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Volume 5, Issue 5
A Multi-Mesh Adaptive Finite Element Approximation to Phase Field Models

Xianliang Hu, Ruo Li & Tao Tang

Commun. Comput. Phys., 5 (2009), pp. 1012-1029.

Published online: 2009-05

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  • Abstract

In this work, we propose an efficient multi-mesh adaptive finite element method for simulating the dendritic growth in two- and three-dimensions. The governing equations used are the phase field model, where the regularity behaviors of the relevant dependent variables, namely the thermal field function and the phase field function, can be very different. To enhance the computational efficiency, we approximate these variables on different h-adaptive meshes. The coupled terms in the system are calculated based on the implementation of the multi-mesh h-adaptive algorithm proposed by Li (J. Sci. Comput., pp. 321-341, 24 (2005)). It is illustrated numerically that the multi-mesh technique is useful in solving phase field models and can save storage and the CPU time significantly.

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@Article{CiCP-5-1012, author = {Xianliang Hu, Ruo Li and Tao Tang}, title = {A Multi-Mesh Adaptive Finite Element Approximation to Phase Field Models}, journal = {Communications in Computational Physics}, year = {2009}, volume = {5}, number = {5}, pages = {1012--1029}, abstract = {

In this work, we propose an efficient multi-mesh adaptive finite element method for simulating the dendritic growth in two- and three-dimensions. The governing equations used are the phase field model, where the regularity behaviors of the relevant dependent variables, namely the thermal field function and the phase field function, can be very different. To enhance the computational efficiency, we approximate these variables on different h-adaptive meshes. The coupled terms in the system are calculated based on the implementation of the multi-mesh h-adaptive algorithm proposed by Li (J. Sci. Comput., pp. 321-341, 24 (2005)). It is illustrated numerically that the multi-mesh technique is useful in solving phase field models and can save storage and the CPU time significantly.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7775.html} }
TY - JOUR T1 - A Multi-Mesh Adaptive Finite Element Approximation to Phase Field Models AU - Xianliang Hu, Ruo Li & Tao Tang JO - Communications in Computational Physics VL - 5 SP - 1012 EP - 1029 PY - 2009 DA - 2009/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7775.html KW - AB -

In this work, we propose an efficient multi-mesh adaptive finite element method for simulating the dendritic growth in two- and three-dimensions. The governing equations used are the phase field model, where the regularity behaviors of the relevant dependent variables, namely the thermal field function and the phase field function, can be very different. To enhance the computational efficiency, we approximate these variables on different h-adaptive meshes. The coupled terms in the system are calculated based on the implementation of the multi-mesh h-adaptive algorithm proposed by Li (J. Sci. Comput., pp. 321-341, 24 (2005)). It is illustrated numerically that the multi-mesh technique is useful in solving phase field models and can save storage and the CPU time significantly.

Xianliang Hu, Ruo Li and Tao Tang. (2009). A Multi-Mesh Adaptive Finite Element Approximation to Phase Field Models. Communications in Computational Physics. 5 (5). 1012-1029. doi:
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