Fast evaluation of nonreflecting boundary conditions for the Schrödinger equation in one dimension

Shidong Jiang, L. Greengard

Research output: Contribution to journalArticle

Abstract

We present a fast algorithm for the evaluation of the exact nonreflecting boundary conditions for the Schrödinger equation in one dimension. The exact nonreflecting boundary condition contains a nonlocal term which is a convolution integral in time, with a kernel proportional to 1/√t. The key observation is that this integral can be split into two parts: a local part and a history part, each of which allows for separate treatment. The local part is computed by a quadrature suited for square-root singularities. For the history part, we approximate the convolution kernel uniformly by a sum of exponentials. The integral can then be evaluated recursively. As a result, the computation of the nonreflecting boundary conditions is both accurate and efficient.

Original languageEnglish (US)
Pages (from-to)955-966
Number of pages12
JournalComputers and Mathematics with Applications
Volume47
Issue number6-7
DOIs
StatePublished - 2004

Keywords

  • Fast algorithm
  • Nonreflecting boundary condition
  • Schrödinger equation

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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