p-Multilevel Preconditioners for HHO Discretizations of the Stokes Equations with Static Condensation

Communications on Applied Mathematics and Computation - Tập 4 Số 3 - Trang 783-822 - 2022
Lorenzo Alessio Botti1, Daniele Antonio Di Pietro2
1Department of Engineering and Applied Sciences, University of Bergamo, Bergamo, Italy
2IMAG, Univ Montpellier, CNRS, Montpellier, France

Tóm tắt

AbstractWe propose a p-multilevel preconditioner for hybrid high-order (HHO) discretizations of the Stokes equation, numerically assess its performance on two variants of the method, and compare with a classical discontinuous Galerkin scheme. An efficient implementation is proposed where coarse level operators are inherited using $$L^2$$ L 2 -orthogonal projections defined over mesh faces and the restriction of the fine grid operators is performed recursively and matrix-free. Both h- and k-dependency are investigated tackling two- and three-dimensional problems on standard meshes and graded meshes. For the two HHO formulations, featuring discontinuous or hybrid pressure, we study how the combination of p-coarsening and static condensation influences the V-cycle iteration. In particular, two different static condensation procedures are considered for the discontinuous pressure HHO variant, resulting in global linear systems with a different number of unknowns and matrix non-zero entries. Interestingly, we show that the efficiency of the solution strategy might be impacted by static condensation options in the case of graded meshes.

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