We consider parallel computational algorithms for the boundary integral solutions of the Laplace equation for use in the simulation of electrorheological fluids and as a model study of a class of elliptic partial differential equations that appear in basic microscopic descriptions of heterogeneous structured continua. The viewpoint is that of constructing large scale simulations that bridge micro- and macro-length and time scales on state-of-the-art parallel supercomputers. Because of long range interactions, fast communications are the key to scalable N-Body algorithms. The communication scheduling strategies of Fuentes and Kim are examined in two contexts on the Thinking Machines CM-5 parallel computer. First, an N-Body simulation implementation in C using the standard send-receive message passing primitives in the CMMD 2.0 library shows that communication scheduling leads to dramatic improvements in computational performance. Second, an implementation in Split-C, which uses highly efficient active messages to implement shared memory communication, reduces communication overhead by an order of magnitude. Taken together, these two developments portend great promise for the development of efficient large scale simulations using portable, high level parallel programming languages.