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A new Fourier-based pseudo-spectral framework for numerical PDE analysis in problems concerning solids, fluids & their interactions: predictions & insights into the underlying physics
Résumé
This talk discusses efforts to study a variety of time-dependent phenomena in realistic physics and engineering applications through the development of a novel high-order methodology for the numerical analysis of hyperbolic/parabolic partial differential equations (PDEs) that govern both linear and nonlinear behavior. Such a framework is based on a Fourier continuation approach for the accurate trigonometric interpolation of a non-periodic function (while avoiding the well-known Gibb's ringing effect), where the ultimate goal is to build high-performance solvers that provide fast, stable and physically-faithful resolution of the underlying mechanical dynamics. With an eye towards mutual validation of both simulation and experiment, the efficacy of these tools will be demonstrated through some of the collaborative scientific problems that have inspired them, including those in materials science (ultrasonic non-destructive testing), cardiovascular medicine (pulsatile blood flow) and geophysics (seismogenic tsunamis).
Short biography
Faisal Amlani is a newly arrived CNRS Chargé de Recherche at the Laboratoire de Mécanique Paris-Saclay (LMPS). He received his BA from Rice University in Texas and his PhD from the California Institute of Technology (Caltech), both in applied mathematics. After some years working as an experimentalist and engineer at an R&D aerospace startup in Los Angeles, he returned to academia by way of Paris through postdocs at INRIA Paris and POEMS (ENSTA Paris), followed by Research Scholar and Research Associate appointments at the University of Southern California. His interests lie at the intersection of applied mathematics and computational mechanics: focused on both the development of mathematical/computational methodologies as well as their subsequent deployment in physics-based/data-driven problems in science and engineering.