南方科技大学知识苑(SUSTech KC): Fast fourier-like mapped chebyshev spectral-galerkin methods for pdes with integral fractional laplacian in unbounded domains

题名	Fast fourier-like mapped chebyshev spectral-galerkin methods for pdes with integral fractional laplacian in unbounded domains
作者	SHENG，CHANGTAO 1; SHEN，JIE 2; TANG，TAO3,4 ; WANG，LI LIAN 1; YUAN，HUIFANG5,6
发表日期	2020
DOI	10.1137/19M128377X
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS 影响因子和分区
ISSN	0036-1429
卷号	58 期号:5页码:2435-2464
摘要	In this paper, we propose a fast spectral-Galerkin method for solving PDEs involving an integral fractional Laplacian in Rd, which is built upon two essential components: (i) the Dunford- Taylor formulation of the fractional Laplacian; and (ii) Fourier-like biorthogonal mapped Chebyshev functions (MCFs) as basis functions. As a result, the fractional Laplacian can be fully diagonalized, and the complexity of solving an elliptic fractional PDE is quasi-optimal, i.e., O((N log2 N)d) with N being the number of modes in each spatial direction. Ample numerical tests for various decaying exact solutions show that the convergence of the fast solver perfectly matches the order of theoretical error estimates. With a suitable time discretization, the fast solver can be directly applied to a large class of nonlinear fractional PDEs. As an example, we solve the fractional nonlinear Schrödinger equation by using the fourth-order time-splitting method together with the proposed MCF-spectral-Galerkin method.
关键词	Biorthogonal basis functions Dunford-Taylor formula Integral fractional Laplacian Mapped Chebyshev functions Nonlocal/singular operators
相关链接	[Scopus记录]
收录类别	SCI ; EI
语种	英语
学校署名	其他
资助项目	Singapore MOE AcRF Tier 2 grants[MOE2018-T2-1-059][MOE2017-T2-2-144] ; National Science Foundation[DMS-2012585] ; AFOSR[FA9550-20-1-0309] ; National Natural Science Foundation of China[11731006] ; NSFC/RGC[11961160718] ; Science Challenge project[TZ2018001]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000584721000001
出版者	SIAM PUBLICATIONS
EI入藏号	20204809534274
EI主题词	Laplace transforms ; Galerkin methods
EI分类号	Mathematical Transformations:921.3 ; Numerical Methods:921.6
ESI学科分类	MATHEMATICS
Scopus记录号	2-s2.0-85089895560
来源库	Scopus
引用统计	被引频次[WOS]：36
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/209596
专题	深圳国际数学中心（杰曼诺夫数学中心）（筹）理学院_数学系
作者单位	1.Division of Mathematical Sciences,School of Physical and Mathematical Sciences,Nanyang Technological University,Singapore,637371,Singapore 2.Department of Mathematics,Purdue University,West Lafayette,47907-1957,United States 3.Division of Science and Technology,BNU-HKBU United International College,Zhuhai, Guangdong,China 4.SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,China 5.Department of Mathematics,Southern University of Science and Technology,Shenzhen,518055,China 6.School of Mathematics and Statistics,Wuhan University,Wuhan,430072,China
推荐引用方式 GB/T 7714	SHENG，CHANGTAO,SHEN，JIE,TANG，TAO,et al. Fast fourier-like mapped chebyshev spectral-galerkin methods for pdes with integral fractional laplacian in unbounded domains[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2020,58(5):2435-2464.
APA	SHENG，CHANGTAO,SHEN，JIE,TANG，TAO,WANG，LI LIAN,&YUAN，HUIFANG.(2020).Fast fourier-like mapped chebyshev spectral-galerkin methods for pdes with integral fractional laplacian in unbounded domains.SIAM JOURNAL ON NUMERICAL ANALYSIS,58(5),2435-2464.
MLA	SHENG，CHANGTAO,et al."Fast fourier-like mapped chebyshev spectral-galerkin methods for pdes with integral fractional laplacian in unbounded domains".SIAM JOURNAL ON NUMERICAL ANALYSIS 58.5(2020):2435-2464.