Effective properties of two-dimensional dispersed composites. Part I. Schwarz's alternating method

Abstract

The generalized alternating method of Schwarz can be presented as an infinite sequence of all the mutual interactions between inclusions in the boundary value problem stated for a composite. Schwarz's method for overlapping domains has been assigned to decomposition methods widely used in pure numerical computations. In the same time, the generalized alternating method for non-overlapping inclusions is convenient in symbolic-numerical computations described in this paper. Implementation of the explicit and implicit schemes yields new approximate analytical formulas for the effective properties of dispersed composites. Moreover, the exactly derived precision of their validity in concentration and in contrast parameter is established. The first order iteration corresponds to the famous Maxwell's self-consistent approach.