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 Gal...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 implementa-tion is proposed where coarse level operators are inherited using L2-orthogonal projec-tions 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 for-mulations,featuring discontinuous or hybrid pressure,we study how the combination of p-coarsening and static condensation influences the V-cycle iteration.In particular,two dif-ferent 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.展开更多
基金Daniele Di Pietro acknowledges the support of Agence Nationale de la Recherche Grant fast4hho(ANR-17-CE23-0019).
文摘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 implementa-tion is proposed where coarse level operators are inherited using L2-orthogonal projec-tions 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 for-mulations,featuring discontinuous or hybrid pressure,we study how the combination of p-coarsening and static condensation influences the V-cycle iteration.In particular,two dif-ferent 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.
