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Volume 36, Issue 1
A Survey of Open Cavity Scattering Problems

Peijun Li

DOI: 10.4208/jcm.1605-m2015-0407

J. Comp. Math., 36 (2018), pp. 1-16.

Published online: 2018-02

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  • Abstract

This paper gives a brief survey of recent developments on mathematical modeling and analysis of the open cavity scattering problems, which arise in diverse scientific areas and have significant industrial and military applications. The scattering problems are studied for the two-dimensional Helmholtz equation corresponding to the transverse magnetic or electric polarization, and the three-dimensional time-harmonic and time-domain Maxwell equations. Since these problems are imposed in open domains, a key step of the analysis is to develop transparent boundary conditions and reformulate them equivalently into boundary value problems in bounded domains. The well-posedness of weak solutions is shown for the associated variational problems by using either the Lax-Milgram theorem or the Fredholm alternative.

  • Keywords

Cavity scattering problem, Helmholtz equation, Maxwell's equations, Transparent boundary condition, Variational problem, Well-posedness.

  • AMS Subject Headings

35Q61, 78A25, 78M30.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

lipeijun@math.purdue.edu (Peijun Li)

  • BibTex
  • RIS
  • TXT
@Article{JCM-36-1, author = {Li , Peijun}, title = {A Survey of Open Cavity Scattering Problems}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {1}, pages = {1--16}, abstract = {

This paper gives a brief survey of recent developments on mathematical modeling and analysis of the open cavity scattering problems, which arise in diverse scientific areas and have significant industrial and military applications. The scattering problems are studied for the two-dimensional Helmholtz equation corresponding to the transverse magnetic or electric polarization, and the three-dimensional time-harmonic and time-domain Maxwell equations. Since these problems are imposed in open domains, a key step of the analysis is to develop transparent boundary conditions and reformulate them equivalently into boundary value problems in bounded domains. The well-posedness of weak solutions is shown for the associated variational problems by using either the Lax-Milgram theorem or the Fredholm alternative.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1605-m2015-0407}, url = {http://global-sci.org/intro/article_detail/jcm/10579.html} }
TY - JOUR T1 - A Survey of Open Cavity Scattering Problems AU - Li , Peijun JO - Journal of Computational Mathematics VL - 1 SP - 1 EP - 16 PY - 2018 DA - 2018/02 SN - 36 DO - http://doi.org/10.4208/jcm.1605-m2015-0407 UR - https://global-sci.org/intro/article_detail/jcm/10579.html KW - Cavity scattering problem, Helmholtz equation, Maxwell's equations, Transparent boundary condition, Variational problem, Well-posedness. AB -

This paper gives a brief survey of recent developments on mathematical modeling and analysis of the open cavity scattering problems, which arise in diverse scientific areas and have significant industrial and military applications. The scattering problems are studied for the two-dimensional Helmholtz equation corresponding to the transverse magnetic or electric polarization, and the three-dimensional time-harmonic and time-domain Maxwell equations. Since these problems are imposed in open domains, a key step of the analysis is to develop transparent boundary conditions and reformulate them equivalently into boundary value problems in bounded domains. The well-posedness of weak solutions is shown for the associated variational problems by using either the Lax-Milgram theorem or the Fredholm alternative.

Li , Peijun. (2018). A Survey of Open Cavity Scattering Problems. Journal of Computational Mathematics. 36 (1). 1-16. doi:10.4208/jcm.1605-m2015-0407
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