Order-N method for force calculation in many-dislocation systems

D. B. Barts, A. E. Carlsson

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


We propose a methodology for calculating the elastic interaction forces of a large (N106 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 N2 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.

Original languageEnglish
Pages (from-to)3195-3204
Number of pages10
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number3
StatePublished - 1995


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