schwarz preconditioners
Recently Published Documents


TOTAL DOCUMENTS

65
(FIVE YEARS 4)

H-INDEX

14
(FIVE YEARS 0)

Author(s):  
Erik Eikeland ◽  
Leszek Marcinkowski ◽  
Talal Rahman

Abstract In this paper, we propose a two-level additive Schwarz domain decomposition preconditioner for the symmetric interior penalty Galerkin method for a second-order elliptic boundary value problem with highly heterogeneous coefficients. A specific feature of this preconditioner is that it is based on adaptively enriching its coarse space with functions created by solving generalized eigenvalue problems on thin patches covering the subdomain interfaces. It is shown that the condition number of the underlined preconditioned system is independent of the contrast if an adequate number of functions are used to enrich the coarse space. Numerical results are provided to confirm this claim.


2020 ◽  
Vol 54 (1) ◽  
pp. 145-180 ◽  
Author(s):  
Michael Karkulik ◽  
Jens Markus Melenk ◽  
Alexander Rieder

We consider fractional Sobolev spaces Hθ(Γ), θ∈[0, 1] on a 2D surface Γ. We show that functions in Hθ(Γ) can be decomposed into contributions with local support in a stable way. Stability of the decomposition is inherited by piecewise polynomial subspaces. Applications include the analysis of additive Schwarz preconditioners for discretizations of the hypersingular integral operator by the p-version of the boundary element method with condition number bounds that are uniform in the polynomial degree p.


Sign in / Sign up

Export Citation Format

Share Document