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首页> 外文期刊>Journal of Computational Physics >A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations
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A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations

机译：不可压缩Navier-Stokes方程的并行块多级预处理器的分类和比较

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摘要

In recent years, considerable effort has been placed on developing efficient and robust solution algorithms for the incompressible Navier-Stokes equations based on preconditioned Krylov methods. These include physics-based methods, such as SIMPLE, and purely algebraic preconditioners based on the approximation of the Schur complement. All these techniques can be represented as approximate block factorization (ABF) type preconditioners. The goal is to decompose the application of the preconditioner into simplified sub-systems in which scalable multi-level type solvers can be applied. In this paper we develop a taxonomy of these ideas based on an adaptation of a generalized approximate factorization of the Navier-Stokes system first presented in [A. Quarteroni, F. Saleri, A. Veneziani, Factorization methods for the numerical approximation of Navier-Stokes equations, Computational Methods in Applied Mechanical Engineering 188 (2000) 505-526]. This taxonomy illuminates the similarities and differences among these preconditioners and the central role played by efficient approximation of certain Schur complement operators. We then present a parallel computational study that examines the performance of these methods and compares them to an additive Schwarz domain decomposition (DD) algorithm. Results are presented for two and three-dimensional steady state problems for enclosed domains and inflow/outflow systems on both structured and unstructured meshes. The numerical experiments are performed using MPSalsa, a stabilized finite element code. (C) 2007 Elsevier Inc. All rights reserved.
机译：近年来，在基于预处理的Krylov方法的不可压缩的Navier-Stokes方程上，开发了高效且鲁棒的求解算法已经投入了大量的精力。这些包括基于物理的方法（例如SIMPLE）和基于Schur补码近似的纯代数前置条件。所有这些技术都可以表示为近似块分解（ABF）类型的预处理器。目的是将预处理器的应用分解为简化的子系统，在其中可以应用可伸缩的多级类型求解器。在本文中，我们根据[A.首次提出]的Navier-Stokes系统的广义近似因式分解对这些思想进行分类。 Quarteroni，F。Saleri，A。Veneziani，“ Navier-Stokes方程数值近似的分解方法，应用机械工程中的计算方法188（2000）505-526]”。这种分类法阐明了这些前置条件之间的异同，以及某些Schur补算子的有效逼近所起的核心作用。然后，我们提出了一项并行计算研究，该研究检查了这些方法的性能并将其与加性Schwarz域分解（DD）算法进行比较。给出了结构化和非结构化网格上的封闭域和流入/流出系统的二维和三维稳态问题的结果。数值实验是使用稳定的有限元代码MPSalsa进行的。 （C）2007 Elsevier Inc.保留所有权利。

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