Performed under the auspices of the U.S. Department of Energy under Contract DE-AC52- 07NA27344 (LLNL-JRNL-710378), supported in part by AFOSR grant FA9550-17-1-0090, and fa- cilitated by equipment acquired using ARO grant W911NF-16-1-0307.
SIAM Journal on Scientific Computing
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.
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.