Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
On deflation and singular symmetric positive semi-definite matrices
Journal of Computational and Applied Mathematics
Fast and robust solvers for pressure-correction in bubbly flow problems
Journal of Computational Physics
Deflated preconditioned conjugate gradient solvers for the Pressure-Poisson equation
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
Shift-Invert Arnoldi's Method with Preconditioned Iterative Solves
SIAM Journal on Matrix Analysis and Applications
Further comparison of additive and multiplicative coarse grid correction
Applied Numerical Mathematics
Journal of Computational Physics
Scalable domain decomposition preconditioners for heterogeneous elliptic problems
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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In this article we introduce new bounds on the effective condition number of deflated and preconditioned-deflated symmetric positive definite linear systems. For the case of a subdomain deflation such as that of Nicolaides [SIAM J. Numer. Anal., 24 (1987), pp. 355--365], these theorems can provide direction in choosing a proper decomposition into subdomains. If grid refinement is performed, keeping the subdomain grid resolution fixed, the condition number is insensitive to the grid size. Subdomain deflation is very easy to implement and has been parallelized on a distributed memory system with only a small amount of additional communication. Numerical experiments for a steady-state convection-diffusion problem are included.