Recent Fourier continuation-based solvers for time-dependent problems in solids, fluids & their interactions

This contribution overviews a spectral methodology for the numerical solution of partial differential equation systems governing various mechanical wave propagation problems. Based on a Fourier continuation (FC) approach for the accurate trigonometric interpolation of a non-periodic function, such a high-order algorithm produces solutions with essentially no numerical dispersion ; possesses mild CFL constraints scaling only linearly with spatial discretization sizes ; and parallelizes efficiently for high performance. Applications to non-destructive testing, blood dynamics, and geophysics are discussed. Mots clés-(pseudo)spectral methods, wave propagation, fluid-structure interactions, non-destructive testing, hemodynamics, tsunami generation