# Adjoint-based Adaptivity for Uncertain HF Problems

Master thesis, Seminar paper

In practice, the manufacturing process of electromagnetic components introduces small variations which usually can only be described statistically.Therefore, Uncertainty Quantification (UQ) aims for realistic predictions by describing the input data of numerical simulations, i.e. geometry and material parameters,as well as output data as random variables.An efficient method to compute statistical information about the output data, i.e. the quantities of interest, relies on spectral polynomial approximations of the mapping from inputs to outputs (generalized Polynomial Chaos). However, problems with many uncertain input parameters still pose a computational challenge. Due to the so-called curse-of-dimensionality, the computational cost grows rapidly with respect to the number of parameters.The focus of this work is the adaptive construction of the polynomial surrogate model in order to mitigate the curse-of-dimensionality. The efficiency of this approach shall be further improved by employing adjoint-based error measures. The algorithm will be tested on high-frequency electromagnetic problems.