Computation of transmission eigenvalues by the regularized Schur complement for the boundary integral operators

TL;DR

This paper introduces a novel regularized Schur complement approach combined with Nyström discretization and recursive integral methods to efficiently compute transmission eigenvalues in inverse acoustic scattering.

Contribution

It develops a new regularized Schur complement technique for boundary integral operators, improving computational efficiency in eigenvalue problems.

Findings

Method reduces computational costs

Numerical results demonstrate efficiency

Effective for inverse acoustic scattering

Abstract

This paper is devoted to the computation of transmission eigenvalues in the inverse acoustic scattering theory. This problem is first reformulated as a two by two boundary system of boundary integral equations. Next, utilizing the Schur complement technique, we develop a Schur complement operator with regularization to obtain a reduced system of boundary integral equations. The Nystr\"{o}m discretization is then used to obtain an eigenvalue problem for a matrix. We employ the recursive integral method for the numerical computation of the matrix eigenvalue. Numerical results show that the proposed method is efficient and reduces computational costs.