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 |
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Pages (from-to) | 2303-2321 |
Number of pages | 19 |
Journal | Journal of Computational Physics |
Volume | 230 |
Issue number | 6 |
DOIs | |
State | Published - 20 Mar 2011 |
Bibliographical 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).
Funding
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).
Funders | Funder number |
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National Science Foundation | DMS-0714612, DMS-0636586 |
Keywords
- Expectation-maximization
- Gaussian beams
- High frequency waves
- Wave equation