Fourier-based numerical approximation of the Weertman equation for moving dislocations

Abstract : This work discusses the numerical approximation of a nonlinear reaction-advection-diffusion equation, which is a dimensionless form of the Weertman equation. This equation models steadily-moving dislocations in materials science. It reduces to the celebrated Peierls-Nabarro equation when its advection term is set to zero. The approach rests on considering a time-dependent formulation, which admits the equation under study as its long-time limit. Introducing a Preconditioned Collocation Scheme based on Fourier transforms, the iterative numerical method presented solves the time-dependent problem, delivering at convergence the desired numerical solution to the Weertman equation. Although it rests on an explicit time-evolution scheme, the method allows for large time steps, and captures the solution in a robust manner. Numerical results illustrate the efficiency of the approach for several types of nonlinearities.
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Pré-publication, Document de travail
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Contributeur : Marc Josien <>
Soumis le : mercredi 19 avril 2017 - 10:39:40
Dernière modification le : jeudi 15 juin 2017 - 09:09:19


  • HAL Id : hal-01510158, version 1
  • ARXIV : 1704.04489



Marc Josien, Yves-Patrick Pellegrini, Frédéric Legoll, Claude Le Bris. Fourier-based numerical approximation of the Weertman equation for moving dislocations. 2017. <hal-01510158>



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