Eur. Phys. J. E (2011) 34: 110
https://doi.org/10.1140/epje/i2011-11110-0

Regular Article

Efficiency of pseudo-spectral algorithms with Anderson mixing for the SCFT of periodic block-copolymer phases

School of Mathematical and Physical Sciences, University of Reading, RG6 6AX, Whiteknights, Reading, UK

^* e-mail: p.stasiak@reading.ac.uk
^** e-mail: m.w.matsen@reading.ac.uk

Received: 23 June 2011
Revised: 18 August 2011
Accepted: 30 August 2011
Published online: 11 October 2011

Abstract

This study examines the numerical accuracy, computational cost, and memory requirements of self-consistent field theory (SCFT) calculations when the diffusion equations are solved with various pseudo-spectral methods and the mean-field equations are iterated with Anderson mixing. The different methods are tested on the triply periodic gyroid and spherical phases of a diblock-copolymer melt over a range of intermediate segregations. Anderson mixing is found to be somewhat less effective than when combined with the full-spectral method, but it nevertheless functions admirably well provided that a large number of histories is used. Of the different pseudo-spectral algorithms, the 4th-order one of Ranjan, Qin and Morse performs best, although not quite as efficiently as the full-spectral method.