Reducing the Computational Expense of Uncertainty Quantification in Computational Electromagnetics: A Goal-Oriented Perspective

We summarize several challenges in uncertainty quantification involving simulations of electromagnetic scattering. While the finite element method (FEM) provides an excellent means of producing approximate solutions to partial differential equations (PDEs), the computational expense mandated by full model solves complicates the application of the standard Monte Carlo method, which converges slowly, albeit independently of the dimension of the parameter space (i.e., the number of uncertain variables). As a result, alternative techniques must be employed to quantify uncertain without incurring inordinate computational costs, both in time and computing power. We summarize one such approach based on the higher order parameter sampling (HOPS) method, which constructs a deterministic response that may be applied for accelerating uncertainty quantification, with the underlying goal-oriented framework supported by applications in error estimation and adaptive refinement that may precede objectives in uncertainty quantification.