Uncertainty quantification for Maxwell\'s equations using stochastic collocation and model order reduction / Peter Benner, Judith Schneider

Abstract

Abstract: Modeling and simulation are important for the design process of new semiconductor structures. Difficulties proceed from shrinking structures, increasing working frequencies, and uncertainties of materials and geometries. Therefore, we consider the time-harmonic Maxwell\'s equations for the simulation of a coplanar waveguide with uncertain material parameters. To analyze the uncertainty of the system, we use stochastic collocation with Stroud and sparse grid points. The results are compared to a Monte Carlo simulation. Both methods rely on repetitive runs of a deterministic solver. Hence, we compute a reduced model by means of proper orthogonal decomposition to reduce the computational cost. The Monte Carlo simulation and the stochastic collocation are both applied to the full and the reduced model. All results are compared concerning accuracy and computation time.