A methodology was proposed for calculating the elastic interaction forces, of a large (106 or more) number of dislocations in a solid, for the purposes of molecular dynamics modelling of problems such as dislocation patterning. In order to avoid the N2 scaling which would result from a 1/r decay of the forces, a variation of the Hockney-Eastwood particle-particle-particle-mesh method was introduced. This was applicable to arrangements of straight parallel dislocations, and could be extended to fully 3-dimensional problems. The present method could treat anisotropic inter-dislocation forces with high accuracy, and was easy to use.

D.B.Barts, A.E.Carlsson: Physical Review E, 1995, 52[3], 3195-204