An overlapping domain decomposition preconditioner for a class of discontinuous Galerkin approximations of advection-diffusion problems
Open access
Date
2000-11Type
- Report
ETH Bibliography
yes
Altmetrics
Abstract
We consider a scalar advection--diffusion problem and a recently proposed discontinuous Galerkin approximation, which employs discontinuous finite element spaces and suitable bilinear forms containing interface terms that ensure consistency. For the corresponding sparse, non-symmetric linear system, we propose and study an additive, two-level overlapping Schwarz preconditioner, consisting of a coarse problem on a coarse triangulation and local solvers associated to suitable problems defined on a family of subdomains. This is a generalization of the corresponding overlapping method for approximations on continuous finite element spaces. Related to the lack of continuity of our approximation spaces, some interesting new features arise in our generalization, which have no analog in the conforming case. We prove an upper bound for the number of iterations obtained by using this preconditioner with GMRES, which is independent of the number of degrees of freedom of the original problem and the number of subdomains. The performance of the method is illustrated by several numerical experiments for different test problems, using linear finite elements in two dimensions. Show more
Permanent link
https://doi.org/10.3929/ethz-a-004289440Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichSubject
advection-diffusion; domain decomposition; discontinuous GalerkinOrganisational unit
02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
More
Show all metadata
ETH Bibliography
yes
Altmetrics