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

Abstract

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:

Chen, C.  ^[1];

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Aubry, S. ^[2]; Oppelstrup, T. ^[2]; Arsenlis, A. ^[2]; Darve, E. ^[1]

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+ Show Author Affiliations

1. Stanford Univ., CA (United States)
2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Publication Date:

Mon Mar 19 00:00:00 EDT 2018

Research Org.:

Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Org.:

USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:

1458681

Report Number(s):

LLNL-JRNL-742868
Journal ID: ISSN 0965-0393; 897727

Grant/Contract Number:  

AC52-07NA27344; NA0002373-1

Resource 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

Country of Publication:

United States

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING; Dislocation dynamics; anisotropic elasticity; fast multipole method