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Spike-Layer Simulation for Steady-State Coupled Schrödinger Equations

Part of: Computational aspects

Published online by Cambridge University Press:  07 September 2017

Liming Liao ,
Guanghua Ji ,
Zhongwei Tang  and
Hui Zhang
Liming Liao
Affiliation:
Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
Guanghua Ji*
Affiliation:
Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
Zhongwei Tang
Affiliation:
Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
Hui Zhang
Affiliation:
Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
*
*Corresponding author. Email address:ghji@bnu.edu.cn (G. Ji)
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Abstract

An adaptive finite element method is adopted to simulate the steady state coupled Schrödinger equations with a small parameter. We use damped Newton iteration to solve the nonlinear algebraic system. When the solution domain is elliptic, our numerical results with Dirichlet or Neumann boundary conditions are consistent with previous theoretical results. For the dumbbell and circular ring domains with Dirichlet boundary conditions, we obtain some new results that may be compared with future theoretical analysis.

Keywords

Schrödinger equationsdamped Newton iterationadaptive finite element methodspike-layer solution

MSC classification

Secondary: 33F05: Numerical approximation and evaluation 68U20: Simulation
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 3 , August 2017 , pp. 566 - 582
Copyright
Copyright © Global-Science Press 2017 

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