JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (4): 8-15.doi: 10.6040/j.issn.1671-9352.0.2021.778

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An efficient spectral approximation for the transmission eigenvalue problem in spherical domains

REN Shi-xian1,2, AN Jing1*   

  1. 1. School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, Guizhou, China 2. School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, Guizhou, China
  • Published:2023-03-27

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Abstract: In order to solve the interior transmission eigenvalue problems in a spherical region, an effective spectral approximation method is proposed. Firstly, a product type Sobolev space is defined, and the corresponding approximation space is constructed by using a class of orthogonal polynomials on the unit sphere. Then, by introducing an auxiliary function, the original problem is transformed into an equivalent fourth-order mixed scheme, and the variational form and discrete form of the fourth-order mixed scheme are derived. Moreover, by using the approximation property of the projection operator and Babuška-Osborn theory, the error estimation of approximation solution is proved. Finally, the implementation process of the algorithm is described in detail, and some numerical examples are given to verify the convergence and high accuracy of the algorithm.

Key words: transmission eigenvalue problem, spectral method, error estimation, numerical algorithm, spherical domain

CLC Number: 

  • O241.82
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