Finite element simulation and efficient algorithm for fractional Cahn–Hilliard equation

This article is devoted to designing efficient linear finite element algorithm for the fractional Cahn–Hilliard equation, an important and newly proposed phase field model. Combining the advantages of the classic BiCG algorithm and the Toeplitz-like structure of the coefficient matrix, we develop a...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2019-08, Vol.356, p.248-266
Main Authors: Wang, Feng, Chen, Huanzhen, Wang, Hong
Format: Article
Language:English
Subjects:
Efficient algorithm
Fast BiCG
Fractional Cahn–Hilliard equation
Linear finite element
Phase field model
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Summary:This article is devoted to designing efficient linear finite element algorithm for the fractional Cahn–Hilliard equation, an important and newly proposed phase field model. Combining the advantages of the classic BiCG algorithm and the Toeplitz-like structure of the coefficient matrix, we develop a fast BiCG(FBiCG) algorithm for the linearized scheme to compute numerically the fractional Cahn–Hilliard equation. Our theoretical analysis and numerical experiments demonstrate that the proposed FBiCG reduces the computation cost and the storage to O(MlogM) and O(M), possesses the same convergence rates as Newton’s algorithm does in space and time, and preserves the energy dissipation and equality laws. The numerical experiments also demonstrate that the FBiCG is almost mass conserved, recognizes accurately the phase separation by a very clear coarse graining process and the influences of different indices r and s of fractional Laplacian and different coefficients K and a on the width of the interfaces.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2019.01.037