A second-order accurate pressure correction scheme for viscous incompressible flow
SIAM Journal on Scientific and Statistical Computing
Deflation of conjugate gradients with applications to boundary value problems
SIAM Journal on Numerical Analysis
Preconditioned conjugate gradients for solving singular systems
Journal of Computational and Applied Mathematics - Special issue on iterative methods for the solution of linear systems
On the conjugate gradient solution of the Schur complement system obtained from domain decomposition
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific and Statistical Computing
A Restarted GMRES Method Augmented with Eigenvectors
SIAM Journal on Matrix Analysis and Applications
On the Construction of Deflation-Based Preconditioners
SIAM Journal on Scientific Computing
A Comparison of Deflation and Coarse Grid Correction Applied to Porous Media Flow
SIAM Journal on Numerical Analysis
A Comparison of Deflation and the Balancing Preconditioner
SIAM Journal on Scientific Computing
The deflation accelerated schwarz method for CFD
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
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
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
Pressure boundary conditions for computing incompressible flows with SPH
Journal of Computational Physics
Two implementations of the preconditioned conjugate gradient method on heterogeneous computing grids
International Journal of Applied Mathematics and Computer Science - Computational Intelligence in Modern Control Systems
Fast iterative solution of large sparse linear systems on geographically separated clusters
International Journal of High Performance Computing Applications
Hi-index | 7.30 |
For various applications, it is well-known that the deflated ICCG is an efficient method for solving linear systems with invertible coefficient matrix. We propose two equivalent variants of this deflated ICCG which can also solve linear systems with singular coefficient matrix, arising from discretization of the discontinuous Poisson equation with Neumann boundary conditions. It is demonstrated both theoretically and numerically that the resulting methods accelerate the convergence of the iterative process. Moreover, in practice the singular coefficient matrix has often been made invertible by modifying the last element, since this can be advantageous for the solver. However, the drawback is that the condition number becomes worse-conditioned. We show that this problem can completely be remedied by applying the deflation technique with just one deflation vector.