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Title: Fast algorithms for evaluating the stress field of dislocation lines in anisotropic elastic media

In dislocation dynamics (DD) simulations, the most computationally intensive step is the evaluation of the elastic interaction forces among dislocation ensembles. Because the pair-wise interaction between dislocations is long-range, this force calculation step can be significantly accelerated by the fast multipole method (FMM). In this study, we implemented and compared four different methods in isotropic and anisotropic elastic media: one based on the Taylor series expansion (Taylor FMM), one based on the spherical harmonics expansion (Spherical FMM), one kernel-independent method based on the Chebyshev interpolation (Chebyshev FMM), and a new kernel-independent method that we call the Lagrange FMM. The Taylor FMM is an existing method, used in ParaDiS, one of the most popular DD simulation softwares. The Spherical FMM employs a more compact multipole representation than the Taylor FMM does and is thus more efficient. However, both the Taylor FMM and the Spherical FMM are difficult to derive in anisotropic elastic media because the interaction force is complex and has no closed analytical formula. The Chebyshev FMM requires only being able to evaluate the interaction between dislocations and thus can be applied easily in anisotropic elastic media. But it has a relatively large memory footprint, which limits its usage. Themore » Lagrange FMM was designed to be a memory-efficient black-box method. Lastly, various numerical experiments are presented to demonstrate the convergence and the scalability of the four methods.« less
Authors:
ORCiD logo [1] ;  [2] ;  [2] ;  [2] ;  [1]
  1. Stanford Univ., CA (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Report Number(s):
LLNL-JRNL-742868
Journal ID: ISSN 0965-0393; 897727
Grant/Contract Number:
AC52-07NA27344; NA0002373-1
Type:
Accepted Manuscript
Journal Name:
Modelling and Simulation in Materials Science and Engineering
Additional Journal Information:
Journal Volume: 26; Journal Issue: 4; Journal ID: ISSN 0965-0393
Publisher:
IOP Publishing
Research Org:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Dislocation dynamics; anisotropic elasticity; fast multipole method
OSTI Identifier:
1458681

Chen, C., Aubry, S., Oppelstrup, T., Arsenlis, A., and Darve, E.. Fast algorithms for evaluating the stress field of dislocation lines in anisotropic elastic media. United States: N. p., Web. doi:10.1088/1361-651X/aab7bb.
Chen, C., Aubry, S., Oppelstrup, T., Arsenlis, A., & Darve, E.. Fast algorithms for evaluating the stress field of dislocation lines in anisotropic elastic media. United States. doi:10.1088/1361-651X/aab7bb.
Chen, C., Aubry, S., Oppelstrup, T., Arsenlis, A., and Darve, E.. 2018. "Fast algorithms for evaluating the stress field of dislocation lines in anisotropic elastic media". United States. doi:10.1088/1361-651X/aab7bb.
@article{osti_1458681,
title = {Fast algorithms for evaluating the stress field of dislocation lines in anisotropic elastic media},
author = {Chen, C. and Aubry, S. and Oppelstrup, T. and Arsenlis, A. and Darve, E.},
abstractNote = {In dislocation dynamics (DD) simulations, the most computationally intensive step is the evaluation of the elastic interaction forces among dislocation ensembles. Because the pair-wise interaction between dislocations is long-range, this force calculation step can be significantly accelerated by the fast multipole method (FMM). In this study, we implemented and compared four different methods in isotropic and anisotropic elastic media: one based on the Taylor series expansion (Taylor FMM), one based on the spherical harmonics expansion (Spherical FMM), one kernel-independent method based on the Chebyshev interpolation (Chebyshev FMM), and a new kernel-independent method that we call the Lagrange FMM. The Taylor FMM is an existing method, used in ParaDiS, one of the most popular DD simulation softwares. The Spherical FMM employs a more compact multipole representation than the Taylor FMM does and is thus more efficient. However, both the Taylor FMM and the Spherical FMM are difficult to derive in anisotropic elastic media because the interaction force is complex and has no closed analytical formula. The Chebyshev FMM requires only being able to evaluate the interaction between dislocations and thus can be applied easily in anisotropic elastic media. But it has a relatively large memory footprint, which limits its usage. The Lagrange FMM was designed to be a memory-efficient black-box method. Lastly, various numerical experiments are presented to demonstrate the convergence and the scalability of the four methods.},
doi = {10.1088/1361-651X/aab7bb},
journal = {Modelling and Simulation in Materials Science and Engineering},
number = 4,
volume = 26,
place = {United States},
year = {2018},
month = {3}
}