Two-Level Additive Schwarz Preconditioners<BR> for the h-p Version

Research Report MRR99-021

Two-Level Additive Schwarz Preconditioners for the h-p Version

Thanh Tran, Ernst P. Stephan

Abstract: We study two-level additive Schwarz preconditioners for the h-p version of the Galerkin boundary element method when used to solve hypersingular integral equations of the first kind. Overlapping and non-overlapping methods are considered. We prove that the non-overlapping preconditioner yields a system of equations having a condition number bounded by $(1+\log p)^2 \max_i(1+\log\frac{H_i}{h_i})$ where $H_i$ is the length of the $i$-th subdomain, $h_i$ is the maximum length of the elements in this subdomain, and $p$ is the maximum polynomial degree used. For the overlapping method, we prove that the condition number is bounded by $(1+\log\frac{H}{\delta})^2(1+\log p)^2$ where $\delta$ is the size of the overlap and $H=\max_i H_i$. We also discuss the use of the non-overlapping method when the mesh is geometrically graded. The condition number in that case is bounded by $\log^2 M$, where $M$ is the degrees of freedom.

Download paper:	PDF file (327K)
	gzipped PostScript file (154K)

This service is maintained by the Mathematical Sciences Institute (MSI)
Comments to webmaster@maths.anu.edu.au URL: http://wwwmaths.anu.edu.au/