eprintid: 1534897
rev_number: 42
eprint_status: archive
userid: 608
dir: disk0/01/53/48/97
datestamp: 2017-01-08 07:05:44
lastmod: 2021-10-05 00:19:55
status_changed: 2017-10-16 14:26:42
type: article
metadata_visibility: show
creators_name: Wise, ES
creators_name: Cox, BT
creators_name: Treeby, BE
title: Mesh Density Functions Based on Local Bandwidth Applied to Moving Mesh Methods
ispublished: pub
divisions: UCL
divisions: B04
divisions: C05
divisions: F42
keywords: Moving mesh method, pseudospectral method, bandwidth
note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
abstract: Moving mesh methods provide an efficient way of solving partial differential equations for which large, localised variations in the solution necessitate locally dense spatial meshes. In one-dimension, meshes are typically specified using the arclength mesh density function. This choice is well-justified for piecewise polynomial interpolants, but it is only justified for spectral methods when model solutions include localised steep gradients. In this paper, one-dimensional mesh density functions are presented which are based on a spatially localised measure of the bandwidth of the approximated model solution. In considering bandwidth, these mesh density functions are well-justified for spectral methods, but are not strictly tied to the error properties of any particular spatial interpolant, and are hence widely applicable. The bandwidth mesh density functions are demonstrated by applying periodic spectral and finite-difference moving mesh methods to a number of model problems in acoustics. These problems include a heterogeneous advection equation, the viscous Burgers' equation, and the Korteweg-de Vries equation. Simulation results demonstrate solution convergence rates that are up to an order of magnitude faster using the bandwidth mesh density functions than uniform meshes, and around three times faster than those using the arclength mesh density function.
date: 2017-11
official_url: http://dx.doi.org/10.4208/cicp.OA-2016-0246
oa_status: green
full_text_type: other
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 1198804
doi: 10.4208/cicp.OA-2016-0246
lyricists_name: Cox, Benjamin
lyricists_name: Treeby, Bradley
lyricists_name: Wise, Elliott
lyricists_id: BTCOX21
lyricists_id: BTREE66
lyricists_id: EWISE92
actors_name: Dewerpe, Marie
actors_id: MDDEW97
actors_role: owner
full_text_status: public
publication: Communications in Computational Physics
volume: 22
number: 5
pagerange: 1286-1308
issn: 1815-2406
citation:        Wise, ES;    Cox, BT;    Treeby, BE;      (2017)    Mesh Density Functions Based on Local Bandwidth Applied to Moving Mesh Methods.                   Communications in Computational Physics , 22  (5)   pp. 1286-1308.    10.4208/cicp.OA-2016-0246 <https://doi.org/10.4208/cicp.OA-2016-0246>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/1534897/1/1612.04156v1.pdf