article

Numerical analysis and implementational aspects of a new multilevel grid deformation method

Authors:

Matthias Grajewski,

Michael Köster,

Stefan TurekAuthors Info & Claims

Applied Numerical Mathematics, Volume 60, Issue 8

Pages 767 - 781

https://doi.org/10.1016/j.apnum.2010.03.017

Published: 01 August 2010 Publication History

Abstract

Recently, we introduced and mathematically analysed a new method for grid deformation (Grajewski et al., 2009) [15] we call basic deformation method (BDM) here. It generalises the method proposed by Liao et al. (Bochev et al., 1996; Cai et al., 2004; Liao and Anderson, 1992) [4,6,20]. In this article, we employ the BDM as core of a new multilevel deformation method (MDM) which leads to vast improvements regarding robustness, accuracy and speed. We achieve this by splitting up the deformation process in a sequence of easier subproblems and by exploiting grid hierarchy. Being of optimal asymptotic complexity, we experience speed-ups up to a factor of 15 in our test cases compared to the BDM. This gives our MDM the potential for tackling large grids and time-dependent problems, where possibly the grid must be dynamically deformed once per time step according to the user's needs. Moreover, we elaborate on implementational aspects, in particular efficient grid searching, which is a key ingredient of the BDM.

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Cited By

Ramani RShkoller S(2023)A fast dynamic smooth adaptive meshing scheme with applications to compressible flowJournal of Computational Physics10.1016/j.jcp.2023.112280490:COnline publication date: 1-Oct-2023
https://dl.acm.org/doi/10.1016/j.jcp.2023.112280
Cottereau RDíez P(2015)Fast r-adaptivity for multiple queries of heterogeneous stochastic material fieldsComputational Mechanics10.1007/s00466-015-1190-x56:4(601-612)Online publication date: 1-Oct-2015
https://dl.acm.org/doi/10.1007/s00466-015-1190-x
Xia KZhan MWan DWei G(2012)Adaptively deformed mesh based interface method for elliptic equations with discontinuous coefficientsJournal of Computational Physics10.1016/j.jcp.2011.10.026231:4(1440-1461)Online publication date: 1-Feb-2012
https://dl.acm.org/doi/10.1016/j.jcp.2011.10.026

Numerical analysis and implementational aspects of a new multilevel grid deformation method
1. Theory of computation

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cover image Applied Numerical Mathematics

Applied Numerical Mathematics Volume 60, Issue 8

August, 2010

111 pages

ISSN:0168-9274

Issue’s Table of Contents

Copyright © IMACS © 2010.

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 August 2010

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Cited By

Ramani RShkoller S(2023)A fast dynamic smooth adaptive meshing scheme with applications to compressible flowJournal of Computational Physics10.1016/j.jcp.2023.112280490:COnline publication date: 1-Oct-2023
https://dl.acm.org/doi/10.1016/j.jcp.2023.112280
Cottereau RDíez P(2015)Fast r-adaptivity for multiple queries of heterogeneous stochastic material fieldsComputational Mechanics10.1007/s00466-015-1190-x56:4(601-612)Online publication date: 1-Oct-2015
https://dl.acm.org/doi/10.1007/s00466-015-1190-x
Xia KZhan MWan DWei G(2012)Adaptively deformed mesh based interface method for elliptic equations with discontinuous coefficientsJournal of Computational Physics10.1016/j.jcp.2011.10.026231:4(1440-1461)Online publication date: 1-Feb-2012
https://dl.acm.org/doi/10.1016/j.jcp.2011.10.026

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