On deflation and singular symmetric positive semi-definite matrices
Journal of Computational and Applied Mathematics
Incremental spectral preconditioners for sequences of linear systems
Applied Numerical Mathematics
Acceleration of Preconditioned Krylov Solvers for Bubbly Flow Problems
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
Fast and robust solvers for pressure-correction in bubbly flow problems
Journal of Computational Physics
Applied Numerical Mathematics
Journal of Scientific Computing
Acceleration of preconditioned Krylov solvers for bubbly flow problems
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
A Comparison of Two-Level Preconditioners Based on Multigrid and Deflation
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
Further comparison of additive and multiplicative coarse grid correction
Applied Numerical Mathematics
Journal of Computational Physics
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In this paper we compare various preconditioners for the numerical solution of partial differential equations. We compare a coarse grid correction preconditioner used in domain decomposition methods with a so-called deflation preconditioner. We prove that the effective condition number of the deflated preconditioned system is always, for all deflation vectors and all restrictions and prolongations, below the condition number of the system preconditioned by the coarse grid correction. This implies that the conjugate gradient method applied to the deflated preconditioned system is expected always to converge faster than the conjugate gradient method applied to the system preconditioned by the coarse grid correction. Numerical results for porous media flows emphasize the theoretical results.