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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Discrete absorbing boundary conditions for Schrödinger-type equations. Practical implementation


Authors: Isaías Alonso-Mallo and Nuria Reguera
Journal: Math. Comp. 73 (2004), 127-142
MSC (2000): Primary 65M12, 65M20; Secondary 65M99
Published electronically: June 6, 2003
MathSciNet review: 2034113
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Abstract: Recently, some absorbing boundary conditions for Schrödinger-type equations have been studied by Fevens, Jiang and Alonso-Mallo, and Reguera. These conditions make it possible to obtain a very high absorption at the boundary avoiding the nonlocality of transparent boundary conditions. However, the implementations used in the literature, where the boundary condition is chosen in a manual way in accordance with the solution or fixed independently of the solution, are not practical because of the small absorption. In this paper, a new practical adaptive implementation is developed that allows us to obtain automatically a very high absorption.


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Additional Information

Isaías Alonso-Mallo
Affiliation: Departamento de Matemática Aplicada y Computación, Universidad de Valladolid, Valladolid, Spain
Email: isaias@mac.cie.uva.es

Nuria Reguera
Affiliation: Departamento de Matemáticas y Computación, Universidad de Burgos, Burgos, Spain
Email: nreguera@ubu.es

DOI: http://dx.doi.org/10.1090/S0025-5718-03-01548-5
PII: S 0025-5718(03)01548-5
Keywords: Schr\"odinger equation, transparent boundary conditions, absorbing boundary conditions
Received by editor(s): November 20, 2001
Received by editor(s) in revised form: May 7, 2002
Published electronically: June 6, 2003
Additional Notes: The authors have obtained financial support from MCYT BFM 2001-2013 and JCYL VA025/01
Article copyright: © Copyright 2003 American Mathematical Society