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Volume 4, Issue 2
Computation of Transmission Eigenvalues by the Regularized Schur Complement for the Boundary Integral Operators

Yunyun Ma, Fuming Ma, Yukun Guo & Jingzhi Li

DOI: 10.4208/csiam-am.SO-2022-0009

CSIAM Trans. Appl. Math., 4 (2023), pp. 306-324.

Published online: 2023-02

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  • Abstract

This paper is devoted to the numerical computation of transmission eigenvalues arising in the inverse acoustic scattering theory. This problem is first reformulated as a two-by-two system of boundary integral equations. Next, we develop a Schur complement operator with regularization to obtain a reduced system of boundary integral equations. The Nyström discretization is then used to obtain an eigenvalue problem for a matrix. In conjunction with the recursive integral method, the numerical computation of the matrix eigenvalue problem produces the indicator for finding the transmission eigenvalues. Numerical implementations are presented and archetypal examples are provided to demonstrate the effectiveness of the proposed method.

  • Keywords

Transmission eigenvalues, inverse scattering, boundary integral equations, Nyström method, Schur complement, spectral projection.

  • AMS Subject Headings

78A46, 45C05, 65F18

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CSIAM-AM-4-306, author = {Ma , YunyunMa , FumingGuo , Yukun and Li , Jingzhi}, title = {Computation of Transmission Eigenvalues by the Regularized Schur Complement for the Boundary Integral Operators}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2023}, volume = {4}, number = {2}, pages = {306--324}, abstract = {

This paper is devoted to the numerical computation of transmission eigenvalues arising in the inverse acoustic scattering theory. This problem is first reformulated as a two-by-two system of boundary integral equations. Next, we develop a Schur complement operator with regularization to obtain a reduced system of boundary integral equations. The Nyström discretization is then used to obtain an eigenvalue problem for a matrix. In conjunction with the recursive integral method, the numerical computation of the matrix eigenvalue problem produces the indicator for finding the transmission eigenvalues. Numerical implementations are presented and archetypal examples are provided to demonstrate the effectiveness of the proposed method.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.SO-2022-0009}, url = {http://global-sci.org/intro/article_detail/csiam-am/21416.html} }
TY - JOUR T1 - Computation of Transmission Eigenvalues by the Regularized Schur Complement for the Boundary Integral Operators AU - Ma , Yunyun AU - Ma , Fuming AU - Guo , Yukun AU - Li , Jingzhi JO - CSIAM Transactions on Applied Mathematics VL - 2 SP - 306 EP - 324 PY - 2023 DA - 2023/02 SN - 4 DO - http://doi.org/10.4208/csiam-am.SO-2022-0009 UR - https://global-sci.org/intro/article_detail/csiam-am/21416.html KW - Transmission eigenvalues, inverse scattering, boundary integral equations, Nyström method, Schur complement, spectral projection. AB -

This paper is devoted to the numerical computation of transmission eigenvalues arising in the inverse acoustic scattering theory. This problem is first reformulated as a two-by-two system of boundary integral equations. Next, we develop a Schur complement operator with regularization to obtain a reduced system of boundary integral equations. The Nyström discretization is then used to obtain an eigenvalue problem for a matrix. In conjunction with the recursive integral method, the numerical computation of the matrix eigenvalue problem produces the indicator for finding the transmission eigenvalues. Numerical implementations are presented and archetypal examples are provided to demonstrate the effectiveness of the proposed method.

Ma , YunyunMa , FumingGuo , Yukun and Li , Jingzhi. (2023). Computation of Transmission Eigenvalues by the Regularized Schur Complement for the Boundary Integral Operators. CSIAM Transactions on Applied Mathematics. 4 (2). 306-324. doi:10.4208/csiam-am.SO-2022-0009
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