Efficient time integration in dislocation dynamics

The efficiencies of one implicit and three explicit time integrators have been compared in line dislocation dynamics simulations using two test cases: a collapsing loop and a Frank-Read (FR) source with a jog. The time-step size and computational efficiency of the explicit integrators is shown to become severely limited due to the presence of so-called stiff modes, which include the oscillatory zig-zag motion of discretization nodes and orientation fluctuations of the jog. In the stability-limited regime dictated by these stiff modes, the implicit integrator shows superior efficiency when using a Jacobian that only accounts for short-range interactions due to elasticity and line tension. However, when a stable dislocation dipole forms during a jogged FR source simulation, even the implicit integrator suffers a substantial drop in the time-step size. To restore computational efficiency, a time-step subcycling algorithm is tested, in which the nodes involved in the dipole are integrated over multiple smaller, local time steps, while the remaining nodes take a single larger, global time step. The time-step subcycling method leads to substantial efficiency gain when combined with either an implicit or an explicit integrator.