TY - JOUR
T1 - An Improved Integration Scheme for Mode-Coupling-Theory Equations
AU - Caraglio , Michele
AU - Schrack , Lukas
AU - Jung , Gerhard
AU - Franosch , Thomas
JO - Communications in Computational Physics
VL - 2
SP - 628
EP - 648
PY - 2020
DA - 2020/12
SN - 29
DO - http://doi.org/10.4208/cicp.OA-2020-0125
UR - https://global-sci.org/intro/article_detail/cicp/18479.html
KW - Glass transition, mode coupling theory
AB - <p style="text-align: justify;">Within the mode-coupling theory (MCT) of the glass transition, we reconsider the numerical schemes to evaluate the MCT functional. Here we propose nonuniform discretizations of the wave number, in contrast to the standard equidistant grid,
in order to decrease the number of grid points without losing accuracy. We discuss in
detail how the integration scheme on the new grids has to be modified from standard
Riemann integration. We benchmark our approach by solving the MCT equations numerically for mono-disperse hard disks and hard spheres and by computing the critical
packing fraction and the nonergodicity parameters. Our results show that significant
improvements in performance can be obtained employing a nonuniform grid.</p>