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.