  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.
