Volume 25, Issue 4
A Novel Second-Order Scheme for the Molecular Beam Epitaxy Model with Slope Selection

Lizhen Chen, Jia Zhao & Yuezheng Gong

Commun. Comput. Phys., 25 (2019), pp. 1024-1044.

Published online: 2018-12

Preview Purchase PDF 125 2439
Export citation
  • Abstract

Molecular beam epitaxy (MBE) is an important and challenging research topic in material science. In this paper, we propose a new fully discrete scheme for the well-celebrated continuum MBE model with slope selection. First of all, we use a multi-step strategy to discretize the MBE model in time. The obtained semi-discrete scheme is proved to possess properties of total mass conservation, unconditionally energy stability and uniquely solvability. The rigorous error estimate is then conducted to show its second-order convergence. The semi-discrete scheme is further discretized in space using the Fourier pseudo-spectral method. The fully discrete scheme is also shown to preserve mass-conservation and energy-dissipation properties. Afterward, several numerical examples are presented to validate the accuracy and efficiency of our proposed scheme. In particular, the scaling law for the roughness growing and effective energy decaying are captured during long-time coarsening dynamic simulations. The idea proposed in this paper could be readily utilized to design accurate and stable numerical approximations for many other energy-based phase field models.

  • Keywords

Phase field, linear scheme, molecular beam epitaxy, energy stable.

  • AMS Subject Headings

65N22, 65M12, 65M70

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-25-1024, author = {}, title = {A Novel Second-Order Scheme for the Molecular Beam Epitaxy Model with Slope Selection}, journal = {Communications in Computational Physics}, year = {2018}, volume = {25}, number = {4}, pages = {1024--1044}, abstract = {

Molecular beam epitaxy (MBE) is an important and challenging research topic in material science. In this paper, we propose a new fully discrete scheme for the well-celebrated continuum MBE model with slope selection. First of all, we use a multi-step strategy to discretize the MBE model in time. The obtained semi-discrete scheme is proved to possess properties of total mass conservation, unconditionally energy stability and uniquely solvability. The rigorous error estimate is then conducted to show its second-order convergence. The semi-discrete scheme is further discretized in space using the Fourier pseudo-spectral method. The fully discrete scheme is also shown to preserve mass-conservation and energy-dissipation properties. Afterward, several numerical examples are presented to validate the accuracy and efficiency of our proposed scheme. In particular, the scaling law for the roughness growing and effective energy decaying are captured during long-time coarsening dynamic simulations. The idea proposed in this paper could be readily utilized to design accurate and stable numerical approximations for many other energy-based phase field models.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0015}, url = {http://global-sci.org/intro/article_detail/cicp/12889.html} }
TY - JOUR T1 - A Novel Second-Order Scheme for the Molecular Beam Epitaxy Model with Slope Selection JO - Communications in Computational Physics VL - 4 SP - 1024 EP - 1044 PY - 2018 DA - 2018/12 SN - 25 DO - http://doi.org/10.4208/cicp.OA-2018-0015 UR - https://global-sci.org/intro/article_detail/cicp/12889.html KW - Phase field, linear scheme, molecular beam epitaxy, energy stable. AB -

Molecular beam epitaxy (MBE) is an important and challenging research topic in material science. In this paper, we propose a new fully discrete scheme for the well-celebrated continuum MBE model with slope selection. First of all, we use a multi-step strategy to discretize the MBE model in time. The obtained semi-discrete scheme is proved to possess properties of total mass conservation, unconditionally energy stability and uniquely solvability. The rigorous error estimate is then conducted to show its second-order convergence. The semi-discrete scheme is further discretized in space using the Fourier pseudo-spectral method. The fully discrete scheme is also shown to preserve mass-conservation and energy-dissipation properties. Afterward, several numerical examples are presented to validate the accuracy and efficiency of our proposed scheme. In particular, the scaling law for the roughness growing and effective energy decaying are captured during long-time coarsening dynamic simulations. The idea proposed in this paper could be readily utilized to design accurate and stable numerical approximations for many other energy-based phase field models.

Lizhen Chen, Jia Zhao & Yuezheng Gong. (2020). A Novel Second-Order Scheme for the Molecular Beam Epitaxy Model with Slope Selection. Communications in Computational Physics. 25 (4). 1024-1044. doi:10.4208/cicp.OA-2018-0015
Copy to clipboard
The citation has been copied to your clipboard