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Volume 35, Issue 6
Recursive Integral Method for the Nonlinear Non-Self-Adjoint Transmission Eigenvalue Problem

Yingxia Xi & Xia Ji

DOI: 10.4208/jcm.1701-m2015-0443

J. Comp. Math., 35 (2017), pp. 828-838.

Published online: 2017-12

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  • Abstract

The transmission eigenvalue problem is an eigenvalue problem that arises in the scattering 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 Morley 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.

  • Keywords

Transmission eigenvalue problem, Nonlinear eigenvalue problem, Contour integrals.

  • AMS Subject Headings

34L16, 65L60.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yxiaxi@lsec.cc.ac.cn (Yingxia Xi)

jixia@lsec.cc.ac.cn (Xia Ji)

  • BibTex
  • RIS
  • TXT
@Article{JCM-35-828, author = {Xi , Yingxia and Ji , Xia}, title = {Recursive Integral Method for the Nonlinear Non-Self-Adjoint Transmission Eigenvalue Problem}, journal = {Journal of Computational Mathematics}, year = {2017}, volume = {35}, number = {6}, pages = {828--838}, abstract = {

The transmission eigenvalue problem is an eigenvalue problem that arises in the scattering 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 Morley 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1701-m2015-0443}, url = {http://global-sci.org/intro/article_detail/jcm/10497.html} }
TY - JOUR T1 - Recursive Integral Method for the Nonlinear Non-Self-Adjoint Transmission Eigenvalue Problem AU - Xi , Yingxia AU - Ji , Xia JO - Journal of Computational Mathematics VL - 6 SP - 828 EP - 838 PY - 2017 DA - 2017/12 SN - 35 DO - http://doi.org/10.4208/jcm.1701-m2015-0443 UR - https://global-sci.org/intro/article_detail/jcm/10497.html KW - Transmission eigenvalue problem, Nonlinear eigenvalue problem, Contour integrals. AB -

The transmission eigenvalue problem is an eigenvalue problem that arises in the scattering 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 Morley 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.

YingxiaXi & XiaJi. (2020). Recursive Integral Method for the Nonlinear Non-Self-Adjoint Transmission Eigenvalue Problem. Journal of Computational Mathematics. 35 (6). 828-838. doi:10.4208/jcm.1701-m2015-0443
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