A Nonintrusive POD-PCE Scheme for Uncertainty Quantification of Stochastic EM Problems

Abstract

The quantification of parameter uncertainty is of particular interest to the computational electromagnetic (EM) community resulting in fast and efficient intrusive and nonintrusive stochastic numerical algorithms. Among these, the nonintrusive-based stochastic algorithms are the preferred choice due to their flexibility in combining with the deterministic EM solver, unlike intrusive, requiring in-house EM solver code. This letter proposes a nonintrusive method to quantify the uncertainty that can be used along with the commercial EM solvers. The proposed method utilizes the proper orthogonal decomposition (POD) method to generate the low-dimensional basis of the original problem. The unknown stochastic electric field is obtained as a linear combination of this low-dimensional basis. The unknown coefficients are computed by interpolating over the initial stochastic response using polynomial chaos expansion (PCE). This method requires only <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1\%$</tex-math> </inline-formula> of the total computation time taken by the Monte Carlo (MC) method, and the results are shown to be accurate.