A New Version Fast Multipole Method for Evaluating the Stress Field of Dislocation Ensembles

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