Adaptive absorbing boundary conditions for Schrödinger-type equations: Application to nonlinear and multi-dimensional problems

Zhenli Xu, Houde Han, Xiaonan WU*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

42 Citations (Scopus)

Abstract

We propose an adaptive approach in picking the wave-number parameter of absorbing boundary conditions for Schrödinger-type equations. Based on the Gabor transform which captures local frequency information in the vicinity of artificial boundaries, the parameter is determined by an energy-weighted method and yields a quasi-optimal absorbing boundary conditions. It is shown that this approach can minimize reflected waves even when the wave function is composed of waves with different group velocities. We also extend the split local absorbing boundary (SLAB) method [Z. Xu, H. Han, Phys. Rev. E 74 (2006) 037704] to problems in multi-dimensional nonlinear cases by coupling the adaptive approach. Numerical examples of nonlinear Schrödinger equations in one and two dimensions are presented to demonstrate the properties of the discussed absorbing boundary conditions.

Original languageEnglish
Pages (from-to)1577-1589
Number of pages13
JournalJournal of Computational Physics
Volume225
Issue number2
DOIs
Publication statusPublished - 10 Aug 2007

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Artificial boundary conditions
  • Finite difference method
  • Fourier transform
  • Group velocity
  • Nonlinear Schrödinger equations
  • Time-splitting

Fingerprint

Dive into the research topics of 'Adaptive absorbing boundary conditions for Schrödinger-type equations: Application to nonlinear and multi-dimensional problems'. Together they form a unique fingerprint.

Cite this