/0041-5553(66)90118-2 10.1016/0041-5553(64)90253-8 10.1134/S2070048210020109 10.1016/0041-5553(62)90031-9 10.2478/cmam-2010-0004 |
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| References | Baker, Graves-Morris (CR11) 1981 Martynenko (CR9) 2015; 6 Martynenko (CR7) 2003; 4 Martynenko (CR6) 2013 Bakhvalov (CR3) 1966; 6 Martynenko (CR5) 2000; 1 Trottenberg, Oosterlee, Schüller (CR4) 2001 Fedorenko (CR1) 1962; 1 Martynenko (CR8) 2010; 10 Martynenko (CR10) 2010; 2 Fedorenko (CR2) 1964; 4 R. P. Fedorenko (3545_CR2) 1964; 4 S. I. Martynenko (3545_CR6) 2013 G. A. Baker (3545_CR11) 1981 U. Trottenberg (3545_CR4) 2001 R. P. Fedorenko (3545_CR1) 1962; 1 S.I. Martynenko (3545_CR5) 2000; 1 S. I. Martynenko (3545_CR9) 2015; 6 N. S. Bakhvalov (3545_CR3) 1966; 6 S. I. Martynenko (3545_CR7) 2003; 4 S. I. Martynenko (3545_CR8) 2010; 10 S. I. Martynenko (3545_CR10) 2010; 2 |
| References_xml | – volume: 6 start-page: 101 year: 1966 end-page: 135 ident: CR3 article-title: On the convergence of a relaxation method with natural constraints on the elliptic operator publication-title: USSR Comput. Math. Math. Phys. doi: 10.1016/0041-5553(66)90118-2 – volume: 6 start-page: 105 year: 2015 end-page: 120 ident: CR9 article-title: On design of parallel multigrid algorithms publication-title: Mat. Model. Chisl. Metody – year: 1981 ident: CR11 publication-title: Padé Approximants, Encyclopedia of Mathematics and Its Applications – year: 2001 ident: CR4 publication-title: Multigrid – volume: 4 start-page: 227 year: 1964 end-page: 235 ident: CR2 article-title: The speed of convergence of one iterative process publication-title: USSR Comput. Math. Math. Phys. doi: 10.1016/0041-5553(64)90253-8 – volume: 2 start-page: 232 year: 2010 end-page: 244 ident: CR10 article-title: Robust Multigrid Technique publication-title: Math. Models Comput. Simul. doi: 10.1134/S2070048210020109 – volume: 1 start-page: 1092 year: 1962 end-page: 1096 ident: CR1 article-title: A relaxation method for solving elliptic difference equations publication-title: USSR Comput. Math. Math. Phys. doi: 10.1016/0041-5553(62)90031-9 – volume: 1 start-page: 83 year: 2000 end-page: 100 ident: CR5 article-title: Robust multigrid technique for solving partial differential equations on structured grids publication-title: Numer. Methods Programm. – volume: 4 start-page: 45 year: 2003 end-page: 51 ident: CR7 article-title: Parallelizing of universal multigrid technology publication-title: Vychisl. Metody Programm. – volume: 10 start-page: 87 year: 2010 end-page: 94 ident: CR8 article-title: Potentialities of the robust multigrid technique publication-title: Comp. Methods Appl. Math. – year: 2013 ident: CR6 publication-title: Robust Multigrid Technology (Inst) – volume-title: Robust Multigrid Technology (Inst) year: 2013 ident: 3545_CR6 – volume: 2 start-page: 232 year: 2010 ident: 3545_CR10 publication-title: Math. Models Comput. Simul. doi: 10.1134/S2070048210020109 – volume: 6 start-page: 101 year: 1966 ident: 3545_CR3 publication-title: USSR Comput. Math. Math. Phys. doi: 10.1016/0041-5553(66)90118-2 – volume: 10 start-page: 87 year: 2010 ident: 3545_CR8 publication-title: Comp. Methods Appl. Math. doi: 10.2478/cmam-2010-0004 – volume: 1 start-page: 1092 year: 1962 ident: 3545_CR1 publication-title: USSR Comput. Math. Math. Phys. doi: 10.1016/0041-5553(62)90031-9 – volume: 4 start-page: 227 year: 1964 ident: 3545_CR2 publication-title: USSR Comput. Math. Math. Phys. doi: 10.1016/0041-5553(64)90253-8 – volume: 1 start-page: 83 year: 2000 ident: 3545_CR5 publication-title: Numer. Methods Programm. – volume-title: Multigrid year: 2001 ident: 3545_CR4 – volume: 4 start-page: 45 year: 2003 ident: 3545_CR7 publication-title: Vychisl. Metody Programm. – volume: 6 start-page: 105 year: 2015 ident: 3545_CR9 publication-title: Mat. Model. Chisl. Metody – volume-title: Padé Approximants, Encyclopedia of Mathematics and Its Applications year: 1981 ident: 3545_CR11 |
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| SubjectTerms | Boundary value problems Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Processors Reduction Simulation and Modeling |
| Title | Parallel multigrid technique: Reduction to independent problems |
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