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A Scalable Preconditioner for a Primal DPG Method
SIAM Journal on Scientific Computing
  • 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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Publication Date
  • 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 post-print version of an article published in the SIAM Journal of Scientific Computing copyright 2018. The article has been published and is available here:

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Barker, A. T., Dobrev, V., Gopalakrishnan, J., & Kolev, T. (2018). A Scalable Preconditioner for a Primal Discontinuous Petrov--Galerkin Method. SIAM Journal on Scientific Computing, 40(2), A1187-A1203.