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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Bibliographic Details
Published in:Applied numerical mathematics Vol. 36; no. 4; pp. 401 - 426
Main Authors: Fournier, L., Lanteri, S.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.03.2001
Elsevier
Subjects:
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
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
ISSN:0168-9274, 1873-5460
Online Access:Get full text
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Summary: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.
ISSN:0168-9274
1873-5460
DOI:10.1016/S0168-9274(00)00017-9