Shape sensitivity analysis of metallic nano particles

Shape sensitivity measures the impact of small perturbations of geometric features of a problem on certain quantities of interest. The shape sensitivity of PDE (partial differential equation) constrained output functionals is derived with the help of shape gradients. In electromagnetic scattering problems, the standard procedure of the Lagrangian approach cannot be applied because of solution of the state problem is complex valued. We derive a closed-form formula of the shape gradient of a generic output functional constrained by Maxwell's equations. We employ cubic B-splines to model local deformations of the geometry and derive sensitivity probings over the surface of the scatterer. We also define a sensitivity representative function over the surface of the scatterer on the basis of local sensitivity measurements. Several numerical experiments are conducted to investigate the shape sensitivity of different output functionals for different geometric settings.