## Stochastic Contour Integral Methodology for the Computation of Two-Dimensional Electromagnetic Wave Propagation

The project will extend the so-called contour integral method (CIM) for the computation of two-dimensional packaging and interconnect structures such as printed circuit boards and planar optical substrates to take into account stochastic boundary conditions and simulation parameters. The stochastic contour integral method will be studied from a mathematical point of view, implemented in a numerically efficient way, and demonstrated with relevant application examples. To take into account stochastic boundary conditions and input parameters, the polynomial chaos expansion (PCE) known from other application areas will for the first time be applied in the context of a contour integral method for electrodynamics. For this purpose, a partially existing Fortran code will be extended by methods that can take into account statistical variations in the excitation as well as in the geometry and material parameters of the structure under investigation. On the one hand, a mathematical analysis of the stochastic contour integral methodology will be carried out, including demonstrations of the methodology with help of suitable examples and investigations with regard to the limitations of the numerical treatment. On the other hand, the methodology and the existing numerical code will be extended specifically for stochastic problems in the areas of microwave engineering and integrated planar optics. The potential of the methodology will be demonstrated by applying the extended code to structures that are relevant from an engineering point of view. By virtue of the cooperation between the Institute of Electromagnetic Theory and the Institute of Mathematics of the Hamburg University of Technology (TUHH) the project will facilitate fundamental research in mathematics and numerics in the context of a relevant and challenging application area in engineering.

**Funding:** German Research Foundation (DFG)

**Contact:** Ph. D. David Dahl