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The DB Boundary Condition in Electromagnetic Scattering Revisited
SIAM Journal on Mathematical Analysis ( IF 2 ) Pub Date : 2021-06-29 , DOI: 10.1137/20m1380144
Rainer Kress

SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3661-3680, January 2021.
For the solution of the scattering problem for time-harmonic electromagnetic waves with boundary conditions for the normal components of both the electric and the magnetic field, an integral equation method proposed by Gülzow in 1988 is reconsidered. It is made more concise, made symmetric with respect to the electric and magnetic field, and also extended from the classical Hölder spaces to a contemporary Sobolev space setting. For this regime, new reciprocity principles for scattering of plane waves and dipole fields are established and a related far field operator is discussed. Finally, the corresponding inverse scattering problem to recover the shape of the scatterer from far field data is discussed with the main emphasis on uniqueness results.


中文翻译:

重新审视电磁散射中的 DB 边界条件

SIAM 数学分析杂志,第 53 卷,第 3 期,第 3661-3680 页,2021 年 1 月。
对于电场和磁场的法向分量均具有边界条件的时谐电磁波散射问题的求解,重新考虑了 Gülzow 于 1988 年提出的积分方程法。它变得更加简洁,相对于电场和磁场对称,并且还从经典的 Hölder 空间扩展到现代的 Sobolev 空间设置。对于这种情况,建立了平面波和偶极场散射的新互易性原理,并讨论了相关的远场算子。最后,讨论了从远场数据恢复散射体形状的相应逆散射问题,主要强调唯一性结果。
更新日期:2021-06-30
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