Assessing the Performance of Leja and Clenshaw-Curtis Collocation for Computational Electromagnetics with Random Input Data

TL;DR

This paper compares Leja and Clenshaw-Curtis collocation methods for uncertainty quantification in electromagnetic simulations with high-dimensional random inputs, evaluating their accuracy and efficiency.

Contribution

It provides a comprehensive comparison of Leja and Clenshaw-Curtis rules for stochastic collocation in electromagnetic problems with high-dimensional uncertainties.

Findings

Leja and Clenshaw-Curtis rules perform differently depending on input distribution.

Numerical experiments show the effectiveness of both methods in high-dimensional settings.

Application to real-world data demonstrates practical utility.

Abstract

We consider the problem of quantifying uncertainty regarding the output of an electromagnetic field problem in the presence of a large number of uncertain input parameters. In order to reduce the growth in complexity with the number of dimensions, we employ a dimension-adaptive stochastic collocation method based on nested univariate nodes. We examine the accuracy and performance of collocation schemes based on Clenshaw-Curtis and Leja rules, for the cases of uniform and bounded, non-uniform random inputs, respectively. Based on numerical experiments with an academic electromagnetic field model, we compare the two rules in both the univariate and multivariate case and for both quadrature and interpolation purposes. Results for a real-world electromagnetic field application featuring high-dimensional input uncertainty are also presented.