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• W2010804587 abstract "In this paper we present a family of scalable preconditioners for matrices arising in the discretization of $H(div)$ problems using the lowest order Raviart--Thomas finite elements. Our approach belongs to the class of “auxiliary space''--based methods and requires only the finite element stiffness matrix plus some minimal additional discretization information about the topology and orientation of mesh entities. We provide a detailed algebraic description of the theory, parallel implementation, and different variants of this parallel auxiliary space divergence solver (ADS) and discuss its relations to the Hiptmair--Xu (HX) auxiliary space decomposition of $H(div)$ [SIAM J. Numer. Anal., 45 (2007), pp. 2483--2509] and to the auxiliary space Maxwell solver AMS [J. Comput. Math., 27 (2009), pp. 604--623]. An extensive set of numerical experiments demonstrates the robustness and scalability of our implementation on large-scale $H(div)$ problems with large jumps in the material coefficients." @default.
• W2010804587 created "2016-06-24" @default.
• W2010804587 creator A5027636165 @default.
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• W2010804587 date "2012-01-01" @default.
• W2010804587 modified "2023-10-16" @default.
• W2010804587 title "Parallel Auxiliary Space AMG Solver for $H(div)$ Problems" @default.
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• W2010804587 doi "https://doi.org/10.1137/110859361" @default.
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