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Dislocation dynamic is a typically gradient flow problem, and most of worksolves it just as ODE, which means that the interacting energy of dislocationsis ignored. We take the interaction energy into account and use it to introducenew methods to speed up the simulation. The non-singular stress field theory isused to make sure that the interacting energy between dislocations is finiteand computational, and using this the two dimensional discrete dislocationdynamics can be rewritten into optimal problems. Based on it, the new problemsfrom 2D dislocation dynamics can be solved by conjugate gradient method andother optimal methods. We introduce several methods into dislocation dynamicsfrom the energy point of view and some numerical experiments are presented tocompare different numerical methods, which show that the new methods are ableto speed up relaxation procedures of dislocation dynamics. Those new approacheshelp to get the stable states of dislocations more quickly and speed up thesimulations of dislocation dynamics.

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