Year: 2022
Author: Yingxia Xi, Xia Ji
Communications in Computational Physics, Vol. 32 (2022), Iss. 2 : pp. 524–546
Abstract
The paper presents a holomorphic operator function approach for the transmission eigenvalue problem of elastic waves using the discontinuous Galerkin method. To use the abstract approximation theory for holomorphic operator functions, we rewrite the elastic transmission eigenvalue problem as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. The convergence for the discontinuous Galerkin method is proved following the abstract theory of the holomorphic Fredholm operator. The spectral indicator method is employed to compute the transmission eigenvalues. Extensive numerical examples are presented to validate the theory.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/ 10.4208/cicp.OA-2022-0050
Communications in Computational Physics, Vol. 32 (2022), Iss. 2 : pp. 524–546
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Discontinuous Galerkin method transmission eigenvalue problem elastic waves Fredholm operator.