High-order explicit PDE solvers using trigonometric interpolations of non-periodic functions: applications to engineering, geophysics and medicine

Abstract : This talk discusses efforts to study a variety of time-dependent diffusion and wave propagation phenomena via the development of a Fourier series-based methodology for the numerical analysis of parabolic/hyperbolic partial differential equations (PDEs) with complex boundary conditions. Such a framework is based on a discrete "extension" approach for the high-order trigonometric interpolation of a non-periodic function (i.e., mitigating the notorious Gibb’s “ringing” effect), where the ultimate goal is to build high-performance, FFT-speed, dynamic PDE solvers on general geometries that can provide stable and efficient resolution while faithfully preserving the dispersion/diffusion characteristics of the underlying continuous operators. With an eye towards mutual validation of both simulation and experiment, the efficacy of the current state of these tools is demonstrated through some of the collaborative scientific problems that have inspired them, including those in engineering (ultrasonic non-destructive testing), geophysics (seismogenic tsunamis), and medicine (fluid-structure hemodynamics).

Le 17 octobre 2023 de 11h00 à 12h00 / Amphithéâtre François Canac, LMA

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