Document Type

Pre-Print

Publication Date

12-2016

Subjects

Discontinuous functions, Galerkin methods, Numerical analysis

Abstract

We show how a scalable preconditioner for the primal discontinuous Petrov-Galerkin (DPG) method can be developed using existing algebraic multigrid (AMG) preconditioning techniques. The stability of the DPG method gives a norm equivalence which allows us to exploit existing AMG algorithms and software. We show how these algebraic preconditioners can be applied directly to a Schur complement system arising from the DPG method. One of our intermediate results shows that a generic stable decomposition implies a stable decomposition for the Schur complement. This justifies the application of algebraic solvers directly to the interface degrees of freedom. Combining such results, we obtain the first massively scalable algebraic preconditioner for the DPG system.

Description

This is the pre-print version of the article.

Persistent Identifier

http://archives.pdx.edu/ds/psu/20538

Included in

Mathematics Commons

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