Recent Advances in Schwarz Waveform Moving Mesh Methods – A New Moving Subdomain Method

  • Ronald D. Haynes
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 78)


It is well accepted that the efficient solution of complex partial differential equations (PDEs) often requires methods which are adaptive in both space and time. In this paper we are interested in a class of spatially adaptive moving mesh (r-refinement) methods introduced in [9, 10, 12]. Our purpose is to introduce and explore a natural coupling of domain decomposition, Schwarz waveform relaxation (SWR) [4], and spatially adaptive moving mesh PDE (MMPDE) methods for time dependent PDEs. SWR allows the focus of computational energy to evolve to the changing behaviour of the solution locally in regions or subdomains of the space-time domain. In particular, this will enable different time steps and indeed integration methods in each subdomain. The spatial mesh, provided by the MMPDE, will react to the local solution dynamics, providing distinct advantages for problems with evolving regions of interesting features.


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The author would like to acknowledge the support of NSERC (Canada) under discovery grant 311796.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMemorial University of NewfoundlandSt. John’sCanada

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