We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic 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. 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 integral operators are infinitely differentiable without loss of regularity and that the solutions of the scattering problem are infinitely shape differentiable away from the boundary of the obstacle, whereas their derivatives lose regularity on the boundary. We also give a characterization of the first shape derivative as a solution of a new electromagnetic scattering problem.
Shape derivatives of boundary integral operators in electromagnetic scattering. Part II : Application to scattering by a homogeneous dielectric obstacle
Université de Rennes 1（雷恩第一大学）；Universität Göttingen（哥廷根大学）
Shape derivatives of boundary integral operators in electromagnetic scattering. Part I: Shape differentiability of pseudo-homogeneous boundary integral operators
Université de Rennes 1（雷恩第一大学）；Universität Göttingen（哥廷根大学）
Integral representations for higher-order Fréchet derivatives of matrix functions: Quadrature algorithms and new results on the level-2 condition number
Robust integral formulations for electromagnetic scattering from three-dimensional cavities
Courant Institute, New York University（纽约大学库朗数学科学研究所）；Simons Center for Data Analysis, Simons Foundation（西蒙斯基金会数据分析中心）；Tandon School of Engineering, New York University（纽约大学坦顿工程学院）
