It was demonstrated that an elementary 3-dimensional dislocation segment was mathematically equivalent to 10 electrostatic charges, and that the elastic interactions between such segments could therefore be computed within O(N) operations via 10-fold applications of the fast multipole method. The technique could be combined with other fast summation methods. In the 2-dimensional case, the number of required charges could be reduced to 5. It was also noted that the technique could be easily generalized so as to compute interaction forces.

Towards Rapid Evaluation of the Elastic Interactions among Three-Dimensional Dislocations. G.J.Rodin: Philosophical Magazine Letters, 1998, 77[4], 187-90