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We consider multigrid cycles based on the recursive use of a two–grid method, in which the coarse–grid system is solved by µ ≥ 1 steps of a Krylov subspace iterative method. The approach is further extended by allowing such inner iterations only at levels of given multiplicity, a V–cycle formulation being used at all other levels. For symmetric positive(More)
Spectral AMGe (ρAMGe), is a new algebraic multigrid method for solving discretizations that arise in Ritz-type finite element methods for partial differential equations. The method assumes access to the element stiffness matrices in order to lessen certain presumptions that can limit other algebraic methods. ρAMGe uses the spectral decomposition of small(More)
This paper proposes a stabilization of the classical hierarchical basis (HB)-nite element method by modifying the standard nodal basis functions that correspond to the hierarchical complement (in the next ner discretization space) of any successive coarse dis-cretization space using computationally feasible approximate L 2 {projections onto the given coarse(More)
This paper provides a framework for developing computation-ally efficient multilevel preconditioners and representations for Sobolev norms. Specifically, given a Hilbert space V and a nested sequence of subspaces V 1 ⊂ V 2 ⊂. .. ⊂ V , we construct operators which are spectrally equivalent to those of the form A = k µ k (Q k − Q k−1). Here µ k , k = 1, 2,.(More)