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Article Dans Une Revue Communications on Applied Mathematics and Computation Année : 2021

p-Multilevel preconditioners for HHO discretizations of the Stokes equations with static condensation

Résumé

We propose a $p$-multilevel preconditioner for Hybrid High-Order discretizations (HHO) of the Stokes equation, numerically assess its performance on two variants of the method, and compare with a classical Discontinuous Galerkin scheme. We specifically investigate how the combination of $p$-coarsening and static condensation influences the performance of the $V$-cycle iteration for HHO. Two different static condensation procedures are considered, resulting in global linear systems with a different number of unknowns and non-zero elements. An efficient implementation is proposed where coarse level operators are inherited using $L^2$-orthogonal projections defined over mesh faces and the restriction of the fine grid operators is performed recursively and matrix-free. The various resolution strategies are thoroughly validated on two-and three-dimensional problems.
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Dates et versions

hal-02951823 , version 1 (29-09-2020)

Identifiants

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Lorenzo Botti, Daniele Antonio Di Pietro. p-Multilevel preconditioners for HHO discretizations of the Stokes equations with static condensation. Communications on Applied Mathematics and Computation, 2021, 4, pp.783-822. ⟨10.1007/s42967-021-00142-5⟩. ⟨hal-02951823⟩
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