A generalized discontinuous Galerkin (GDG) method for Schrodinger equations with nonsmooth solutions

摘要

In this paper, we propose a new generalized discontinuous Galerkin (GDG) method for Schrodinger equations with nonsmooth solutions. The numerical method is based on a reformulation of Schrodinger equations, using split distributional variables and their related integration by parts formulae to account for solution jumps across material interfaces. The proposed GDG method can handle time dependent and nonlinear jump conditions [phi] = f (phi(-), phi(+)). Numerical results for 1 D and 2D time dependent Schrodinger equations validate the high order accuracy and the flexibility of the method for various types of interface conditions. (c) 2007 Elsevier Inc. All rights reserved.