CONVERGENCE TO EQUILIBRIUM OF A DC ALGORITHM FOR AN EPITAXIAL GROWTH MODEL

Hamza Khalfi; Morgan Pierre; Nour Eddine Alaa; Mohammed Guedda

Article dans une revue

CONVERGENCE TO EQUILIBRIUM OF A DC ALGORITHM FOR AN EPITAXIAL GROWTH MODEL

Hamza Khalfi Morgan Pierre ¹ Nour Eddine Alaa ² Mohammed Guedda ³

1 LMA-Poitiers - Laboratoire de Mathématiques et Applications

2 CALVI - Scientific computation and visualization

IRMA - Institut de Recherche Mathématique Avancée, LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine

3 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

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 analyzis.

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Article dans une revue

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Mathématiques [math]

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https://hal-u-picardie.archives-ouvertes.fr/hal-03621261
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Soumis le : lundi 28 mars 2022 - 10:01:36
Dernière modification le : mardi 29 mars 2022 - 03:58:36

CONVERGENCE TO EQUILIBRIUM OF A DC ALGORITHM FOR AN EPITAXIAL GROWTH MODEL

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CONVERGENCE TO EQUILIBRIUM OF A DC ALGORITHM FOR AN EPITAXIAL GROWTH MODEL

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