Shape sensitivity analysis in the Maxwell's equations

Abstract : The shape sensitivity analysis for hyperbolic problems yields some specific complications due to the hyperbolic regularity, or the lack thereof. In previous works we investigated the wave equation and came up with some shape sensistivity results. In this paper we investigate sensitivity of the solutions to the Maxwell equation with respect to the shape of the domain. We explicit a derivative with respect to a deformation parameter. The transport of the free divergence property requires a specific shape different quotient that is not necessary in the scalar case.