@Article{CiCP-22-5,
author = {},
title = {Mesh Density Functions Based on Local Bandwidth Applied to Moving Mesh Methods},
journal = {Communications in Computational Physics},
year = {2017},
volume = {22},
number = {5},
pages = {1286--1308},
abstract = {<p style="text-align: justify;">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 illustrated in two ways. First, by applying them to
Chebyshev polynomial approximation of two test functions, and second, through use
in periodic spectral and finite-difference moving mesh methods applied 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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2016-0246},
url = {https://global-sci.com/article/80179/mesh-density-functions-based-on-local-bandwidth-applied-to-moving-mesh-methods}
}