Convergence to Equilibrium of a DC Algorithm for an Epitaxial Growth Model

 Convergence to Equilibrium of a DC Algorithm for an Epitaxial Growth Model

Year:    2019

Author:    Hamza Khalfi, Morgan Pierre, Nour Eddine Alaa, Mohammed Guedda

International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 3 : pp. 398–411

Abstract

A linear numerical scheme for an epitaxial growth model is analyzed in this work. The considered scheme is already established in the literature using a convexity splitting argument. We show that it can be naturally derived from an optimization viewpoint using a DC (difference of convex functions) programming framework. Moreover, we prove the convergence of the scheme towards equilibrium by means of the Lojasiewicz-Simon inequality. The fully discrete version, based on a Fourier collocation method, is also analyzed. Finally, numerical simulations are carried out to accommodate our analysis.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2019-IJNAM-12875

International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 3 : pp. 398–411

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    Thin film epitaxy DC programming coarsening dynamics Lojasiewicz-Simon inequality epitaxial growth model without slope selection Fourier spectral method convergence to equilibrium pattern formation.

Author Details

Hamza Khalfi

Morgan Pierre

Nour Eddine Alaa

Mohammed Guedda