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2013 Schwarz Waveform Relaxation for Heat Equations with Nonlinear Dynamical Boundary Conditions
Shu-Lin Wu
Abstr. Appl. Anal. 2013: 1-7 (2013). DOI: 10.1155/2013/474608

Abstract

We are interested in solving heat equations with nonlinear dynamical boundary conditions by using domain decomposition methods. In the classical framework, one first discretizes the time direction and then solves a sequence of state steady problems by the domain decomposition method. In this paper, we consider the heat equations at spacetime continuous level and study a Schwarz waveform relaxation algorithm for parallel computation purpose. We prove the linear convergence of the algorithm on long time intervals and show how the convergence rate depends on the size of overlap and the nonlinearity of the nonlinear boundary functions. Numerical experiments are presented to verify our theoretical conclusions.

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Shu-Lin Wu. "Schwarz Waveform Relaxation for Heat Equations with Nonlinear Dynamical Boundary Conditions." Abstr. Appl. Anal. 2013 1 - 7, 2013. https://doi.org/10.1155/2013/474608

Information

Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 1291.65281
MathSciNet: MR3147807
Digital Object Identifier: 10.1155/2013/474608

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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