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Global geometrical optics approximation to the high frequency helmholtz equation with discontinuous media

Chunxiong Zheng Tsinghua University

Numerical Analysis and Scientific Computing mathscidoc:1611.25003

Communications in Mathematical Sciences, 13, (8), 1949-1974, 2015.1
Global geometrical optics method is a new semi-classical approach for the high frequency linear waves proposed by the author in [13]. In this paper, we rederive it in a more concise way. It is shown that the right candidate of solution ansatz for the high frequency wave equations is the extended WKB function, other than the WKB function used in the classical geometrical optics approximation. A new and main contribution of this paper is an interface analysis for the Helmholtz equation when the incident wave is of extended WKB-type. We derive asymptotic expressions for the reflected and/or transmitted propagating waves in the general case. These expressions are valid even when the incident rays include caustic points.
high frequency waves, global geometrical optics approximation, caustics, WKB analysis, discontinuous media.
[ Download ] [ 2016-11-23 16:41:50 uploaded by czheng ] [ 1241 downloads ] [ 0 comments ] 
@inproceedings{chunxiong2015global,
  title={GLOBAL GEOMETRICAL OPTICS APPROXIMATION TO THE HIGH FREQUENCY HELMHOLTZ EQUATION WITH DISCONTINUOUS MEDIA},
  author={Chunxiong Zheng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161123164150278827632},
  booktitle={Communications in Mathematical Sciences},
  volume={13},
  number={8},
  pages={1949-1974},
  year={2015},
}
Chunxiong Zheng. GLOBAL GEOMETRICAL OPTICS APPROXIMATION TO THE HIGH FREQUENCY HELMHOLTZ EQUATION WITH DISCONTINUOUS MEDIA. 2015. Vol. 13. In Communications in Mathematical Sciences. pp.1949-1974. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161123164150278827632.
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