Scalable algebraic multigrid on 3500 processors.
Schwarz alternating and iterative refinemnt methods for mixed formulations of elliptic problems, part II: convergence theory.
Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: non-overlapping case
We propose and study some new additive, two-level non-overlapping Schwarz preconditioners for the solution of the algebraic linear systems arising from a wide class of discontinuous Galerkin approximations of elliptic problems that have been proposed up to now. In particular, two-level methods for both symmetric and non-symmetric schemes are introduced and some interesting features, which have no analog in the conforming case, are discussed. Both the construction and analysis of the proposed domain...
Schwarz methods over the course of time.
Semicoarsening multigrid for systems.
Smoothed prolongation multigrid with rapid coarsening and massive smoothing
We prove that within the frame of smoothed prolongations, rapid coarsening between first two levels can be compensated by massive prolongation smoothing and pre- and post-smoothing derived from the prolongator smoother.
Some algebraic aspects of multigrid methods
Some remarks on averaging in the BDDC method
In this paper, we introduce a general framework for derivation of the averaging operator, from which the standard choices are recovered by simplifications. Then, an alternative approach derived by another simplification is proposed and tested on a 2D example.
Spectral discretization of Darcy equations coupled with Navier-Stokes equations by vorticity-velocity-pressure formulation
We consider a model coupling the Darcy equations in a porous medium with the Navier-Stokes equations in the cracks, for which the coupling is provided by the pressure's continuity on the interface. We discretize the coupled problem by the spectral element method combined with a nonoverlapping domain decomposition method. We prove the existence of solution for the discrete problem and establish an error estimation. We conclude with some numerical tests confirming the results of our analysis.
Spectral methods for singular perturbation problems
We study spectral discretizations for singular perturbation problems. A special technique of stabilization for the spectral method is proposed. Boundary layer problems are accurately solved by a domain decomposition method. An effective iterative method for the solution of spectral systems is proposed. Suitable components for a multigrid method are presented.
Stabilization of a non standard FETI-DP mortar method for the Stokes problem
In a recent paper [E. Chacón Vera and D. Franco Coronil, J. Numer. Math. 20 (2012) 161–182.] a non standard mortar method for incompressible Stokes problem was introduced where the use of the trace spaces H1 / 2and H1/200and a direct computation of the pairing of the trace spaces with their duals are the main ingredients. The importance of the reduction of the number of degrees of freedom leads naturally to consider the stabilized version and this is the results we present in this work. We prove...
Steplength optimization and linear multigrid methods.