Multiplicative and additive parallel multigrid algorithms for the acceleration of compressible flow computations on unstructured meshes
In this paper we examine how parallel multigrid acceleration can be used to improve the efficiency of two-dimensional compressible steady flow calculations on unstructured meshes. We study two parallel multigrid formulations. The first one is based on the standard approach that relies on domain part...
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| Vydáno v: | Applied numerical mathematics Ročník 36; číslo 4; s. 401 - 426 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
01.03.2001
Elsevier |
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| ISSN: | 0168-9274, 1873-5460 |
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| Abstract | In this paper we examine how parallel multigrid acceleration can be used to improve the efficiency of two-dimensional compressible steady flow calculations on unstructured meshes. We study two parallel multigrid formulations. The first one is based on the standard approach that relies on domain partitioning for the parallel treatment of the pre- and post-smoothing steps whereas the coarse grid levels are visited sequentially according to predefined cycles (V-cycle, F-cycle or W-cycle). Reducing communication overheads is of crucial importance for parallel multigrid methods. When adopting the standard parallelization technique (i.e.,
intra-level parallelism based on domain partitioning) the usual drawback is that, as the calculation in a given cycling strategy proceeds from the finest level to the coarsest ones, the ratio between communication and calculation becomes worse resulting in a notable degradation of the parallel efficiency. In order to improve this situation, the second formulation considered in this study makes use of residual and correction filtering techniques allowing a parallel treatment of the various grid levels. This leads to the notion of
inter-level parallelism. We propose distributed memory parallel versions of these two multigrid formulations and evaluate them through numerical experiments that are performed on a cluster of
Pentium Pro computers interconnected via a 100 Mbit/s
FastEthernet switch. |
|---|---|
| AbstractList | In this paper we examine how parallel multigrid acceleration can be used to improve the efficiency of two-dimensional compressible steady flow calculations on unstructured meshes. We study two parallel multigrid formulations. The first one is based on the standard approach that relies on domain partitioning for the parallel treatment of the pre- and post-smoothing steps whereas the coarse grid levels are visited sequentially according to predefined cycles (V-cycle, F-cycle or W-cycle). Reducing communication overheads is of crucial importance for parallel multigrid methods. When adopting the standard parallelization technique (i.e.,
intra-level parallelism based on domain partitioning) the usual drawback is that, as the calculation in a given cycling strategy proceeds from the finest level to the coarsest ones, the ratio between communication and calculation becomes worse resulting in a notable degradation of the parallel efficiency. In order to improve this situation, the second formulation considered in this study makes use of residual and correction filtering techniques allowing a parallel treatment of the various grid levels. This leads to the notion of
inter-level parallelism. We propose distributed memory parallel versions of these two multigrid formulations and evaluate them through numerical experiments that are performed on a cluster of
Pentium Pro computers interconnected via a 100 Mbit/s
FastEthernet switch. |
| Author | Lanteri, S. Fournier, L. |
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| Cites_doi | 10.2514/6.1998-612 10.1007/978-94-011-5412-3_7 10.1016/0743-7315(86)90030-4 10.1016/0021-9991(81)90128-5 10.1137/0913005 10.1016/0021-9991(81)90210-2 10.1016/0021-9991(89)90187-3 10.1016/S0045-7930(96)00045-X 10.1016/0021-9991(79)90145-1 10.1137/1034116 10.1002/(SICI)1097-0363(19980430)26:8<927::AID-FLD679>3.0.CO;2-0 10.1016/0167-8191(96)00036-1 10.1002/(SICI)1097-0363(19960930)23:6<527::AID-FLD429>3.0.CO;2-Z 10.1016/0045-7930(92)90047-Y |
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| Keywords | Multigrid method Parallel computing Computational fluid dynamics Additive and multiplicative algorithms Euler equations Finite volume Finite element Transonic flow Steady flow Finite volume method Parallel Parallel algorithms Processing Degradation Distributed memory Finite element method Numerical computation Multigrid Numerical solution Mach number Filtering Grid pattern Fluid dynamics Convergence acceleration Communications Two dimensional flow Cycle Flow Algorithms Subsonic flow Parallel computation Compressible flow Parallelization |
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Methods Fluids doi: 10.1002/(SICI)1097-0363(19960930)23:6<527::AID-FLD429>3.0.CO;2-Z – year: 1999 ident: 10.1016/S0168-9274(00)00017-9_BIB028 article-title: Fourier analysis of GMRES(m) preconditioned by multigrid – ident: 10.1016/S0168-9274(00)00017-9_BIB007 – volume: 4 year: 1985 ident: 10.1016/S0168-9274(00)00017-9_BIB014 – ident: 10.1016/S0168-9274(00)00017-9_BIB005 – volume: 21 start-page: 397 year: 1992 ident: 10.1016/S0168-9274(00)00017-9_BIB016 article-title: Unstructured multigridding by volume agglomeration: current status publication-title: Comput. Fluids doi: 10.1016/0045-7930(92)90047-Y |
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| SubjectTerms | Additive and multiplicative algorithms Compressible flows; shock and detonation phenomena Computational fluid dynamics Euler equations Exact sciences and technology Finite element Finite volume Fluid dynamics Fundamental areas of phenomenology (including applications) Mathematics Multigrid method Numerical analysis Numerical analysis. Scientific computation Ordinary differential equations Parallel computing Physics Sciences and techniques of general use |
| Title | Multiplicative and additive parallel multigrid algorithms for the acceleration of compressible flow computations on unstructured meshes |
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