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Journal of Scientific Computing

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24-12-2016

Exact Boundary Condition for Semi-discretized Schrödinger Equation and Heat Equation in a Rectangular Domain

Authors: Gang Pang, Yibo Yang, Shaoqiang Tang

Published in: Journal of Scientific Computing | Issue 1/2017

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Abstract

A convolution type exact/transparent boundary condition is proposed for simulating a semi-discretized linear Schrödinger equation on a rectangular computational domain. We calculate the kernel functions for a single source problem, and subsequently those over the rectangular domain. Approximate kernel functions are pre-computed numerically from discrete convolutionary equations. With a Crank–Nicolson scheme for time integration, the resulting approximate boundary conditions effectively suppress boundary reflections, and resolve the corner effect. The proposed boundary treatment, with a parameter modified, applies readily to a semi-discretized heat equation.

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Title: Exact Boundary Condition for Semi-discretized Schrödinger Equation and Heat Equation in a Rectangular Domain
Authors: Gang Pang
Yibo Yang
Shaoqiang Tang
Publication date: 24-12-2016
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 1/2017
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-016-0344-0

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