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Preconditioning the Poincare-Steklov operator by using Green's function
Xu, JC; Zhang, S
1997
Source PublicationMATHEMATICS OF COMPUTATION
ISSN0025-5718
Volume66Issue:217Pages:125-138
AbstractThis paper is concerned with the Poincare-Steklov operator that is widely used in domain decomposition methods. It is proved that the inverse of the Poincare-Steklov operator can je expressed explicitly by an integral operator with a kernel being the Green's function restricted to the interface. As an application, for the discrete Poincare-Steklov operator with respect to either a line (edge) or a star-shaped web associated with a single vertex point, a preconditioner can be constructed by first imbedding the line as the diameter of a disk, or the web as a union of radii of a disk, and then using the Green's function on the disk. The proposed technique can be effectively used in conjunction with various existing domain decomposition techniques, especially with the methods based on vertex spaces (from multi-subdomain decomposition). Some numerical results are reported.
Keyworddomain decomposition preconditioner Schur complement Green's function multigrid Poincare-Steklov operator
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:A1997WE36600008
PublisherAMER MATHEMATICAL SOC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29013
Collection中国科学院数学与系统科学研究院
AffiliationCHINESE ACAD SCI,CTR COMP,STATE KEY LAB SCI & ENGN COMP,BEIJING 100080,PEOPLES R CHINA
Recommended Citation
GB/T 7714
Xu, JC,Zhang, S. Preconditioning the Poincare-Steklov operator by using Green's function[J]. MATHEMATICS OF COMPUTATION,1997,66(217):125-138.
APA Xu, JC,&Zhang, S.(1997).Preconditioning the Poincare-Steklov operator by using Green's function.MATHEMATICS OF COMPUTATION,66(217),125-138.
MLA Xu, JC,et al."Preconditioning the Poincare-Steklov operator by using Green's function".MATHEMATICS OF COMPUTATION 66.217(1997):125-138.
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