Computation of Transmission Eigenvalues by the Regularized Schur Complement for the Boundary Integral Operators (CSIAM Transactions on Applied Mathematics, 2023)
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 developa Schur complement operator with regularization to obtain a reduced system of boundary integral equations. The Nyström discretization is then used to obtain an eigenvalueproblem for a matrix. In conjunction with the recursive integral method, the numericalcomputation of the matrix eigenvalue problem produces the indicator for finding thetransmission eigenvalues. Numerical implementations are presented and archetypalexamples are provided to demonstrate the effectiveness of the proposed method.
Keywords: Transmission eigenvalues; inverse scattering; boundary integral equations; Nyström method; Schur complement; spectral projection.