@Article{JMS-48-106,
author = {Bihlo , AlexanderHaynes , 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 = {<p style="text-align: justify;">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.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v48n2.15.02},
url = {http://global-sci.org/intro/article_detail/jms/9913.html}
}