Domain Decomposition Preconditioners for Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains

Antonietti, Paola; Giani, Stefano; Houston, Paul

doi:10.1007/s10915-013-9792-y

Domain Decomposition Preconditioners for Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains

Antonietti, Paola; Giani, Stefano; Houston, Paul

Authors

Paola Antonietti

Dr Stefano Giani stefano.giani@durham.ac.uk
Associate Professor

Paul Houston

Abstract

In this article we consider the application of Schwarz-type domain decomposition preconditioners for discontinuous Galerkin finite element approximations of elliptic partial differential equations posed on complicated domains, which are characterized by small details in the computational domain or microstructures. In this setting, it is necessary to define a suitable coarse-level solver, in order to guarantee the scalability of the preconditioner under mesh refinement. To this end, we exploit recent ideas developed in the so-called composite finite element framework, which allows for the definition of finite element methods on general meshes consisting of agglomerated elements. Numerical experiments highlighting the practical performance of the proposed preconditioner are presented.

Citation

Antonietti, P., Giani, S., & Houston, P. (2014). Domain Decomposition Preconditioners for Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains. Journal of Scientific Computing, 60(1), 203-227. https://doi.org/10.1007/s10915-013-9792-y

Journal Article Type	Article
Acceptance Date	Oct 9, 2013
Publication Date	Jul 1, 2014
Deposit Date	Sep 29, 2014
Publicly Available Date	Jun 22, 2015
Journal	Journal of Scientific Computing
Print ISSN	0885-7474
Electronic ISSN	1573-7691
Publisher	Springer
Peer Reviewed	Peer Reviewed
Volume	60
Issue	1
Pages	203-227
DOI	https://doi.org/10.1007/s10915-013-9792-y
Keywords	Composite finite element methods, Discontinuous Galerkin methods, Domain decomposition, Schwarz preconditioners.