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 ope...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.展开更多
The transmission eigenvalue problem is an eigenvalue problem that arises in the scatter- ing of time-harmonic waves by an inhomogeneous medium of compact support. Based on a fourth order formulation, the transmission ...The transmission eigenvalue problem is an eigenvalue problem that arises in the scatter- ing of time-harmonic waves by an inhomogeneous medium of compact support. Based on a fourth order formulation, the transmission eigenvalue problem is discretized by the Mor- ley element. For the resulting quadratic eigenvalue problem, a recursive integral method is used to compute real and complex eigenvalues in prescribed regions in the complex plane. Numerical examples are presented to demonstrate the effectiveness of the proposed method.展开更多
基金supported in part by the National Natural Science Foundation of China with Grant No.11901295Natural Science Foundation of Jiangsu Province under BK20190431+1 种基金partially supported by the National Natural Science Foundation of China with Grant No.11971468Beijing Natural Science Foundation Z200003,Z210001.
文摘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.
文摘The transmission eigenvalue problem is an eigenvalue problem that arises in the scatter- ing of time-harmonic waves by an inhomogeneous medium of compact support. Based on a fourth order formulation, the transmission eigenvalue problem is discretized by the Mor- ley element. For the resulting quadratic eigenvalue problem, a recursive integral method is used to compute real and complex eigenvalues in prescribed regions in the complex plane. Numerical examples are presented to demonstrate the effectiveness of the proposed method.
