Gaussian beam decomposition of high frequency wave fields using expectation-maximization

Gil Ariel; Björn Engquist; Nicolay M. Tanushev; Richard Tsai

doi:https://doi.org/10.1016/j.jcp.2010.12.018

Gaussian beam decomposition of high frequency wave fields using expectation-maximization

Gil Ariel, Björn Engquist, Nicolay M. Tanushev, Richard Tsai

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

A new numerical method for approximating highly oscillatory wave fields as a superposition of Gaussian beams is presented. The method estimates the number of beams and their parameters automatically. This is achieved by an expectation-maximization algorithm that fits real, positive Gaussians to the energy of the highly oscillatory wave fields and its Fourier transform. Beam parameters are further refined by an optimization procedure that minimizes the difference between the Gaussian beam superposition and the highly oscillatory wave field in the energy norm.

Original language	English
Pages (from-to)	2303-2321
Number of pages	19
Journal	Journal of Computational Physics
Volume	230
Issue number	6
DOIs	https://doi.org/10.1016/j.jcp.2010.12.018
State	Published - 20 Mar 2011

Keywords

Expectation-maximization
Gaussian beams
High frequency waves
Wave equation

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics
Numerical Analysis
General Physics and Astronomy
Computer Science Applications
Modelling and Simulation
Physics and Astronomy (miscellaneous)

Access to Document

https://doi.org/10.1016/j.jcp.2010.12.018

Cite this

@article{3dc437e92e964076bebeec945a6f2d85,

title = "Gaussian beam decomposition of high frequency wave fields using expectation-maximization",

abstract = "A new numerical method for approximating highly oscillatory wave fields as a superposition of Gaussian beams is presented. The method estimates the number of beams and their parameters automatically. This is achieved by an expectation-maximization algorithm that fits real, positive Gaussians to the energy of the highly oscillatory wave fields and its Fourier transform. Beam parameters are further refined by an optimization procedure that minimizes the difference between the Gaussian beam superposition and the highly oscillatory wave field in the energy norm.",

keywords = "Expectation-maximization, Gaussian beams, High frequency waves, Wave equation",

author = "Gil Ariel and Bj{\"o}rn Engquist and Tanushev, {Nicolay M.} and Richard Tsai",

note = "Funding Information: The authors were partially supported by the NSF under Grant No. DMS-0714612 . N.T. was also partially supported by the NSF under Grant No. DMS-0636586 (UT Austin RTG).",

year = "2011",

month = mar,

day = "20",

doi = "https://doi.org/10.1016/j.jcp.2010.12.018",

language = "الإنجليزيّة",

volume = "230",

pages = "2303--2321",

journal = "Journal of Computational Physics",

issn = "0021-9991",

publisher = "Academic Press Inc.",

number = "6",

}

TY - JOUR

T1 - Gaussian beam decomposition of high frequency wave fields using expectation-maximization

AU - Ariel, Gil

AU - Engquist, Björn

AU - Tanushev, Nicolay M.

AU - Tsai, Richard

N1 - Funding Information: The authors were partially supported by the NSF under Grant No. DMS-0714612 . N.T. was also partially supported by the NSF under Grant No. DMS-0636586 (UT Austin RTG).

PY - 2011/3/20

Y1 - 2011/3/20

N2 - A new numerical method for approximating highly oscillatory wave fields as a superposition of Gaussian beams is presented. The method estimates the number of beams and their parameters automatically. This is achieved by an expectation-maximization algorithm that fits real, positive Gaussians to the energy of the highly oscillatory wave fields and its Fourier transform. Beam parameters are further refined by an optimization procedure that minimizes the difference between the Gaussian beam superposition and the highly oscillatory wave field in the energy norm.

AB - A new numerical method for approximating highly oscillatory wave fields as a superposition of Gaussian beams is presented. The method estimates the number of beams and their parameters automatically. This is achieved by an expectation-maximization algorithm that fits real, positive Gaussians to the energy of the highly oscillatory wave fields and its Fourier transform. Beam parameters are further refined by an optimization procedure that minimizes the difference between the Gaussian beam superposition and the highly oscillatory wave field in the energy norm.

KW - Expectation-maximization

KW - Gaussian beams

KW - High frequency waves

KW - Wave equation

UR - http://www.scopus.com/inward/record.url?scp=78751701178&partnerID=8YFLogxK

U2 - https://doi.org/10.1016/j.jcp.2010.12.018

DO - https://doi.org/10.1016/j.jcp.2010.12.018

M3 - مقالة

SN - 0021-9991

VL - 230

SP - 2303

EP - 2321

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 6

ER -

Gaussian beam decomposition of high frequency wave fields using expectation-maximization

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this