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.
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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.
| Type: | Article |
|---|---|
| Title: | Mesh Density Functions Based on Local Bandwidth Applied to Moving Mesh Methods |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4208/cicp.OA-2016-0246 |
| Publisher version: | http://dx.doi.org/10.4208/cicp.OA-2016-0246 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Moving mesh method, pseudospectral method, bandwidth |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Med Phys and Biomedical Eng |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1534897 |
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