Numerical Analysis of Multiscale Computations
Volume 82 of the series Lecture Notes in Computational Science and Engineering pp 401420
A Coupled Finite Difference – Gaussian Beam Method for High Frequency Wave Propagation
 Nicolay M. TanushevAffiliated withDepartment of Mathematics and Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin Email author
 , YenHsi Richard TsaiAffiliated withDepartment of Mathematics and Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin
 , Björn EngquistAffiliated withDepartment of Mathematics and Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin
Abstract
Approximations of geometric optics type are commonly used in simulations of high frequency wave propagation. This form of technique fails when there is strong local variation in the wave speed on the scale of the wavelength or smaller. We propose a domain decomposition approach, coupling Gaussian beam methods where the wave speed is smooth with finite difference methods for the wave equations in domains with strong wave speed variation. In contrast to the standard domain decomposition algorithms, our finite difference domains follow the energy of the wave and change in time. A typical application in seismology presents a great simulation challenge involving the presence of irregularly located sharp inclusions on top of a smoothly varying background wave speed. These sharp inclusions are small compared to the domain size. Due to the scattering nature of the problem, these small inclusions will have a significant effect on the wave field. We present examples in two dimensions, but extensions to higher dimensions are straightforward.
 Title
 A Coupled Finite Difference – Gaussian Beam Method for High Frequency Wave Propagation
 Book Title
 Numerical Analysis of Multiscale Computations
 Book Subtitle
 Proceedings of a Winter Workshop at the Banff International Research Station 2009
 Pages
 pp 401420
 Copyright
 2012
 DOI
 10.1007/9783642219436_16
 Print ISBN
 9783642219429
 Online ISBN
 9783642219436
 Series Title
 Lecture Notes in Computational Science and Engineering
 Series Volume
 82
 Series ISSN
 14397358
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
 Topics
 Industry Sectors
 eBook Packages
 Editors

 Björn Engquist ^{(ID1)}
 Olof Runborg ^{(ID2)}
 YenHsi R. Tsai ^{(ID3)}
 Editor Affiliations

 ID1. , Department of Mathematics, University of Texas
 ID2. Dept. Numerical Analysis &, Computer Science (NADA), Royal Institute of Technology (KTH)
 ID3. , Department of Mathematics, University of Texas at Austin
 Authors

 Nicolay M. Tanushev ^{(1)}
 YenHsi Richard Tsai ^{(1)}
 Björn Engquist ^{(1)}
 Author Affiliations

 1. Department of Mathematics and Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, 1 University Station, C1200, Austin, TX, 78712, USA
Continue reading...
To view the rest of this content please follow the download PDF link above.