NDLI: Schwarz Waveform Relaxation Algorithms for the Linear Viscous Equatorial Shallow Water Equations

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Martin, Vronique
Copyright Year	2009
Abstract	We are interested in numerically solving the viscous shallow water equations with a small Coriolis force on a large domain. Specifically, we develop and analyze Schwarz waveform relaxation algorithms: we split the domain of computation into two subdomains and with appropriate transmission conditions an iterative procedure leads to the global solution. We first analyze the Dirichlet-type transmission conditionscomputing the convergence rate in FourierLaplace variables and proving it is less than 1 yields the convergence of the algorithm. The algorithm requires an overlap between subdomains, and the convergence is slow. We propose a better algorithm for which the overlap is unnecessary: the transmission conditions are now an approximation of the absorbing boundary conditions. We also prove convergence; if the domains overlap, the arguments are similar to the Dirichlet-type problem, if not, we use variational arguments. A numerical scheme is then proposed and numerical results are shown which highlight the efficiency of the new transmission conditions. The influence of the time window lengths is discussed.
Starting Page	3595
Ending Page	3625
Page Count	31
File Format	PDF
ISSN	10648275
DOI	10.1137/070691450
e-ISSN	10957197
Issue Number	5
Volume Number	31
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2009-09-23
Access Restriction	Subscribed
Subject Keyword	Schwarz waveform relaxation domain decomposition shallow water equations Multigrid methods; domain decomposition
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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