Regularization of the volume integral operator of electromagnetic scattering. (English) Zbl 1540.35388
Summary: We consider the scattering of time-harmonic electromagnetic waves by a bounded, penetrable, homogeneous obstacle. This problem admits an equivalent formulation in terms of a strongly singular volume integral equation (VIE). In this paper, and for smooth interfaces, we construct a regularizer for the operator that describes the VIE, i.e., we give an explicit representation of an integral operator, which, applied to the VIE, transforms it into the form “identity plus a compact operator”. The employed strategy is inspired by the previous work [M. Costabel et al., C. R., Math., Acad. Sci. Paris 350, No. 3–4, 193–197 (2012; Zbl 1247.78011)].
MSC:
| 35Q61 | Maxwell equations |
| 78A45 | Diffraction, scattering |
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
| 45B05 | Fredholm integral equations |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35R09 | Integro-partial differential equations |
Keywords:
Fredholm operator; Maxwell’s equations; regularizer; scattering theory; volume integral equationCitations:
Zbl 1247.78011References:
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