Elastostatic computations on aggregates of grains with sharp interfaces, corners, and triple-junctions

We present a fast algorithm for the calculation of elastostatic fields in two-dimensional assemblies of elastic grains, separated by sharp grain boundaries. The algorithm uses an integral equation approach, combined with the fast multipole method and recursive compression to resolve stress concentrations also very close to grain boundary junctions. Singular basis functions on analytic form are not required. Accurate results can be obtained at a cost roughly proportional to the number of grains in the assembly. Large-scale problems, with thousands of grains, are solved using modest computational resources.