Spatial resolution properties of mapped spectral Chebyshev methods

Bruno Costa; Wai Sun Don; Alina Simas

Spatial resolution properties of mapped spectral Chebyshev methods

Bruno Costa, Wai Sun Don, Alina Simas

Department of Mathematics

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

Abstract

In this article we clarify some fundamental questions on the resolution power of a modified spectral Chebyshev method proposed by Kosloff and Tal-Ezer and state approximation properties of general mappings of Chebyshev points. We develop a technique based on the method of the stationary phase which provides a straightforward way to determine the spatial resolution power of the Chebyshev method with mappings. In particular, we prove a conjecture about the resolution power of the Kosloff–Tal-Ezer mapping, yielding, as a corollary, a rigorous demonstration that a minimum of π polynomials per wavelength are needed in the original Chebyshev method, a well known fact which has been only heuristically demonstrated in the past literature.

Original language	English
Title of host publication	Recent Progress in Scientific Computing
Subtitle of host publication	Proceedings of SCPDE05
Editors	Wenbin Liu, Michael Ng, Zhongci Shi
Place of Publication	Beijing
Publisher	Science Press
Pages	179-188
Number of pages	10
ISBN (Print)	9787030190437
Publication status	Published - 1 Feb 2007
Event	The 2nd International Conference on Scientific Computing and Partial Differential Equations & The First East Asia SIAM Symposium - Hong Kong Baptist University, Hong Kong Duration: 12 Dec 2005 → 16 Dec 2005 https://www.math.hkbu.edu.hk/SCPDE05/

Conference

Conference	The 2nd International Conference on Scientific Computing and Partial Differential Equations & The First East Asia SIAM Symposium
Abbreviated title	SCPDE05
Country/Territory	Hong Kong
Period	12/12/05 → 16/12/05
Internet address	https://www.math.hkbu.edu.hk/SCPDE05/

Cite this

@inproceedings{2f3378c02306435cb59a8fba442ffa4f,

title = "Spatial resolution properties of mapped spectral Chebyshev methods",

abstract = "In this article we clarify some fundamental questions on the resolution power of a modified spectral Chebyshev method proposed by Kosloff and Tal-Ezer and state approximation properties of general mappings of Chebyshev points. We develop a technique based on the method of the stationary phase which provides a straightforward way to determine the spatial resolution power of the Chebyshev method with mappings. In particular, we prove a conjecture about the resolution power of the Kosloff–Tal-Ezer mapping, yielding, as a corollary, a rigorous demonstration that a minimum of π polynomials per wavelength are needed in the original Chebyshev method, a well known fact which has been only heuristically demonstrated in the past literature.",

author = "Bruno Costa and Don, {Wai Sun} and Alina Simas",

year = "2007",

month = feb,

day = "1",

language = "English",

isbn = "9787030190437",

pages = "179--188",

editor = "Wenbin Liu and Michael Ng and Zhongci Shi",

booktitle = "Recent Progress in Scientific Computing",

publisher = "Science Press",

address = "China",

note = "The 2nd International Conference on Scientific Computing and Partial Differential Equations & The First East Asia SIAM Symposium, SCPDE05 ; Conference date: 12-12-2005 Through 16-12-2005",

url = "https://www.math.hkbu.edu.hk/SCPDE05/",

}

Costa, B, Don, WS & Simas, A 2007, Spatial resolution properties of mapped spectral Chebyshev methods. in W Liu, M Ng & Z Shi (eds), Recent Progress in Scientific Computing: Proceedings of SCPDE05. Science Press, Beijing, pp. 179-188, The 2nd International Conference on Scientific Computing and Partial Differential Equations & The First East Asia SIAM Symposium, Hong Kong, 12/12/05.

TY - GEN

T1 - Spatial resolution properties of mapped spectral Chebyshev methods

AU - Costa, Bruno

AU - Don, Wai Sun

AU - Simas, Alina

PY - 2007/2/1

Y1 - 2007/2/1

N2 - In this article we clarify some fundamental questions on the resolution power of a modified spectral Chebyshev method proposed by Kosloff and Tal-Ezer and state approximation properties of general mappings of Chebyshev points. We develop a technique based on the method of the stationary phase which provides a straightforward way to determine the spatial resolution power of the Chebyshev method with mappings. In particular, we prove a conjecture about the resolution power of the Kosloff–Tal-Ezer mapping, yielding, as a corollary, a rigorous demonstration that a minimum of π polynomials per wavelength are needed in the original Chebyshev method, a well known fact which has been only heuristically demonstrated in the past literature.

AB - In this article we clarify some fundamental questions on the resolution power of a modified spectral Chebyshev method proposed by Kosloff and Tal-Ezer and state approximation properties of general mappings of Chebyshev points. We develop a technique based on the method of the stationary phase which provides a straightforward way to determine the spatial resolution power of the Chebyshev method with mappings. In particular, we prove a conjecture about the resolution power of the Kosloff–Tal-Ezer mapping, yielding, as a corollary, a rigorous demonstration that a minimum of π polynomials per wavelength are needed in the original Chebyshev method, a well known fact which has been only heuristically demonstrated in the past literature.

M3 - Conference proceeding

SN - 9787030190437

SP - 179

EP - 188

BT - Recent Progress in Scientific Computing

A2 - Liu, Wenbin

A2 - Ng, Michael

A2 - Shi, Zhongci

PB - Science Press

CY - Beijing

T2 - The 2nd International Conference on Scientific Computing and Partial Differential Equations & The First East Asia SIAM Symposium

Y2 - 12 December 2005 through 16 December 2005

ER -

Spatial resolution properties of mapped spectral Chebyshev methods

Abstract

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