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Shape derivatives of boundary integral operators in electromagnetic scattering
, 2010
"... We develop the shape derivative analysis of solutions to the problem of scattering of timeharmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic scattering problems, we study the shape differentiability proper ..."
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We develop the shape derivative analysis of solutions to the problem of scattering of timeharmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic scattering problems, we study the shape differentiability properties of the standard electromagnetic boundary integral operators. To this end, we start with the Gâteaux differentiability analysis with respect to deformations of the obstacle of boundary integral operators with pseudohomogeneous kernels acting between Sobolev spaces. The boundary integral operators of electromagnetism are typically bounded on the space of tangential vector fields of mixed regularity TH− 1 2 (divΓ,Γ). Using Helmholtz decomposition, we can base their analysis on the study of scalar integral operators in standard Sobolev spaces, but we then have to study the Gâteaux differentiability of surface differential operators. We prove that the electromagnetic boundary in
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"... Shape derivatives of boundary integral operators in electromagnetic scattering. Part II: Application to scattering by a homogeneous dielectric obstacle ..."
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Shape derivatives of boundary integral operators in electromagnetic scattering. Part II: Application to scattering by a homogeneous dielectric obstacle