Integral Equation Method for a Non-Selfadjoint Steklov Eigenvalue Problem (Communications in Computational Physics, 2022)
We propose a numerical method for a non-selfadjoint Steklov eigenvalueproblem of the Helmholtz equation. The problem is formulated using boundary integrals. The Nyström method is employed to discretize the integral operators, whichleads 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) compactoperators. Numerical examples are presented for validation.