An efficient high order method for dislocation climb in two dimensions

Shidong Jiang, Manas Rachh, Yang Xiang

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

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 resulting linear system and demonstrate via numerical examples that fast direct solvers (FDSs) perform best for dislocation arrays, while the fast multipole method (FMM) accelerated iterative solver on the low accuracy FDS preconditioned system performs well for the general setting.

Original languageEnglish (US)
Pages (from-to)235-253
Number of pages19
JournalMultiscale Modeling and Simulation
Volume15
Issue number1
DOIs
StatePublished - 2017

All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Modeling and Simulation
  • Ecological Modeling
  • Physics and Astronomy(all)
  • Computer Science Applications

Keywords

  • Dislocation climb
  • Dislocation dynamics
  • Fast direct solver
  • Fast multipole method
  • Second kind integral equation

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