Additive Schwarz preconditioned GMRES is a powerful method for solving large sparse linear systems of equations on parallel computers. The algorithm is often implemented in the Euclidean norm, or the discrete l norm, however, the optimal convergence result is available only in the energy norm (or the equivalent Sobolev H 1 norm). Very little progress has been made in the theoretical understandi...

Additive Schwarz preconditioned GMRES is a powerful method for solving large sparse linear systems of equations on parallel computers. The algorithm is often implemented in the Euclidean norm, or the discrete l norm, however, the optimal convergence theory is available only in the energy norm (or the equivalent Sobolev H norm). Very little progress has been made in the theoretical understanding...

SUMMARY In this paper an algebraic substructuring preconditioner is considered for non-conforming nite element approximations of second order elliptic problems in 3D domains with a piecewise constant diiusion coeecient. Using a substructuring idea and a block Gauss elimination part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent very ...

Abstract In this paper an algebraic substructuring preconditioner is considered for nonconforming nite element approximations of second order elliptic problems in D domains with diagonal anisotropic di usion tensor Using a block Gauss elimination and a substructuring idea part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent matrix Whe...

Abstract In this paper an algebraic substructuring preconditioner is considered for nonconforming nite element approximations of second order elliptic problems in D domains with diagonal anisotropic di usion tensor Using a block Gauss elimination and a substructuring idea part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent matrix Whe...

this paper deals with scrutinizing the convergence properties of iterative methods to solve linear system of equations. recently, several types of the preconditioners have been applied for ameliorating the rate of convergence of the accelerated overrelaxation (aor) method. in this paper, we study the applicability of a general class of the preconditioned iterative methods under certain conditio...

Additive Schwarz preconditioned GMRES is a powerful method for solving large sparse linear systems of equations on parallel computers. The algorithm is often implemented in the Euclidean norm, or the discrete l norm, however, the optimal convergence theory is available only in the energy norm (or the equivalent Sobolev H norm). Very little progress has been made in the theoretical understanding...

this study develops and analyzes preconditioned krylov subspace methods to solve linear systemsarising from discretization of the time-independent space-fractional models. first, we apply shifted grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. then, we employee two preconditioned iterative methods, namely, the preconditioned gene...

This work presents a new approach for selecting the coarse grids allowing a faster algebraic multigrid (AMG) preconditioned conjugate gradient solver. This approach is based on an appropriate choice of the parameter a considering the matrix density during the coarsening process which implies in a significant reduction in the matrix dimension at all AMG levels. 2005 Elsevier Inc. All rights rese...