O(N) ALGORITHM FOR DISLOCATION DYNAMICS

We present an extension of the fast-multipole method of Greengard and Rokhlin to the case of the long-range interactions between parallel ed ge (in arbitrary orientations) and screw dislocations. By finding comp lex potentials from which the stress terms can be calculated, and expa nding those potentials in multipole series, we convert a computational ly difficult O(N2) poroblem into a much faster O(N) approach. To reach sufficient numerical accuracy, only a few terms are needed in the mul tipole expansions (four screws and six for edges) so that the interact ions between millions of dislocations can be calculated in a few minut es on a workstation. We present results of a study of the relaxed conf igurations of 16384 edge dislocations of arbitrary orientations.