FAST AND ACCURATE CALCULATIONS OF STRUCTURAL PARAMETERS FOR SUSPENSIONS

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.