J. Helsing, FAST AND ACCURATE CALCULATIONS OF STRUCTURAL PARAMETERS FOR SUSPENSIONS, Proceedings - Royal Society. Mathematical and physical sciences, 445(1923), 1994, pp. 127-140
The calculation of effective properties of periodic suspensions is oft
en problematic. Particularly difficult are calculations involving unit
cells with many, close to touching, inclusions and high desired accur
acy. In this paper we apply the conjugate gradient method and the fast
multipole method to simplify calculations of this kind. We show how t
o dramatically speed up the computation of the effective conductivitie
s and structural parameters for suspensions of disks and spheres. This
enables accurate treatment of unit cells with thousands of inclusions
. Direct estimates of the effective conductivity are compared with est
imates via bounds. Accuracy of twelve digits is obtained for a suspens
ion of disks which has been studied previously, but for which no accur
ate digit has been determined.