Efficient time integration in dislocation dynamics

Ryan B. Sills, Wei Cai

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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.

Original languageEnglish (US)
Article number025003
JournalModelling and Simulation in Materials Science and Engineering
Issue number2
StatePublished - Mar 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Computer Science Applications


  • dislocation dynamics
  • implicit method
  • subcycling
  • time integrator


Dive into the research topics of 'Efficient time integration in dislocation dynamics'. Together they form a unique fingerprint.

Cite this