Volume 48, Issue 2
Stochastic Domain Decomposition for Time Dependent Adaptive Mesh Generation

Alexander Bihlo, Ronald D. Haynes & Emily J. Walsh

J. Math. Study, 48 (2015), pp. 106-124.

Published online: 2015-06

[An open-access article; the PDF is free to any online user.]

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  • Abstract

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. A small scaling study is provided to demonstrate the parallel performance of this stochastic domain decomposition approach to mesh generation. We demonstrate the approach numerically and compare the mesh obtained with the corresponding single domain mesh using a representative mesh quality measure.

  • Keywords

Mesh generation Domain decomposition Monte Carlo methods

  • AMS Subject Headings

65N50, 65M50, 65L50, 65C05, 65N55, 65M55

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

abihlo@mun.ca (Alexander Bihlo)

rhaynes@mun.ca (Ronald D. Haynes)

emily3.walsh@uwe.ac.uk (Emily J. Walsh)

  • BibTex
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@Article{JMS-48-106, author = {Bihlo , Alexander and Haynes , Ronald D. and Walsh , Emily J. }, title = {Stochastic Domain Decomposition for Time Dependent Adaptive Mesh Generation}, journal = {Journal of Mathematical Study}, year = {2015}, volume = {48}, number = {2}, pages = {106--124}, abstract = {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. A small scaling study is provided to demonstrate the parallel performance of this stochastic domain decomposition approach to mesh generation. We demonstrate the approach numerically and compare the mesh obtained with the corresponding single domain mesh using a representative mesh quality measure.}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v48n2.15.02}, url = {http://global-sci.org/intro/article_detail/jms/9913.html} }
TY - JOUR T1 - Stochastic Domain Decomposition for Time Dependent Adaptive Mesh Generation AU - Bihlo , Alexander AU - Haynes , Ronald D. AU - Walsh , Emily J. JO - Journal of Mathematical Study VL - 2 SP - 106 EP - 124 PY - 2015 DA - 2015/06 SN - 48 DO - http://doi.org/10.4208/jms.v48n2.15.02 UR - https://global-sci.org/intro/article_detail/jms/9913.html KW - Mesh generation KW - Domain decomposition KW - Monte Carlo methods AB - 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. A small scaling study is provided to demonstrate the parallel performance of this stochastic domain decomposition approach to mesh generation. We demonstrate the approach numerically and compare the mesh obtained with the corresponding single domain mesh using a representative mesh quality measure.
Alexander Bihlo, Ronald D. Haynes & Emily J. Walsh. (2019). Stochastic Domain Decomposition for Time Dependent Adaptive Mesh Generation. Journal of Mathematical Study. 48 (2). 106-124. doi:10.4208/jms.v48n2.15.02
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