Computation of Transmission Eigenvalues by the Regularized Schur Complement for the Boundary Integral Operators

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.

Author Details

Yunyun Ma

Fuming Ma

Yukun Guo

Jingzhi Li