Volume 5, Issue 2-4
A Fourier Spectral Moving Mesh Method for the Cahn-Hilliard Equation with Elasticity

W. M. Feng, P. Yu, S. Y. Hu, Z. K. Liu, Q. Du & L. Q. Chen

Commun. Comput. Phys., 5 (2009), pp. 582-599.

Published online: 2009-02

Preview Full PDF 275 2145
Export citation
  • Abstract

In recent years, Fourier spectral methods have emerged as competitive numerical methods for large-scale phase field simulations of microstructures in computational materials sciences. To further improve their effectiveness, we recently developed a new adaptive Fourier-spectral semi-implicit method (AFSIM) for solving the phase field equation by combining an adaptive moving mesh method and the semi-implicit Fourier spectral algorithm. In this paper, we present the application of AFSIM to the Cahn-Hilliard equation with inhomogeneous, anisotropic elasticity. Numerical implementations and test examples in both two and three dimensions are considered with a particular illustration using the well-studied example of mis-fitting particles in a solid as they approach to their equilibrium shapes. It is shown that significant savings in memory and computational time is achieved while accurate solutions are preserved.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-5-582, author = {}, title = {A Fourier Spectral Moving Mesh Method for the Cahn-Hilliard Equation with Elasticity}, journal = {Communications in Computational Physics}, year = {2009}, volume = {5}, number = {2-4}, pages = {582--599}, abstract = {

In recent years, Fourier spectral methods have emerged as competitive numerical methods for large-scale phase field simulations of microstructures in computational materials sciences. To further improve their effectiveness, we recently developed a new adaptive Fourier-spectral semi-implicit method (AFSIM) for solving the phase field equation by combining an adaptive moving mesh method and the semi-implicit Fourier spectral algorithm. In this paper, we present the application of AFSIM to the Cahn-Hilliard equation with inhomogeneous, anisotropic elasticity. Numerical implementations and test examples in both two and three dimensions are considered with a particular illustration using the well-studied example of mis-fitting particles in a solid as they approach to their equilibrium shapes. It is shown that significant savings in memory and computational time is achieved while accurate solutions are preserved.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7751.html} }
TY - JOUR T1 - A Fourier Spectral Moving Mesh Method for the Cahn-Hilliard Equation with Elasticity JO - Communications in Computational Physics VL - 2-4 SP - 582 EP - 599 PY - 2009 DA - 2009/02 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7751.html KW - AB -

In recent years, Fourier spectral methods have emerged as competitive numerical methods for large-scale phase field simulations of microstructures in computational materials sciences. To further improve their effectiveness, we recently developed a new adaptive Fourier-spectral semi-implicit method (AFSIM) for solving the phase field equation by combining an adaptive moving mesh method and the semi-implicit Fourier spectral algorithm. In this paper, we present the application of AFSIM to the Cahn-Hilliard equation with inhomogeneous, anisotropic elasticity. Numerical implementations and test examples in both two and three dimensions are considered with a particular illustration using the well-studied example of mis-fitting particles in a solid as they approach to their equilibrium shapes. It is shown that significant savings in memory and computational time is achieved while accurate solutions are preserved.

W. M. Feng, P. Yu, S. Y. Hu, Z. K. Liu, Q. Du & L. Q. Chen. (2020). A Fourier Spectral Moving Mesh Method for the Cahn-Hilliard Equation with Elasticity. Communications in Computational Physics. 5 (2-4). 582-599. doi:
Copy to clipboard
The citation has been copied to your clipboard