Hammerschmidt, M.; Barth, C.; Pomplun, J.; Burger, S.; Becker, C.; Schmidt, F: Reconstruction of photonic crystal geometries using a reduced basis method for nonlinear outputs. Berlin: ZIB, 2016 ZIB-Report (16-06)
Open Accesn Version

Maxwell solvers based on the hp-adaptive finite element method allow for accurate geometrical modeling and high numerical accuracy. These features are indispensable for the optimization of optical properties or reconstruction of parameters through inverse processes. High computational complexity prohibits the evaluation of the solution for many parameters. We present a reduced basis method (RBM) for the time-harmonic electromagnetic scattering problem allowing to compute solutions for a parameter configuration orders of magnitude faster. The RBM allows to evaluate linear and nonlinear outputs of interest like Fourier transform or the enhancement of the electromagnetic field in milliseconds. We apply the RBM to compute light-scattering off two dimensional photonic crystal structures made of silicon and reconstruct geometrical parameters.