Efficiency of pseudo-spectral algorithms with Anderson mixing for the SCFT of periodic block-copolymer phases
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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.
- 2.G.H. Fredrickson, The Equilibrium Theory of Inhomogeneous Polymers (Oxford University Press, New York, 2006)Google Scholar
- 3.M.W. Matsen, in Soft Matter, Vol. 1: Polymer Melts and Mixtures, edited by G. Gompper, M. Schick (Wiley-VCH, Weinheim, 2006)Google Scholar
- 20.Simple mixing equates to Anderson mixing without any histories (i.e., $n_r=0$), which requires the mixing parameter to be relatively small (e.g., $\lambda \approx 0.1$)Google Scholar
- 21.M. Frigo, S.G. Johnson, The Design and Implementation of FFTW3, Proc. IEEE 93, 216 (2005). The FFT subroutine, version 3.2.2, was obtained from www.fftw.org
- 24.E.W. Cochran, private communicationGoogle Scholar