Conservative local discontinuous Galerkin methods for time dependent Schrödinger equation
Tiao Lu 1, Wei Cai 2, Pingwen Zhang 11 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
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
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