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	Computational high frequency waves through curved interfaces via the Liouville equation and geometric theory of diffraction
	Jin, Shi ; Yin, Dongsheng
	2010-05-06 ; 2010-05-06
关键词	high frequency waves Lionville equation geometrical theory of diffraction geometric optics creeping wave numerical methods MULTIPHASE SEMICLASSICAL APPROXIMATION DIMENSIONAL CRYSTALLINE LATTICE HAMILTONIAN-PRESERVING SCHEME SMOOTH TRANSPARENT OBJECT PHASE-SPACE METHOD LEVEL SET METHODS TRANSPORT-EQUATIONS DELTA-FUNCTION RANDOM-MEDIA OPTICS Computer Science, Interdisciplinary Applications Physics, Mathematical
中文摘要	We construct a class of numerical schemes for the Lionville equation of geometric optics coupled with the Geometric Theory of Diffractions to simulate the high frequency linear waves with a discontinuous index of refraction. In this work [S. Jin, X. Wen, A Hamiltonian-preserving scheme for the Lionville equation of geometric optics with partial transmissions and reflections, SIAM J. Numer. Anal. 44 (2006) 1801-1828], a Hamiltonian-preserving scheme for the Liouville equation was constructed to capture partial transmissions and reflections at the interfaces. This scheme is extended by incorporating diffraction terms derived from Geometric Theory of Diffraction into the numerical flux in order to capture diffraction at the interface. We give such a scheme for curved interfaces. This scheme is proved to be positive under a suitable time step constraint. Numerical experiments show that it can capture diffraction phenomena without fully resolving the wave length of the original wave equation. (c) 2008 Elsevier Inc. All rights reserved.
语种	英语 ; 英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE ; SAN DIEGO ; 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/14293]
专题	清华大学
推荐引用方式 GB/T 7714	Jin, Shi,Yin, Dongsheng. Computational high frequency waves through curved interfaces via the Liouville equation and geometric theory of diffraction[J],2010, 2010.
APA	Jin, Shi,&Yin, Dongsheng.(2010).Computational high frequency waves through curved interfaces via the Liouville equation and geometric theory of diffraction..
MLA	Jin, Shi,et al."Computational high frequency waves through curved interfaces via the Liouville equation and geometric theory of diffraction".(2010).

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