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Stochastic domain decomposition for time dependent adaptive mesh generation

Bihlo, Alexander; Haynes, Ronald D; Walsh, Emily

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Alexander Bihlo

Ronald D Haynes

Emily Walsh
Associate Director Mathematics & Statistics


The efficient generation of meshes is an important component in the numerical solution of problems in physics and engineering. Of interest are situations where global mesh quality and a tight coupling to the solution of the physical partial differential equation (PDE) is important. We consider parabolic PDE mesh generation and present a method for the construction of adaptive meshes in two spatial dimensions using stochastic domain decomposition that is suitable for an implementation in a multi– or many–core environment. Methods for mesh generation on periodic domains are also provided. The mesh generator is coupled to a time dependent physical PDE and the system is evolved using an alternating solution procedure. The method uses the stochastic representation of the exact solution of a parabolic linear mesh generator to find the location of an adaptive mesh along the (artificial) subdomain interfaces. The deterministic evaluation of the mesh over each subdomain can then be obtained completely independently using the probabilistically computed solutions as boundary conditions. The parallel performance of this general stochastic domain decomposition approach has previously been shown. We demonstrate the approach numerically for the mesh generation context and compare the mesh obtained with the corresponding single domain mesh using a representative mesh quality measure.


Bihlo, A., Haynes, R. D., & Walsh, E. (2015). Stochastic domain decomposition for time dependent adaptive mesh generation.

Journal Article Type Article
Publication Date Jun 1, 2015
Deposit Date Apr 16, 2015
Publicly Available Date Mar 3, 2016
Journal Journal of Mathematical Study
Print ISSN 1006-6837
Peer Reviewed Peer Reviewed
Volume 48
Issue 2
Pages 106-124
Keywords domain decomposition, adaptive mesh
Public URL
Publisher URL


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