Domain uncertainty quantification in computational electromagnetics

In this talk, we will focus on solving time‑harmonic electromagnetic (EM) wave scattering problems when the domains are not fully known but can be modeled as random perturbations departing from a nominal shape. Specifically, we will consider two novel approaches depending on the relative size of these perturbations. For small ones, we will employ sparse tensor approximations of deterministic statistical moments, whereas for larger perturbations, we will use the framework of affine‑parametric shape parametrizations. Along the way, we will encounter and combine many mathematical tools, some new and some old, ranging from (i) shape derivatives and Hadamard’s structure theorem; (ii) integral representation formulas and boundary integral equations; (iii) sparse tensor equations; (iv) operator preconditioning; to (v) infinite‑parameter holomorphy; (vi) edge or Nédélec finite‑elements and new Strang‑type lemmas, (vii) domain‑to‑solutions maps, (viii) multilevel Monte Carlo methods, and (ix) multilevel sparse‑grid quadrature. Fortunately, several numerical experiments will help us understand the problems at hand and confirm our error convergence and complexity bounds. Moreover, these results will show that one can beat, to a certain extent, the curse of dimensionality. Also, they pose new questions you may have the answer to!

Carlos Jerez-Hanckes is currently an Associate Researcher at Inria Chile, following a year at the University of Bath as the David Parkin Visiting Professor. He completed his PhD at École Polytechnique (France) and held a postdoctoral fellowship at ETH Zurich, followed by visiting positions there and at TU Delft, Chalmers, KTH and Notre Dame, with invited lectures at the University of Cambridge, Imperial College, and many other leading institutions worldwide. He is also a former Erasmus Mundus Visiting Scholar.

Carlos is internationally recognized for his contributions to computational wave propagation, uncertainty quantification, and boundary integral methods, including the development of the Multiple Trace Formulation, as well as advances in operator preconditioning and spectral methods. His research spans applications in electromagnetics, photonics, energy and water harvesting, astronomy, and biomedical modeling.

Beyond research, he served as Dean of Engineering and Sciences at Universidad Adolfo Ibáñez, Executive Director of the Institute for Mathematical & Computational Engineering (IMC) at Pontificia Universidad Católica de Chile, and founding Executive Director of Chile’s national Data Observatory. He is a member of the Executive Committee of the International Association for Boundary Element Methods (IABEM).