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

  • Authors:

  • Zhenli Xu;Houde Han;Xiaonan Wu

  • Affiliations:

  • Department of Mathematics, University of Science and Technology of China, Hefei 230026, China;Department of Mathematics, University of Science and Technology of China, Hefei 230026, China and Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China;Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong, China

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

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Abstract

We propose an adaptive approach in picking the wave-number parameter of absorbing boundary conditions for Schrodinger-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 Schrodinger equations in one and two dimensions are presented to demonstrate the properties of the discussed absorbing boundary conditions.