Integral Equation Method for a Non-Selfadjoint Steklov Eigenvalue Problem

We propose a numerical method for a non-selfadjoint Steklov eigenvalue problem of the Helmholtz equation. The problem is formulated using boundary integrals. The Nystro??m 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. spectral projection.

Automated summary

A numerical method for solving a non-selfadjoint Steklov eigenvalue problem of the Helmholtz equation is proposed, using boundary integrals and the Nystro??m method for discretization, and the spectral indicator method for eigenvalue calculation. Convergence is proven using spectral approximation theory for compact operators, and the method's effectiveness is validated through numerical examples.