A taxonomy and comparison of parallel block multilevel preconditioners for the incompressible NavierStokes equations.
Abstract
In recent years, considerable effort has been placed on developing efficient and robust solution algorithms for the incompressible NavierStokes equations based on preconditioned Krylov methods. These include physicsbased 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 subsystems in which scalable multilevel 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 NavierStokes 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 threedimensional 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:

 Sandia National Laboratories, Albuquerque, NM
 University of Maryland, College Park, MD
 Publication Date:
 Research Org.:
 Sandia National Laboratories
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 920807
 Report Number(s):
 SAND20072761
TRN: US200803%%31
 DOE Contract Number:
 AC0494AL85000
 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; NAVIERSTOKES 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 multilevel preconditioners for the incompressible NavierStokes 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 multilevel preconditioners for the incompressible NavierStokes 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 multilevel preconditioners for the incompressible NavierStokes 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 multilevel preconditioners for the incompressible NavierStokes 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 NavierStokes equations based on preconditioned Krylov methods. These include physicsbased 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 subsystems in which scalable multilevel 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 NavierStokes 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 threedimensional 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}
}