Séminaire

Titre : Carlos Jerez Hanckes (Faculty of Engineering and Sciences, Universidad Adolfo Ibañez) - Bi-parametric (Fast) Operator Preconditioning and Applications to Wave Scattering Problems.
Contact : Sarah Al Humaikani
Date : 14/11/2024
Lieu : Amphi 2329, ENSTA Paris
Résumé de C. Jerez Hanckes: We extend the operator preconditioning framework (Hiptmair, 2006) to Petrov-Galerkin methods while accounting for parameter-dependent perturbations of both variational forms and their preconditioners, as occurs when performing numerical approximations. By considering different perturbation parameters for the original form and its preconditioner, our bi-parametric abstract setting leads to robust and controlled schemes. For Hilbert spaces, we derive exhaustive linear and super-linear convergence estimates for iterative solvers, such as $h$-independent convergence bounds, when preconditioning with low-accuracy or, equivalently, with highly compressed approximations. Moreover, we present multiple numerical results in the context of boundary integral equations. In particular, we show highly efficient preconditioners for the electrical field integral equation as well as for the Maxwell transmission problem with almost 99% matrix compression, largely outperforming standard Calderón-type versions.