Periodic smoothing splines for FFT-based solvers

Léo Morin (1) , Renald Brenner (2) , Katell Derrien (1) , Khaoula Dorhmi (1)

1 PIMM - Laboratoire Procédés et Ingénierie en Mécanique et Matériaux
2 DALEMBERT - Institut Jean Le Rond d'Alembert

The aim of this paper is to develop a periodic smoother based on splines for FFT-based solvers. Spurious oscillations in FFT-based methods are shown to be due to pseudo-spectral differentiation of discontinuous fields. An automatic smoother based on polynomial splines is developed, which permits to add smoothness to initial material properties. The method, which is applied in various problems including conductivity, elasticity and field dislocation mechanics, improves significantly the local fields and reduces spurious oscillations.

Mots clés: Fourier transforms; Smoothing splines; Spurious oscillations; Local fields

Domaines: Mécanique des solides [physics.class-ph]

Léo Morin, Renald Brenner, Katell Derrien, Khaoula Dorhmi. Periodic smoothing splines for FFT-based solvers. Computer Methods in Applied Mechanics and Engineering, 2021, 373, pp.113549. ⟨10.1016/j.cma.2020.113549⟩. ⟨hal-03025665⟩