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	A Hamiltonian-preserving scheme for the Liouville equation of geometrical optics with partial transmissions and reflections
	Jin, Shi ; Wen, Xin
	2010-05-06 ; 2010-05-06
关键词	geometrical optics Liouville equation transmission and reflection Hamiltonian-preserving schemes MULTIVALUED PHYSICAL OBSERVABLES TRANSPORT-EQUATIONS LEVEL SET SCHRODINGER-EQUATION EULERIAN METHOD SPACE WAVES COEFFICIENTS COMPUTATION INTERFACES Mathematics, Applied
中文摘要	We construct a class of Hamiltonian-preserving numerical schemes for the Liouville equation of geometrical optics, with partial transmissions and reflections. This equation arises in the high frequency limit of the linear wave equation, with a discontinuous index of refraction. In our previous work [Hamiltonian-preserving schemes for the Liouville equation of geometrical optics with discontinuous local wave speeds, J. Comput. Phys. 214 (2006), pp. 672-697], we introduced the Hamiltonian-preserving schemes for the same equation when only complete transmissions or reflections occur at the interfaces. These schemes are extended in this paper to the general case of partial transmissions and reflections. The key idea is to build into the numerical flux the behavior of waves at the interface, namely, partial transmissions and reflections that satisfy Snell's law of refraction with the correct transmission and reflection coeficients. This scheme allows a hyperbolic stability condition, under which positivity, and stabilities in both l(1) and l(infinity) norms, are established. Numerical experiments are carried out to study the numerical accuracy.
语种	英语 ; 英语
出版者	SIAM PUBLICATIONS ; PHILADELPHIA ; 3600 UNIV CITY SCIENCE CENTER, PHILADELPHIA, PA 19104-2688 USA
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/14152]
专题	清华大学
推荐引用方式 GB/T 7714	Jin, Shi,Wen, Xin. A Hamiltonian-preserving scheme for the Liouville equation of geometrical optics with partial transmissions and reflections[J],2010, 2010.
APA	Jin, Shi,&Wen, Xin.(2010).A Hamiltonian-preserving scheme for the Liouville equation of geometrical optics with partial transmissions and reflections..
MLA	Jin, Shi,et al."A Hamiltonian-preserving scheme for the Liouville equation of geometrical optics with partial transmissions and reflections".(2010).

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