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 methods are shown be due pseudo-spectral differentiation discontinuous fields. An automatic polynomial developed, which permits add smoothness initial material properties. method, applied various problems including conductivity, elasticity and field dislocation mechanics, improves significantly the local fields reduces spurious oscillations.