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Overlapping Schwarz waveform relaxation method for the solution of the convection–diffusion equation
Author(s) -
Daoud Daoud S.
Publication year - 2008
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.959
Subject(s) - mathematics , convergence (economics) , schwarz alternating method , relaxation (psychology) , diffusion , waveform , convection , mathematical analysis , convection–diffusion equation , diffusion equation , domain decomposition methods , finite element method , mechanics , physics , thermodynamics , psychology , social psychology , economy , service (business) , quantum mechanics , voltage , economics , economic growth
In this article we study the convergence of the overlapping Schwarz wave form relaxation method for solving the convection–diffusion equation over multi‐overlapped subdomains. It is shown that the method converges linearly and superlinearly over long and short time intervals, and the convergence depends on the size of the overlap. Numerical results are presented from solving specific types of model problems to demonstrate the convergence and the role of the size of the overlap. Copyright © 2007 John Wiley & Sons, Ltd.