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
Two multigrid methods for three-dimensional problems with discontinuous and anisotropic coefficients
SIAM Journal on Scientific and Statistical Computing
Black box multigrid for periodic and singular problems
Applied Mathematics and Computation
Cell-centered multigrid for interface problems
Journal of Computational Physics
Preconditioned conjugate gradients for solving singular systems
Journal of Computational and Applied Mathematics - Special issue on iterative methods for the solution of linear systems
Applied Mathematics and Computation
SIAM Journal on Scientific and Statistical Computing
Vertex-centered and cell-centered multigrid for interface problems
Journal of Computational Physics
Journal of Computational Physics
Iterative methods for solving linear systems
Iterative methods for solving linear systems
The black box multigrid numerical homogenization algorithm
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A Deflated Version of the Conjugate Gradient Algorithm
SIAM Journal on Scientific Computing
Multigrid
A front-tracking method for the computations of multiphase flow
Journal of Computational Physics
Journal of Computational Physics
On the Construction of Deflation-Based Preconditioners
SIAM Journal on Scientific Computing
SIAM Journal on Matrix Analysis and Applications
BoomerAMG: a parallel algebraic multigrid solver and preconditioner
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Vectorization and Parallelization of FISHPAK
Proceedings of the Fifth SIAM Conference on Parallel Processing for Scientific Computing
Journal of Computational Physics
A lattice Boltzmann method for incompressible two-phase flows with large density differences
Journal of Computational Physics
A Comparison of Deflation and Coarse Grid Correction Applied to Porous Media Flow
SIAM Journal on Numerical Analysis
Recycling Subspace Information for Diffuse Optical Tomography
SIAM Journal on Scientific Computing
A sharp interface method for incompressible two-phase flows
Journal of Computational Physics
Numerical simulation of bubble rising in viscous liquid
Journal of Computational Physics
Recycling Krylov Subspaces for Sequences of Linear Systems
SIAM Journal on Scientific Computing
Journal of Computational Physics
On deflation and singular symmetric positive semi-definite matrices
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Computing three-dimensional two-phase flows with a mass-conserving level set method
Computing and Visualization in Science
Multilevel Projection-Based Nested Krylov Iteration for Boundary Value Problems
SIAM Journal on Scientific Computing
Journal of Scientific Computing
A Comparison of Two-Level Preconditioners Based on Multigrid and Deflation
SIAM Journal on Matrix Analysis and Applications
Algebraic Multigrid for Linear Systems Obtained by Explicit Element Reduction
SIAM Journal on Scientific Computing
Journal of Computational Physics
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We consider the numerical simulation of two-phase fluid flow, where bubbles or droplets of one phase move against a background of the other phase. Such flows are governed by the Navier-Stokes equations, the solution of which may be approximated using a pressure-correction approach. Within such an approach, the computational cost is often dominated by the solution of a linear system corresponding to a discrete Poisson equation with discontinuous coefficients. In this paper, we explore the efficient solution of these linear systems using robust multilevel solvers, such as deflated variants of the preconditioned conjugate gradient method, or robust multigrid techniques. We consider these families of methods in more detail and compare their performance in the simulation of bubbly flows. Some of these methods turn out to be very effective and reduce the amount of work to solve the pressure-correction system substantially, resulting in efficient calculations for two-phase flows on highly resolved grids.