Comparison of Pseudo-Spectral Algorithms for Field-Theoretic Simulations of Polymers

We compare three pseudo-spectral algorithms for mean-field polymer self-consistent field theory (SCFT) simulations and beyond mean-field field-theoretic simulations (FTS) using the complex Langevin (CL) sampling technique. In agreement with a study by Stasiak and Matsen, we find that for SCFT the fourth-order algorithm developed by Ranjan, Qin and Morse usually outperforms the other pseudo-spectral algorithms. In contrast, for CL simulations we find that the second-order algorithm adapted to SCFT by Rasmussen and coworkers often outperforms the fourth-order methods not only in computational speed but also, surprisingly, in accuracy at a fixed contour resolution. This suggests an intricate coupling between pseudo-spectral ∗To whom correspondence should be addressed †Materials Research Laboratory, University of California, Santa Barbara, CA, 93106 ‡Department of Chemical Engineering, University of California, Santa Barbara, CA, 93106 ¶Department of Mathematics, University of California, Santa Barbara, CA, 93106 §Department of Materials, University of California, Santa Barbara, CA, 93106