Adaptive approximation of solutions to problems with multiple layers by Chebyshev pseudo-spectral methods
type: Item
instance of: scholarly article
title: Adaptive approximation of solutions to problems with multiple layers by Chebyshev pseudo-spectral methods
zbMATH Open document ID: 0822.65074
author: A. Bayliss
author: B. J. Matkowsky
author: A. G. Class
published in: Journal of Computational Physics
publication date: 1995-04-05T00:00:00Z
review text: The objective of this paper is to describe an extension of the family of mappings which enhance the accuracy of Chebyshev pseudo-spectral methods in approximating functions with multiple layers. The mapping family depends on \(3N- 1\) free parameters, where \(N\) denotes the number of layers. \(N\) parameters are related to the locations of layers, \(N\) parameters depend on the width of the layers, while the other \(N- 1\) parameters depend on the resolution of each layer relative to the first layer. All parameters can be determined adaptively by minimizing the error of the approximation. The authors propose some techniques to simplify the minimization problem, and demonstrate that the appropriate choice of mappings can lead to a significant reduction in the condition number of associated differentiation matrices. In my opinion the paper is very interesting and should be mentioned by everyone involved in research of the solutions of partial differential equations occurring in many areas of applications, such as fluid dynamics, solid mechanics, combustion, solidification, and wave propagation.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65D25
zbMATH DE Number: 740618
zbMATH Keywords: Chebyshev pseudo-spectral methods
zbMATH Keywords: multiple layers
zbMATH Keywords: condition number
zbMATH Keywords: differentiation matrices
reviewed by: Andrzej Marciniak
MaRDI profile type: Publication
full work available at URL: jcph.1995.1014
OpenAlex ID: W2050980167
DOI: 10.1006/JCPH.1995.1014
description: scientific article; zbMATH DE number 740618