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 - <p style="text-align: justify;">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.</p>