New methods derived from energy minimization problems for solving two dimensional discrete dislocation dynamics

Dislocation dynamic is a typically gradient flow problem, and most of work solves it just as ODE, which means that the interacting energy of dislocations is ignored. We take the interaction energy into account and use it to introduce new methods to speed up the simulation. The non-singular stress field theory is used to make sure that the interacting energy between dislocations is finite and computational, and using this the two dimensional discrete dislocation dynamics can be rewritten into optimal problems. Based on it, the new problems from 2D dislocation dynamics can be solved by conjugate gradient method and other optimal methods. We introduce several methods into dislocation dynamics from the energy point of view and some numerical experiments are presented to compare different numerical methods, which show that the new methods are able to speed up relaxation procedures of dislocation dynamics. Those new approaches help to get the stable states of dislocations more quickly and speed up the simulations of dislocation dynamics.