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

In this paper, we propose a new generalized discontinuous Galerkin (GDG) method for Schrödinger equations with nonsmooth solutions. The numerical method is based on a reformulation of Schrödinger 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 [ φ ] = f ( φ - , φ + ) . Numerical results for 1D and 2D time dependent Schrödinger equations validate the high order accuracy and the flexibility of the method for various types of interface conditions.