An Efficient High Order Method for Dislocation Climb in Two Dimensions
An Efficient High Order Method for Dislocation Climb in Two Dimensions
复制标题
二维位错爬升的高效高阶方法
DOI：
10.1137/16m1081920
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Y. Xiang
中科院分区：
文献类型：
--
作者：
Shidong Jiang;M. Rachh;Y. Xiang
我们提出了一种有效的高阶方法，用于二维空位辅助位错爬行的位错动力学模拟。该方法基于第二类积分方程 (SKIE) 公式，该公式通过位于每个位错处的双层势和点源之和来表示空位浓度，其中每个位错的爬升速度（或每个点源的强度）与每个位错边界上的未知密度的积分成正比。该方法仅离散化接口。与以前使用的公式不同，所提出的方法不需要引入额外的未知数或对具有对数奇异性的核进行积分，并且公式中的边界积分可以通过具有谱精度的梯形规则轻松离散。因此，线性系统中达到一定精度的未知数对于位错动力学中的典型设置来说是最佳的。我们比较了解决问题的三种不同方法...
We present an efficient high order method for dislocation dynamics simulation of vacancy-assisted dislocation climb in two dimensions. The method is based on a second kind integral equation (SKIE) formulation that represents the vacancy concentration via the sum of double layer potentials and point sources located at each dislocation, where the climb velocity of each dislocation (or the strength of each point source) is proportional to the integral of the unknown density on the boundary of each dislocation. The method discretizes the interfaces only. Unlike previously used formulations, the proposed method avoids the need for introducing additional unknowns or integrating kernels with logarithmic singularity, and the boundary integrals in the formulation are easily discretized via the trapezoidal rule with spectral accuracy. Thus, the number of unknowns in the linear system to achieve certain accuracy is optimal for typical settings in dislocation dynamics. We compare three different methods for solving r...