论文标题
从能量最小化问题得出的新方法用于解决二维离散位错动力学
New methods derived from energy minimization problems for solving two dimensional discrete dislocation dynamics
论文作者
论文摘要
脱位动态是通常的梯度流问题，大多数工作都像ODE一样解决了，这意味着忽略了位错的相互作用能量。我们将相互作用的能量考虑在内，并使用它引入新方法以加快模拟。非单个应力场理论用于确保位错之间的相互作用能量是有限的和计算的，并且使用它可以将二维离散脱位动力学重写为最佳问题。基于它，可以通过共轭梯度方法和其他最佳方法来解决2D位错动力学的新问题。我们从能量的角度将几种方法引入了脱位动力学，并提出了一些数值实验来比较不同的数值方法，这些方法表明新方法能够加快脱位动力学的放松过程。这些新方法有助于更快地使稳定的位错状态加快脱位动力学的模拟。
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.
