Periodic smoothing splines for FFT-based solvers

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. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This paper develops a periodic smoother based on splines for FFT-based solvers, addressing spurious oscillations caused by pseudo-spectral differentiation of discontinuous fields. The automatic smoother improves local fields significantly and reduces spurious oscillations in various problems including conductivity, elasticity, and field dislocation mechanics.