| Residential College | false |
| Status | 已發表Published |
| Numerical Study of a Fast Two-Level Strang Splitting Method for Spatial Fractional Allen–Cahn Equations | |
| Cai, Yao Yuan; Sun, Hai Wei; Tam, Sik Chung | |
| 2023-06-01 | |
| Source Publication | Journal of Scientific Computing
 |
| ISSN | 0885-7474 |
| Volume | 95Issue:3 |
| Abstract | In this paper, a numerical method to solve the multi-dimensional spatial fractional Allen–Cahn equations has been investigated. After semi-discretizating the equations, a system of nonlinear ordinary differential equations with a Toeplitz structure is induced. We propose to split the Toeplitz matrix into the sum of a circulant matrix and a skew-circulant matrix, and apply the Strang splitting method. Such a two-level Strang splitting method will reduce the computational complexity to O(qlog q). Moreover, it preserves not only the discrete maximum principle unconditionally but also second-order convergence as well. By introducing a new modified energy formula, the energy dissipation property can be guaranteed. Finally, some numerical experiments are conducted to confirm the theories we put forward. |
| Keyword | Altered two-level Strang splitting method Circulant and skew-circulant matrix Discrete maximum principle Fast Fourier transform Modified energy decay |
| DOI | 10.1007/s10915-023-02196-4 |
| URL | View the original |
| Language | 英語English |
| Scopus ID | 2-s2.0-85153289773 |
| Fulltext Access | |
| Citation statistics | |
| Document Type | Journal article |
| Collection | University of Macau |
| Affiliation | Department of Mathematics, University of Macau, Macao |
| First Author Affilication | University of Macau |
| Recommended Citation GB/T 7714 | Cai, Yao Yuan,Sun, Hai Wei,Tam, Sik Chung. Numerical Study of a Fast Two-Level Strang Splitting Method for Spatial Fractional Allen–Cahn Equations[J]. Journal of Scientific Computing, 2023, 95(3). |
| APA | Cai, Yao Yuan., Sun, Hai Wei., & Tam, Sik Chung (2023). Numerical Study of a Fast Two-Level Strang Splitting Method for Spatial Fractional Allen–Cahn Equations. Journal of Scientific Computing, 95(3). |
| MLA | Cai, Yao Yuan,et al."Numerical Study of a Fast Two-Level Strang Splitting Method for Spatial Fractional Allen–Cahn Equations".Journal of Scientific Computing 95.3(2023). |
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