Paper Info
Title
Convergence Analysis of the Gauss-Seidel Preconditioner for Discretized One Dimensional Euler Equations
Abstract
We consider the nonlinear system of equations that results from the Van Leer flux vector-splitting discretization of the one dimensional Euler equations. This nonlinear system is linearized at the discrete solution. The main topic of this paper is a convergence analysis of block-Gauss-Seidel methods applied to this linear system of equations. Both the lexicographic and the symmetric block-Gauss-Seidel method are considered. We derive results which quantify the quality of these methods as preconditioners. These results show, for example, that for the subsonic case the symmetric Gauss-Seidel method can be expected to be a much better preconditioner than the lexicographic variant. Sharp bounds for the condition number of the preconditioned matrix are derived.
Year
DOI
Venue
2003
10.1137/S0036142902407393
SIAM J. Numerical Analysis
Keywords
Field
DocType
gauss-seidel preconditioner,dimensional euler equations,convergence analysis,block-gauss-seidel method,better preconditioner,symmetric block-gauss-seidel method,nonlinear system,linear system,lexicographic variant,symmetric gauss-seidel method,van leer flux,condition number,gauss seidel,gauss seidel method,linear system of equations,euler equation,euler equations
Discretization,Mathematical optimization,Nonlinear system,Linear system,Preconditioner,System of linear equations,Mathematical analysis,Numerical analysis,Euler equations,Mathematics,Gauss–Seidel method
Journal
Volume
Issue
ISSN
41
4
0036-1429
Citations 
PageRank 
References 
0
0.34
4
Authors
1
Name
Order
Citations
PageRank
Arnold Reusken130544.91