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

Kai Fan; Wei Cai; Xia Ji

doi:10.1016/j.jcp.2007.10.023

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

Kai Fan, Wei Cai^*, Xia Ji

^*Corresponding author for this work

University of North Carolina at Charlotte

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	2387-2410
Number of pages	24
Journal	Journal of Computational Physics
Volume	227
Issue number	4
DOIs	https://doi.org/10.1016/j.jcp.2007.10.023
Publication status	Published - 1 Feb 2008
Externally published	Yes

Keywords

Discontinuous Galerkin method
Schrödinger equation
Split distributions

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10.1016/j.jcp.2007.10.023

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abstract = "In this paper, we propose a new generalized discontinuous Galerkin (GDG) method for Schr{\"o}dinger equations with nonsmooth solutions. The numerical method is based on a reformulation of Schr{\"o}dinger 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 Schr{\"o}dinger equations validate the high order accuracy and the flexibility of the method for various types of interface conditions.",

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AU - Fan, Kai

AU - Cai, Wei

AU - Ji, Xia

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N2 - 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.

AB - 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.

KW - Discontinuous Galerkin method

KW - Schrödinger equation

KW - Split distributions

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JF - Journal of Computational Physics

IS - 4

ER -

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

Abstract

Keywords

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