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Shape sensitivity analysis of metallic nano particles

by S. Sargheini and A. Paganini and R. Hiptmair and C. Hafner

(Report number 2016-15)

Abstract
Shape sensitivity measures the impact of small perturbations of geometric features of a problem on certain quantities of interest. The shape sensitivity of PDE 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 due to the fact that the 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 based on local sensitivity measurements. Several numerical experiments are conducted to investigate the shape sensitivity of different output functionals for different geometric settings.

Keywords: Shape sensitivity analysis, Shape gradients, Maxwell's equations, Finite elements, Nano particles, Plasmonic

@Techreport{SPHH16_652,
  author = {S. Sargheini and A. Paganini and R. Hiptmair and C. Hafner},
  title = {Shape sensitivity analysis of metallic nano particles},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2016-15},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2016/2016-15.pdf },
  year = {2016}
}

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