Preconditioning the Poincaré-Steklov Operator by Using Green ' s Function

  • Xu J
  • Zhang S
  • 10

    Readers

    Mendeley users who have this article in their library.
  • 18

    Citations

    Citations of this article.

Abstract

This paper is concerned with the Poincar{é}-Steklov operator that is widely used in domain decomposition methods. It is proved that the inverse of the Poincar{é}-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 Poincar{é}-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

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Authors

  • Jinchao Xu

  • Sheng Zhang

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free