A fast, high-order, parallel numerical methodology for hyperbolic PDEs : applications to elastodynamics problems in ultrasonic non-destructive testing and seismic wave propagation

This contribution presents developments of a Fourier series-based methodology for the numerical analysis of time-dependent 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 highperformance, FFT-speed, dynamic PDE solvers on general (structured, curvilinear) geometries that can provide stable and efficient resolution while faithfully preserving the dispersion/diffusion characteristics of the underlying continuous operators.