Evolution of Probability Distribution in Time for Solutions of Hyperbolic Equations
Journal of Scientific Computing
Numerical analysis of the Burgers' equation in the presence of uncertainty
Journal of Computational Physics
Wave scattering by randomly shaped objects
Applied Numerical Mathematics
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We discuss computationally efficient ways of accounting for the impact of uncertainty, e.g., lack of detailed knowledge about sources, materials, shapes, etc., in computational time-domain electromagnetics. In contrast to classic statistical Monte Carlo--based methods, we explore a probabilistic approach based on high-order accurate expansions of general stochastic processes. We show this to be highly efficient and accurate on both one- and two-dimensional examples, enabling the computation of global sensitivities of measures of interest, e.g., radar-cross-sections (RCS) in scattering applications, for a variety of types of uncertainties.