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Volume 16, Issue 2
Convexity Splitting in a Phase Field Model for Surface Diffusion

Rainer Backofen, Steven M. Wise, Marco Salvalaglio & Axel Voigt

Int. J. Numer. Anal. Mod., 16 (2019), pp. 192-209.

Published online: 2018-10

[An open-access article; the PDF is free to any online user.]

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  • Abstract

Convexity splitting like schemes with improved accuracy are proposed for a phase field model for surface diffusion. The schemes are developed to enable large scale simulations in three spatial dimensions describing experimentally observed solid state dewetting phenomena. We carefully elaborate the loss in accuracy associated with large time steps in such schemes and show the existence of a maximal numerical timestep to achieve a prescribed accuracy. We demonstrate the increase of this maximal numerical time step by at least one order of magnitude using a Rosenbrock method. This convexity splitting scheme with improved accuracy is used to study the effect of contact angle on solid state dewetting phenomena.

  • Keywords

Convexity splitting, Rosenbrock time discretization, surface diffusion, solid-state dewetting.

  • AMS Subject Headings

65M15, 35K25, 35K55

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

rainer.backofen@tu-dresden.de (Rainer Backofen)

swise1@utk.edu (Steven M. Wise)

marco.salvalaglio@tu-dresden.de (Marco Salvalaglio)

axel.voigt@tu-dresden.de (Axel Voigt)

  • BibTex
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  • TXT
@Article{IJNAM-16-192, author = {Rainer and Backofen and rainer.backofen@tu-dresden.de and 12935 and Department of Mathematics, Technische Universit¨at Dresden 01062 Dresden, Germany and Rainer Backofen and Steven and M. Wise and swise1@utk.edu and 4949 and Department of Mathematics, University of Tennessee, Knoxville, 37996-1320, USA. and Steven M. Wise and Marco and Salvalaglio and marco.salvalaglio@tu-dresden.de and 11930 and Department of Mathematics, Technische Universität Dresden 01062 Dresden, Germany and Marco Salvalaglio and Axel and Voigt and axel.voigt@tu-dresden.de and 11914 and Department of Mathematics, Technische Universität Dresden 01062 Dresden, Germany and Axel Voigt}, title = {Convexity Splitting in a Phase Field Model for Surface Diffusion}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {16}, number = {2}, pages = {192--209}, abstract = {

Convexity splitting like schemes with improved accuracy are proposed for a phase field model for surface diffusion. The schemes are developed to enable large scale simulations in three spatial dimensions describing experimentally observed solid state dewetting phenomena. We carefully elaborate the loss in accuracy associated with large time steps in such schemes and show the existence of a maximal numerical timestep to achieve a prescribed accuracy. We demonstrate the increase of this maximal numerical time step by at least one order of magnitude using a Rosenbrock method. This convexity splitting scheme with improved accuracy is used to study the effect of contact angle on solid state dewetting phenomena.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12799.html} }
TY - JOUR T1 - Convexity Splitting in a Phase Field Model for Surface Diffusion AU - Backofen , Rainer AU - M. Wise , Steven AU - Salvalaglio , Marco AU - Voigt , Axel JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 192 EP - 209 PY - 2018 DA - 2018/10 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12799.html KW - Convexity splitting, Rosenbrock time discretization, surface diffusion, solid-state dewetting. AB -

Convexity splitting like schemes with improved accuracy are proposed for a phase field model for surface diffusion. The schemes are developed to enable large scale simulations in three spatial dimensions describing experimentally observed solid state dewetting phenomena. We carefully elaborate the loss in accuracy associated with large time steps in such schemes and show the existence of a maximal numerical timestep to achieve a prescribed accuracy. We demonstrate the increase of this maximal numerical time step by at least one order of magnitude using a Rosenbrock method. This convexity splitting scheme with improved accuracy is used to study the effect of contact angle on solid state dewetting phenomena.

Rainer Backofen, Steven M. Wise, Marco Salvalaglio & Axel Voigt. (2020). Convexity Splitting in a Phase Field Model for Surface Diffusion. International Journal of Numerical Analysis and Modeling. 16 (2). 192-209. doi:
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