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

We propose a methodology for calculating the elastic interaction forces 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 problems such as dislocation patterning and strain hardening. In order to avoid the N-2 scaling resulting from the 1/r decay of the forces, we introduce a variation of the particle-particle-particle-mesh method of Hockney and Eastwood [Computer Simulations Using Particles (Institute of Physics, Bristol, 1988)], applicable to arrangements of straight, parallel dislocations; extension to fully three-dimensional problems is discussed. Our version handles the anisotropic interdislocation forces with high accuracy and is easy to implement. Precision estimates are obtained; they indicate a very favorable scaling of CPU time with accuracy, which is supported by numerical results.