New trends in uncertainty quantification for large-scale electromagnetic analysis: From tensor product cubature rules to spectral quantic tensor-train approximation

In this chapter, efficient collocation methods for EM analysis are reviewed. Traditional SC methods leveraging tensor-product, sparse grid, and Stroud cubature rules are described first. These methods are rather straightforward to implement and suitable for EM problems involving smoothly varying QoI. Then, the ME-PC method for efficiently constructing a surrogate model of a rapidly varying QoI is presented. Also detailed is the iterative HDMR technique for EM problems involving large numbers of random variables. Finally, an approximation technique based on the spectral quantic TT (QTT) (SQTT) for constructing a surrogate model in a high-dimensional random domain is briefly reviewed, before the chapter is concluded by numerical examples demonstrating applications of cutting-edge UQ methods to various EM problems.