Panayot S. Vassilevski

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We consider the construction of multiplier spaces for use with the mortar finite element method in three spatial dimensions. Abstract conditions are given for the multiplier spaces which are sufficient to guarantee a stable and convergent mortar approximation. Three examples of multipliers satisfying these conditions are given. The first one is a dual basis(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)
We present a theory for algebraic multigrid (AMG) methods that allows for general smoothing processes and general coarsening approaches. The goal of the theory is to provide guidance in the development of new, more robust, AMG algorithms. In particular, we introduce several compatible relaxation methods and give theoretical justification for their use as(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)
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)