Dislocations were the primary carriers of plastic deformation in crystals. Dislocation dynamics simulation was becoming an important tool for the study of plastic behaviours of crystalline materials. A crucial part of dislocation dynamics simulation was the calculation of the stress field of dislocation ensembles due to the long-range interaction of dislocations. Here, a new version of the fast multipole method was used to compute the stress field of dislocation ensembles, in which exponential expansions were introduced to diagonalize the multipole-to-local translations. Numerical experiments showed that, for a dislocation ensemble discretized into N dislocation segments, the new version of the fast multipole method was asymptotically O(N) with an optimized prefactor, and very efficient for prescribed accuracy requirements.

A New Version Fast Multipole Method for Evaluating the Stress Field of Dislocation Ensembles. D.Zhao, J.Huang, X.Yang: Modelling and Simulation in Materials Science and Engineering, 2010, 18[4], 045006