TY - JOUR
T1 - Integral Equation Method for a Non-Selfadjoint Steklov Eigenvalue Problem
AU - Ma , Yunyun
AU - Sun , Jiguang
JO - Communications in Computational Physics
VL - 5
SP - 1546
EP - 1560
PY - 2022
DA - 2022/05
SN - 31
DO - http://doi.org/10.4208/cicp.OA-2022-0016
UR - https://global-sci.org/intro/article_detail/cicp/20514.html
KW - Steklov eigenvalues, non-selfadjoint problems, integral equations, Nyström method, spectral projection.
AB - <p style="text-align: justify;">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.</p>