Discrete absorbing boundary conditions for Schrödinger-type equations: practical implementation

Authors:
Isaías Alonso-Mallo;Nuria Reguera
Affiliations:
Departamento De Matemática Aplicada Y Computación, Universidad De Valladolid, Valladolid, Spain;Departamento de Matemáticas Y Computación, Universidad De Burgos, Burgos, Spain
Venue:
Mathematics of Computation
Year:
2004

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Abstract

Recently, some absorbing boundary conditions for Schrödingertype 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.