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Taylor expansion and discretization errors in Gaussian beam superposition
Department of Mathematics, Simon Fraser University.
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.ORCID iD: 0000-0002-6321-8619
2010 (English)In: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 47, no 7, 421-439 p.Article in journal (Refereed) Published
Abstract [en]

The Gaussian beam superposition method is an asymptotic method for computing high frequency wave fields in smoothly varying inhomogeneous media. In this paper we study the accuracy of the Gaussian beam superposition method and derive error estimates related to the discretization of the superposition integral and the Taylor expansion of the phase and amplitude off the center of the beam. We show that in the case of odd order beams, the error is smaller than a simple analysis would indicate because of error cancellation effects between the beams. Since the cancellation happens only when odd order beams are used, there is no remarkable gain in using even order beams. Moreover, applying the error estimate to the problem with constant speed of propagation, we show that in this case the local beam width is not a good indicator of accuracy, and there is no direct relation between the error and the beam width. We present numerical examples to verify the error estimates.

Place, publisher, year, edition, pages
2010. Vol. 47, no 7, 421-439 p.
Keyword [en]
Accuracy, Asymptotic approximation, Error estimates, Gaussian beam superposition, High frequency, Wave propagation
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-24257DOI: 10.1016/j.wavemoti.2010.02.001ISI: 000282076100003Scopus ID: 2-s2.0-77955843316OAI: oai:DiVA.org:kth-24257DiVA: diva2:346074
Note
QC 20100830Available from: 2010-08-30 Created: 2010-08-30 Last updated: 2017-12-12Bibliographically approved

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Runborg, Olof

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