TY - JOUR
T1 - A Holomorphic Operator Function Approach for the Transmission Eigenvalue Problem of Elastic Waves
AU - Xi , Yingxia
AU - Ji , Xia
JO - Communications in Computational Physics
VL - 2
SP - 524
EP - 546
PY - 2022
DA - 2022/08
SN - 32
DO - http://doi.org/ 10.4208/cicp.OA-2022-0050
UR - https://global-sci.org/intro/article_detail/cicp/20867.html
KW - Discontinuous Galerkin method, transmission eigenvalue problem, elastic waves, Fredholm operator.
AB - <p style="text-align: justify;">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.</p>