We 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 L2-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.

(2022). p-Multilevel Preconditioners for HHO Discretizations of the Stokes Equations with Static Condensation [journal article - articolo]. In COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION. Retrieved from http://hdl.handle.net/10446/194067

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

Botti, Lorenzo;
2022-01-01

Abstract

We 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 L2-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.
articolo
2022
Botti, Lorenzo Alessio; Di Pietro, Daniele A.
(2022). p-Multilevel Preconditioners for HHO Discretizations of the Stokes Equations with Static Condensation [journal article - articolo]. In COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION. Retrieved from http://hdl.handle.net/10446/194067
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/194067
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