Uncertainty Quantification of Waveguide Dispersion Using Sparse Grid Stochastic Testing

To quantify waveguide dispersion uncertainty, we propose a stochastic analysis technique based on the polynomial chaos method, where Smolyak sparse grids are used as sample spaces for the recently developed nonintrusive stochastic testing (ST) technique. This strategy allows for a smaller set of candidate collocation nodes in the ST algorithm compared with the computationally expensive tensor grid approach. The method is tailored to the analysis of waveguide structures with a statistically spatially varying dielectric-property profile, which is then captured by a discrete set of uncorrelated random variables by means of Karhunen–Loeve transforms. In this way, the propagation properties of realistic stochastic waveguides can be predicted, which is of major importance in the electronic design process. The presented method, which is constructed around a second-order full-wave deterministic finite element solver, is illustrated through the uncertainty quantification of two waveguide dispersion problems and is validated using commercial electromagnetic field solvers and the Monte Carlo method.