ORDER-N METHOD FOR FORCE CALCULATION IN MANY-DISLOCATION SYSTEMS

We propose a methodology for calculating the elastic interaction force s of a large (N similar to 10(6) or more) number of dislocations in a solid, for the purposes of molecular-dynamics type modeling of problem s such as dislocation patterning and strain hardening. In order to avo id the N-2 scaling resulting from the 1/r decay of the forces, we intr oduce a variation of the particle-particle-particle-mesh method of Hoc kney and Eastwood [Computer Simulations Using Particles (Institute of Physics, Bristol, 1988)], applicable to arrangements of straight, para llel dislocations; extension to fully three-dimensional problems is di scussed. Our version handles the anisotropic interdislocation forces w ith high accuracy and is easy to implement. Precision estimates are ob tained; they indicate a very favorable scaling of CPU time with accura cy, which is supported by numerical results.