Int. J. Numer. Anal. Mod., 2 (2005), pp. 75-84.


Conservative local discontinuous Galerkin methods for time dependent Schrödinger equation

Tiao Lu 1, Wei Cai 2, Pingwen Zhang 1

1 LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China
2 Department of Mathematics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA

Received by the editors July 15, 2004 and, in revised form, September 9, 2004
Abstract

This paper presents a high order local discontinuous Galerkin time-domain method for solving time dependent Schrodinger equations. After rewriting the Schrodinger equation in terms of a first order system of equations, a numerical flux is constructed to preserve the conservative property for the density of the particle described. Numerical results for a model square potential scattering problem is included to demonstrate the high order accuracy of the proposed numerical method.

AMS subject classifications: 65N30, 47N40, 81Q05
Key words: Conservative local discontinuous Galerkin methods for time dependent Schrodinger equation
Email: tlu@uncc.edu (T. Lu), wcai@uncc.edu (W. Cai), pzhang@math.pku.edu.cn (P. Zhang)
 

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