Integral Equation Method for a Non-Selfadjoint Steklov Eigenvalue Problem

Abstract

We propose a numerical method for a non-selfadjoint Steklov eigenvalue problem of the Helmholtz equation. The problem is formulated using boundary integrals. The Nyström method is employed to discretize the integral operators, which leads to a non-Hermitian generalized matrix eigenvalue problems. The spectral indicator method (SIM) is then applied to calculate the (complex) eigenvalues. The convergence is proved using the spectral approximation theory for (non-selfadjoint) compact operators. Numerical examples are presented for validation.