Carlos Jerez-Hanckes - Pontificia Universidad Catolica de Chile


‘Multiple traces formulation: a marriage between domain decomposition and boundary element methods’

For the past few years, a novel kind of boundary integral formulations dubbed Multiple Traces Formulations (MTFs) have appeared aiming to tackle wave scattering by heterogenous objects. Broadly speaking, these formulations are characterized by regarding solution traces over each subdomain as independent unknowns and imposing adequate transmission weakly. Such an approach is reminiscent to the more established Domain Decomposition methods (DDMs) but portraying several novelties, in particular, considerable improvements over current DDM for wave propagation problems. Specifically, under general conditions, MTFs can be shown to be well posed, robust, parallelizable and either well conditioned or easy to precondition with Krylov methods converging quickly. In this talk, we will explain the construction of MTFs, their intrinsic properties and discuss several numerical implementations under high-performance computing environments along with some applications and future work.

Short biography:

Prof. Jerez-Hanckes is currently head of theMathematical and Computational Engineering program and associate professor at the School of Engineering of the Pontificia Universidad Cat´olica de Chile (PUC Chile). At this institution, he received B.Sc. (2002) and M.Sc. (2005) degrees in Electrical and Industrial engineering with honors. In 2005, he moved to France to pursue a Master degree in Applied Mathematics from ´Ecole Poly- technique in a joint program with Universit´e Paris VI and other grandes ´ecoles. Under the supervision of Jean-Claude N´ed´elec, Jerez-Hanckes obtained his doctoral degree with honors in Applied Mathematics in 2008, funded by an industry-government scholarship with Epcos A.G., modelling piezoelectric and electromagnetic wave propagation over layered media for next generation mobile devices. Between 2008–2011, he was awarded an ETH Zurich postdoctoral fellowship to carry out research, together with Prof. Ralf Hiptmair at the Seminar for Applied Mathematics, on novel boundary integral formulations. This was motivated by modeling of active phased-array radar systems developed by Thales. In 2011, Jerez-Hanckes moved back to PUC Chile where he has been leading the recent Mathematical and Computational Engineering program. His current research interests include: boundary integral equations; domain decomposition methods; uncertainty quantification; fast computational methods for acoustic and electromagnetic waves in complex media; quasi-periodic structures; with applications ranging from the design of radio-astronomy instrumentation, thermo-photovoltaic cells andbiomedical devices.