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A UNIFORM SPECTRAL ANALYSIS FOR A PRECONDITIONED ALL-AT-ONCE SYSTEM FROM FIRST-ORDER AND SECOND-ORDER EVOLUTIONARY PROBLEMS
Wu, Shu-Lin1; Zhou, Tao2; Zhou, Zhi3
2022
Source PublicationSIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
ISSN0895-4798
Volume43Issue:3Pages:1331-1353
AbstractSolving evolutionary equations in a parallel-in-time manner is an attractive topic. The iterative algorithm based on the block alpha-circulant preconditioning technique has shown promising advantages, especially for hyperbolic problems. By fast Fourier transform for factorizing the involved circulant matrices, the preconditioned iteration can be computed efficiently via the so-called diagonalization technique, which yields a direct parallel implementation across all time levels. In recent years, considerable efforts have been devoted to exploring the spectral property of the iteration matrix arising from the used time-integrator, which leads to many case-by-case studies. Denoting by K and P-alpha the all-at-once matrix of the evolutionary PDEs and the corresponding block alpha-circulant preconditioner, we will present a systematic spectral analysis for the matrix P-alpha(-1) K for both the first-order and second-order evolutionary problems. For the first-order problems our analysis works for all stable single-step time-integrators, while for the second-order problems our analysis works for a large class of symmetric two-step methods which could be arbitrarily high-order. Illustrative numerical experiments are presented to complement our theory.
Keywordtime-parallel algorithm diagonalization technique alpha-circulant preconditioner stability spectral analysis Runge-Kutta method two-step methods
DOI10.1137/21M145358X
Indexed BySCI
Language英语
Funding ProjectNational Natural Science Foundation of China (NSFC)[12171080] ; Natural Science Foundation of Jilin Province[JC010284408] ; NSFC[12288201] ; NSFC[11731006] ; National Key R\&D Program of China[2020YFA0712000] ; Strategic Priority Research Program of Chinese Academy of Sciences[XDA25010404] ; Hong Kong Research Grants Council[15304420] ; Hong Kong Polytechnic University[P0030125]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000861196300013
PublisherSIAM PUBLICATIONS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/60875
Collection中国科学院数学与系统科学研究院
Corresponding AuthorWu, Shu-Lin
Affiliation1.Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China
2.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, AMSS, LSEC, Beijing 100190, Peoples R China
3.Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China
Recommended Citation
GB/T 7714
Wu, Shu-Lin,Zhou, Tao,Zhou, Zhi. A UNIFORM SPECTRAL ANALYSIS FOR A PRECONDITIONED ALL-AT-ONCE SYSTEM FROM FIRST-ORDER AND SECOND-ORDER EVOLUTIONARY PROBLEMS[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,2022,43(3):1331-1353.
APA Wu, Shu-Lin,Zhou, Tao,&Zhou, Zhi.(2022).A UNIFORM SPECTRAL ANALYSIS FOR A PRECONDITIONED ALL-AT-ONCE SYSTEM FROM FIRST-ORDER AND SECOND-ORDER EVOLUTIONARY PROBLEMS.SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,43(3),1331-1353.
MLA Wu, Shu-Lin,et al."A UNIFORM SPECTRAL ANALYSIS FOR A PRECONDITIONED ALL-AT-ONCE SYSTEM FROM FIRST-ORDER AND SECOND-ORDER EVOLUTIONARY PROBLEMS".SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 43.3(2022):1331-1353.
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