A well-conditioned direct PinT algorithm for first- and second-order evolutionary equations
文献类型：期刊论文
| 作者 | Liu, Jun4; Wang, Xiang-Sheng3; Wu, Shu-Lin2; Zhou, Tao1 |
| 刊名 | ADVANCES IN COMPUTATIONAL MATHEMATICS
 |
| 出版日期 | 2022-06-01 |
| 卷号 | 48期号:3页码:29 |
| 关键词 | Direct PinT algorithms Diagonalization technique Condition number Wave-type equations |
| ISSN号 | 1019-7168 |
| DOI | 10.1007/s10444-022-09928-4 |
| 英文摘要 | In this paper, we study a direct parallel-in-time (PinT) algorithm for first- and second-order time-dependent differential equations. We use a second-order boundary value method as the time integrator. Instead of solving the corresponding all-at-once system iteratively, we diagonalize the time discretization matrix B, which yields a direct parallel implementation across all time steps. A crucial issue of this methodology is how the condition number (denoted by Cond(2)(V)) of the eigenvector matrix V of B behaves as n grows, where n is the number of time steps. A large condition number leads to large roundoff error in the diagonalization procedure, which could seriously pollute the numerical accuracy. Based on a novel connection between the characteristic equation and the Chebyshev polynomials, we present explicit formulas for V and V-1, by which we prove that Cond(2)(V) = O (n(2)). This implies that the diagonalization process is well-conditioned and the roundoff error only increases moderately as n grows, and thus, compared to other direct PinT algorithms, a much larger n can be used to yield satisfactory parallelism. A fast structure-exploiting algorithm is also designed for computing the spectral diagonalization of B. Numerical results on parallel machine are given to support our findings, where over 60 times speedup is achieved with 256 cores. |
| 资助项目 | National Natural Science Foundation of China (NSFC)[12171080] ; Natural Science Foundation of Jilin Province[JC010284408] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000779137200001 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/60215]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Wu, Shu-Lin |
| 作者单位 | 1.Chinese Acad Sci, LSEC, Inst Computat Math & Sci Engn Comp, AMSS, Beijing 100190, Peoples R China 2.Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China 3.Univ Louisiana Lafayette, Dept Math, Lafayette, LA 70503 USA 4.Southern Illinois Univ Edwardsville, Dept Math & Stat, Edwardsville, IL 62026 USA |
| 推荐引用方式 GB/T 7714 | Liu, Jun,Wang, Xiang-Sheng,Wu, Shu-Lin,et al. A well-conditioned direct PinT algorithm for first- and second-order evolutionary equations[J]. ADVANCES IN COMPUTATIONAL MATHEMATICS,2022,48(3):29. |
| APA | Liu, Jun,Wang, Xiang-Sheng,Wu, Shu-Lin,&Zhou, Tao.(2022).A well-conditioned direct PinT algorithm for first- and second-order evolutionary equations.ADVANCES IN COMPUTATIONAL MATHEMATICS,48(3),29. |
| MLA | Liu, Jun,et al."A well-conditioned direct PinT algorithm for first- and second-order evolutionary equations".ADVANCES IN COMPUTATIONAL MATHEMATICS 48.3(2022):29. |
入库方式： OAI收割
来源：数学与系统科学研究院
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