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Journal articles
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.
Cited literature [37 references]
https://hal.archives-ouvertes.fr/hal-01510158
Contributor : Marc Josien <>
Submitted on : Wednesday, April 19, 2017 - 10:39:40 AM
Last modification on : Wednesday, March 24, 2021 - 1:58:08 PM
Contributor : Marc Josien <>
Submitted on : Wednesday, April 19, 2017 - 10:39:40 AM
Last modification on : Wednesday, March 24, 2021 - 1:58:08 PM