Abstract
We consider the computation of the transmission eigenvalue problem based on a boundary integral formulation. The problem is formulated as the eigenvalue problem of a holomorphic Fredholm operator function. A Fourier–Galerkin method is proposed for the integral equations. The approximation properties of the associated discrete operators are analyzed and some convergence results of the eigenvalues are obtained. We present the details of the implementation and employ the spectral projection method to compute the eigenvalues. Numerical examples validate the effectiveness and accuracy of the proposed method.
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Funding
The research of Y. Ma was supported by the NSFC under Grant No. 11901085. The research of J. Sun was partially supported by Simons Foundation under Grant No. 711922.
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Ma, Y., Sun, J. Analysis of a Fourier–Galerkin Method for the Transmission Eigenvalue Problem based on a Boundary Integral Formulation. J Sci Comput 95, 60 (2023). https://doi.org/10.1007/s10915-023-02197-3
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DOI: https://doi.org/10.1007/s10915-023-02197-3