Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

Moving mesh methods based on the equidistribution principle are powerful techniques for the space-time adaptive solution of evolution problems. Solving the resulting coupled system of equations, namely the original PDE and the mesh PDE, however, is challenging in parallel. Recently several Schwarz domain decomposition algorithms were proposed for this task and analyzed at the continuous level. However, after discretization, the resulting problems may not even be well posed, so the discrete algorithms require a different analysis, which is the subject of this paper. We prove that when the number of grid points is large enough, the classical parallel and alternating Schwarz methods converge to the unique monodomain solution. Thus, such methods can be used in place of Newton's method, which can suffer from convergence difficulties for challenging problems. The analysis for the nonlinear domain decomposition algorithms is based on M-function theory and is valid for an arbitrary number of subdomains. An asymptotic convergence rate is provided and numerical experiments illustrate the results.

Keywords

Domain decomposition, Schwarz methods, moving meshes, equidistribution, discretization, M-functions

Publication Date

1-2017

Source Publication Title

Mathematics of Computation

Volume

86

Issue

303

Start Page

233

End Page

273

Publisher

American Mathematical Society

DOI

10.1090/mcom/3095

Link to Publisher's Edition

https://doi.org/10.1090/mcom/3095

ISSN (print)

00255718

ISSN (electronic)

10886842

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