Preconditioning the Poincaré-Steklov operator by using Green's function

Jinchao Xu, Sheng Zhang

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


This paper is concerned with the Poincaré-Steklov operator that is widely used in domain decomposition methods. It is proved that the inverse of the Poincaré-Steklov operator can be expressed explicitly by an integral operator with a kernel being the Green's function restricted to the interface. As an application, for the discrete Poincaré-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.
Original languageEnglish (US)
Pages (from-to)125-138
Number of pages14
JournalMathematics of Computation
Issue number217
StatePublished - Jan 1 1997
Externally publishedYes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics


Dive into the research topics of 'Preconditioning the Poincaré-Steklov operator by using Green's function'. Together they form a unique fingerprint.

Cite this