Dislocation transport using an explicit Galerkin-Least Squares formulation

Abstract : An explicit Galerkin/least squares formulation is introduced for a quasilinear transport equation in Field Dislocation Mechanics (FDM) and applied to the study of the kinematics of dislocation density evolution in the following physical contexts: annihilation of dislocations, expansion of a dislocation loop, simulation of Frank-Read sources. This conditionnaly stable method leads to a symmetric well-conditioned system of equations with constant coefficients, making it attractive for large-scale problems. The weak solutions to these equations are not unique, and the method is able to capture shock formation as well as rarefraction waves by appropriate algorithmic modifications.
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https://hal.archives-ouvertes.fr/hal-00119274
Contributor : Claude Fressengeas <>
Submitted on : Monday, December 11, 2006 - 8:38:28 AM
Last modification on : Thursday, August 1, 2019 - 2:12:06 PM

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  • HAL Id : hal-00119274, version 1

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S. Varadhan, A. Beaudoin, A. Acharya, C. Fressengeas. Dislocation transport using an explicit Galerkin-Least Squares formulation. Modelling Simul. Mater. Sci. Eng., 2006, 14, pp.1245-1270. ⟨hal-00119274⟩

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