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https://doi.org/10.1007/BF01029499

has been cited by the following article:

• TITLE: An Efficient Method for Local Base Transform in Pekeris Waveguide with Radiation Condition

  AUTHORS: Jianxin Zhu, Haibo Chen

  KEYWORDS: Helmholtz Operator, Radiation Boundary Condition, Conjugate Operator, Eigenfunction Expansion, Orthogonality, Pekeris Waveguide

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.8 No.5, April 26, 2020

  ABSTRACT: In this paper, for the fast computation of the coordinates under the basis of the eigenfunctions of Helmholtz operator, we derive the conjugate operator with the radiation boundary condition. Further, we prove the cross orthogonality between the linearly-independent eigenfunctions of the Helmholtz operator and the linearly-independent eigenfunctions of the conjugate operator. The numerical simulations demonstrate the effectiveness of our treatment.