Computation of Transmission Eigenvalues by the Regularized Schur Complement for the Boundary Integral Operators
Year: 2023
Author: Yunyun Ma, Fuming Ma, Yukun Guo, Jingzhi Li
CSIAM Transactions on Applied Mathematics, Vol. 4 (2023), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.SO-2022-0009
CSIAM Transactions on Applied Mathematics, Vol. 4 (2023), Iss. 2 : pp. 306–324
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Transmission eigenvalues inverse scattering boundary integral equations Nyström method Schur complement spectral projection.