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Efficient Implementation and Numerical Analysis of Finite Element Method for Fractional Allen-Cahn Equation
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-07-28
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
We embed the fractional Allen-Cahn equation into a Galerkin variational framework and thus develop its corresponding finite element procedure and then prove rigorously its mathematical and physical properties for the finite element solution.
Combining the merits of the conjugate gradient (CG) algorithm and the Toeplitz structure of the coefficient matrix, we design a fast CG for the linearized finite element scheme to reduce the computation cost and the storage to O(M log M ) and O(M), respectively.
Numerical experiments confirm that the proposed fast CG algorithm recognizes accurately the mass and energy dissipation, the phase separation through a very clear coarse graining process, and the influences of different indices r of fractional Laplacian and different coefficients K,η on the width of the interfaces.
American Psychological Association (APA)
Wang, Guozhen& Chen, Huan-zhen. 2019. Efficient Implementation and Numerical Analysis of Finite Element Method for Fractional Allen-Cahn Equation. Mathematical Problems in Engineering،Vol. 2019, no. 2019, pp.1-14.
https://search.emarefa.net/detail/BIM-1197268
Modern Language Association (MLA)
Wang, Guozhen& Chen, Huan-zhen. Efficient Implementation and Numerical Analysis of Finite Element Method for Fractional Allen-Cahn Equation. Mathematical Problems in Engineering No. 2019 (2019), pp.1-14.
https://search.emarefa.net/detail/BIM-1197268
American Medical Association (AMA)
Wang, Guozhen& Chen, Huan-zhen. Efficient Implementation and Numerical Analysis of Finite Element Method for Fractional Allen-Cahn Equation. Mathematical Problems in Engineering. 2019. Vol. 2019, no. 2019, pp.1-14.
https://search.emarefa.net/detail/BIM-1197268
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1197268