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Title: A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations.

Abstract

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 [25]. 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.

Authors:
 [1];  [2];  [2]; ;
  1. Sandia National Laboratories, Albuquerque, NM
  2. University of Maryland, College Park, MD
Publication Date:
Research Org.:
Sandia National Laboratories
Sponsoring Org.:
USDOE
OSTI Identifier:
920807
Report Number(s):
SAND2007-2761
TRN: US200803%%31
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; INCOMPRESSIBLE FLOW; ALGORITHMS; APPROXIMATIONS; FACTORIZATION; NAVIER-STOKES EQUATIONS; PERFORMANCE; FINITE ELEMENT METHOD; Finite element method.; Mesh generation.; Navier stokes equations

Citation Formats

Shadid, John Nicolas, Elman, Howard, Shuttleworth, Robert R, Howle, Victoria E, and Tuminaro, Raymond Stephen. A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations.. United States: N. p., 2007. Web. doi:10.2172/920807.
Shadid, John Nicolas, Elman, Howard, Shuttleworth, Robert R, Howle, Victoria E, & Tuminaro, Raymond Stephen. A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations.. United States. doi:10.2172/920807.
Shadid, John Nicolas, Elman, Howard, Shuttleworth, Robert R, Howle, Victoria E, and Tuminaro, Raymond Stephen. Sun . "A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations.". United States. doi:10.2172/920807. https://www.osti.gov/servlets/purl/920807.
@article{osti_920807,
title = {A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations.},
author = {Shadid, John Nicolas and Elman, Howard and Shuttleworth, Robert R and Howle, Victoria E and Tuminaro, Raymond Stephen},
abstractNote = {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 [25]. 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.},
doi = {10.2172/920807},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2007},
month = {4}
}

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