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A Scalable Preconditioner for a Primal DPG Method
Portland Institute for Computational Science Publications
  • Andrew T. Barker, Lawrence Livermore National Laboratory
  • Veselin A. Dobrev, Lawrence Livermore National Laboratory
  • Jay Gopalakrishnan, Portland State University
  • Tzanio Kolev, Lawrence Livermore National Laboratory
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  • Discontinuous functions,
  • Galerkin methods,
  • Numerical analysis
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.

This is the pre-print version of the article.

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Andrew T. Barker, Veselin A. Dobrev, Jay Gopalakrishnan and Tzanio Kolev. "A Scalable Preconditioner for a Primal DPG Method" (2016)
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