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Bi-Parametric Operator Preconditioning and Extensions

In this talk, Paul Escapil-Inchauspé will present results related to the framework of operator preconditioning for efficient Galerkin schemes, focusing on recent advances in the preconditioning of bi-parametric operators. Paul will showcase the theoretical developments that have enabled the construction of highly compressed preconditioners, particularly in the context of electromagnetic and acoustic scattering problems. These advances have led to provably stable convergence limits for iterative solvers. Additionally, he will explore the natural connection between operator preconditioning and the operator learning paradigm, outlining future directions towards the implementation of data-driven solvers.