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Volume 16, Issue 3
Convergence to Equilibrium of a DC Algorithm for an Epitaxial Growth Model

Hamza Khalfi, Morgan Pierre, Nour Eddine Alaa & Mohammed Guedda

Int. J. Numer. Anal. Mod., 16 (2019), pp. 398-411.

Published online: 2018-11

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  • 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.

  • 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.

  • AMS Subject Headings

35R35, 49J40, 60P40

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hamza.khalfi@edu.uca.ma (Hamza Khalfi)

morgan.pierre@math.univ-poitiers.fr (Morgan Pierre)

n.alaa@uca.ac.ma (Nour Eddine Alaa)

mohamed.guedda@u-picardie.fr (Mohammed Guedda)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-16-398, author = {Khalfi , HamzaPierre , MorganAlaa , Nour Eddine and Guedda , Mohammed}, title = { Convergence to Equilibrium of a DC Algorithm for an Epitaxial Growth Model}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {16}, number = {3}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12875.html} }
TY - JOUR T1 - Convergence to Equilibrium of a DC Algorithm for an Epitaxial Growth Model AU - Khalfi , Hamza AU - Pierre , Morgan AU - Alaa , Nour Eddine AU - Guedda , Mohammed JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 398 EP - 411 PY - 2018 DA - 2018/11 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12875.html KW - Thin film epitaxy, DC programming, coarsening dynamics, Lojasiewicz-Simon inequality, epitaxial growth, model without slope selection, Fourier spectral method, convergence to equilibrium, pattern formation. AB -

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.

Khalfi , HamzaPierre , MorganAlaa , Nour Eddine and Guedda , Mohammed. (2018). Convergence to Equilibrium of a DC Algorithm for an Epitaxial Growth Model. International Journal of Numerical Analysis and Modeling. 16 (3). 398-411. doi:
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