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Volume 31, Issue 5
Integral Equation Method for a Non-Selfadjoint Steklov Eigenvalue Problem

Yunyun Ma & Jiguang Sun

DOI: 10.4208/cicp.OA-2022-0016

Commun. Comput. Phys., 31 (2022), pp. 1546-1560.

Published online: 2022-05

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  • 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.

  • Keywords

Steklov eigenvalues, non-selfadjoint problems, integral equations, Nyström method, spectral projection.

  • AMS Subject Headings

65N25, 35P15, 45C05, 35P25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-31-1546, author = {Ma , Yunyun and Sun , Jiguang}, title = {Integral Equation Method for a Non-Selfadjoint Steklov Eigenvalue Problem}, journal = {Communications in Computational Physics}, year = {2022}, volume = {31}, number = {5}, pages = {1546--1560}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0016}, url = {http://global-sci.org/intro/article_detail/cicp/20514.html} }
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 -

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.

Yunyun Ma & Jiguang Sun. (2022). Integral Equation Method for a Non-Selfadjoint Steklov Eigenvalue Problem. Communications in Computational Physics. 31 (5). 1546-1560. doi:10.4208/cicp.OA-2022-0016
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