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Gaussian beam methods for the helmholtz equation
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, Centres, SeRC - Swedish e-Science Research Centre.ORCID iD: 0000-0002-6321-8619
2014 (English)In: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 74, no 3, 771-793 p.Article in journal (Refereed) Published
Abstract [en]

In this work we construct Gaussian beam approximations to solutions of the high frequency Helmholtz equation with a localized source. Under the assumption of nontrapping rays we show error estimates between the exact outgoing solution and Gaussian beams in terms of the wave number k, both for single beams and superposition of beams. The main result is that the relative local L-2 error in the beam approximations decay as k(-N/2) independent of dimension and presence of caustics for Nth order beams.

Place, publisher, year, edition, pages
2014. Vol. 74, no 3, 771-793 p.
Keyword [en]
Helmholtz equation, high frequency wave propagation, localized source, radiation condition
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-148654DOI: 10.1137/130916072ISI: 000338833400009Scopus ID: 2-s2.0-84903946369OAI: oai:DiVA.org:kth-148654DiVA: diva2:736915
Funder
Swedish eā€Science Research Center
Note

QC 20140811

Available from: 2014-08-11 Created: 2014-08-11 Last updated: 2017-12-05Bibliographically approved

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Runborg, Olof

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