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	Hamiltonian-preserving schemes for the Liouville equation with discontinuous potentials
	Shi, J ; Xin, W
	2010-05-06 ; 2010-05-06
关键词	Liouville equation discontinuous potential Hamiltonian-preserving semiclassical limit SCHRODINGER-EQUATION TRANSPORT-EQUATIONS SEMICLASSICAL LIMIT WAVES COEFFICIENTS INTERFACES WIGNER Mathematics, Applied
中文摘要	When numerically solving the Liouville equation with a discontinuous potential, one faces the problem of selecting a unique, physically relevant solution across the potential barrier, and the problem of a severe time step constraint due to the CFL condition. In this paper, we introduce two classes of Hamiltonian-preserving schemes for such problems. By using the constant Hamiltonian across the potential barrier, we introduce a selection criterion for a unique, physically relevant solution to the underlying linear hyperbolic equation with singular coefficients. These schemes have a hyperbolic CFL condition, which is a significant improvement over a conventional discretization. These schemes are proved to be positive, and stable in both l(infinity) and l(1) norms. Numerical experiments are conducted to study the numerical accuracy. This work is motivated by the well-balanced kinetic schemes by Perthame and Simeoni for the shallow water equations with a discontinuous bottom topography, and has applications to the level set methods for the computations of multivalued physical observables in the semiclassical limit of the linear Schrodinger equation with a discontinuous potential, among other applications.
语种	英语 ; 英语
出版者	INT PRESS ; SOMERVILLE ; PO BOX 43502, SOMERVILLE, MA 02143 USA
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/13806]
专题	清华大学
推荐引用方式 GB/T 7714	Shi, J,Xin, W. Hamiltonian-preserving schemes for the Liouville equation with discontinuous potentials[J],2010, 2010.
APA	Shi, J,&Xin, W.(2010).Hamiltonian-preserving schemes for the Liouville equation with discontinuous potentials..
MLA	Shi, J,et al."Hamiltonian-preserving schemes for the Liouville equation with discontinuous potentials".(2010).

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