KMS Of Academy of mathematics and systems sciences, CAS
| PARALLEL ENERGY-STABLE SOLVER FOR A COUPLED ALLEN-CAHN AND CAHN-HILLIARD SYSTEM | |
| Huang, Jizu1,2; Yang, Chao3; Wei, Ying4 | |
| 2020 | |
| Source Publication | SIAM JOURNAL ON SCIENTIFIC COMPUTING
 |
| ISSN | 1064-8275 |
| Volume | 42Issue:5Pages:C294-C312 |
| Abstract | In this paper, we study numerical methods for solving the coupled Allen-Cahn/Cahn-Hilliard system associated with a free energy functional of logarithmic type. To tackle the challenge posed by the special free energy functional, we propose a method to approximate the discrete variational derivatives in polynomial forms, such that the corresponding finite difference scheme is unconditionally energy stable and the energy dissipation law is maintained. To further improve the performance of the algorithm, a modified adaptive time stepping strategy is adopted such that the time step size can be flexibly controlled based on the dynamical evolution of the problem. To achieve high performance on parallel computers, we introduce a domain decomposition based, parallel Newton-Krylov-Schwarz method to solve the nonlinear algebraic system constructed from the discretization at each time step. Numerical experiments show that the proposed algorithm is second-order accurate in both space and time, energy stable with large time steps, and highly scalable to over ten thousands processor cores on the Sunway TaihuLight supercomputer. |
| Keyword | coupled Allen-Cahn/Cahn-Hilliard system discrete variational derivative method unconditionally energy stable scheme Newton-Krylov-Schwarz domain decomposition method |
| DOI | 10.1137/20M1331160 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11871069] ; Beijing Natural Science Foundation[JQ18001] ; Beijing Academy of Artificial Intelligence |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000600650100050 |
| Publisher | SIAM PUBLICATIONS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/57911 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Yang, Chao |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China 4.Chinese Acad Sci, Inst Software, Beijing 100190, Peoples R China |
| Recommended Citation GB/T 7714 | Huang, Jizu,Yang, Chao,Wei, Ying. PARALLEL ENERGY-STABLE SOLVER FOR A COUPLED ALLEN-CAHN AND CAHN-HILLIARD SYSTEM[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2020,42(5):C294-C312. |
| APA | Huang, Jizu,Yang, Chao,&Wei, Ying.(2020).PARALLEL ENERGY-STABLE SOLVER FOR A COUPLED ALLEN-CAHN AND CAHN-HILLIARD SYSTEM.SIAM JOURNAL ON SCIENTIFIC COMPUTING,42(5),C294-C312. |
| MLA | Huang, Jizu,et al."PARALLEL ENERGY-STABLE SOLVER FOR A COUPLED ALLEN-CAHN AND CAHN-HILLIARD SYSTEM".SIAM JOURNAL ON SCIENTIFIC COMPUTING 42.5(2020):C294-C312. |
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