A Fourier Spectral Moving Mesh Method for the Cahn-Hilliard Equation with Elasticity  

作　　者：W.M.Feng P.Yu S.Y.Hu Z.K.Liu Q.Du L.Q.Chen 

机构地区：[1]Department of Materials Science and Engineering,Pennsylvania State University,University Park,PA 16802,USA [2]Department of Mathematics,Pennsylvania State University,University Park,PA 16802,USA [3]Pacific Northwest National Laboratory,Richland,WA 99354,USA

出　　处：《Communications in Computational Physics》2009年第2期582-599,共18页计算物理通讯（英文）

基　　金：This work has been supported by the National Science Foundation Information Technol-ogy Research Project(NSF-ITR)through Grant DMR-0205232;The work of Qiang Du is also supported by NSF-DMS 0712744.

摘　　要：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.

关 键 词：Phase field diffuse interface moving mesh adaptive mesh Fourier-spectral method adaptive spectral method Cahn-Hilliard equation ELASTICITY 

分 类 号：O17[理学—数学]