A high order finite element discretization with local absorbing boundary conditions of the linear Schrödinger equation

Authors:
Isaías Alonso-Mallo;Nuria Reguera
Affiliations:
Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Valladolid, C/Dr. Mergelina s/n, 47011 Valladolid, Spain;Departamento de Matemáticas y Computación, Universidad de Burgos, Avda. Cantabria, s/n, Burgos, Spain
Venue:
Journal of Computational Physics
Year:
2006

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Abstract

The goal of this paper is to obtain a high order full discretization of the initial value problem for the linear Schrodinger equation in a finite computational domain. For this we use a high order finite element discretization in space together with an adaptive implementation of local absorbing boundary conditions specifically obtained for linear finite elements, and a high order symplectic time integrator. The numerical results show that it is possible to obtain simultaneously a very good absorption at the boundary and a very small error in the interior of the computational domain.