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
Parallel Preconditioning with Sparse Approximate Inverses
SIAM Journal on Scientific Computing
Approximate sparsity patterns for the inverse of a matrix and preconditioning
IMACS'97 Proceedings on the on Iterative methods and preconditioners
Journal of Computational Physics
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Journal of Computational Physics
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
On deflation and singular symmetric positive semi-definite matrices
Journal of Computational and Applied Mathematics
Simulation of Multiphysics Multiscale Systems: Introduction to the ICCS'2007 Workshop
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
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We consider the linear system which arises from discretization of the pressure Poisson equation with Neumann boundary conditions, coming from bubbly flow problems. In literature, preconditioned Krylov iterative solvers are proposed, but these show slow convergence for relatively large and complex problems. We extend these traditional solvers with the so-called deflation technique, which accelerates the convergence substantially. Several numerical aspects are considered, like the singularity of the coefficient matrix and the varying density field at each time step. We demonstrate theoretically that the resulting deflation method accelerates the convergence of the iterative process. Thereafter, this is also demonstrated numerically for 3-D bubbly flow applications, both with respect to the number of iterations and the computational time.