Computer Methods in Applied Mechanics and Engineering
Finite element analysis of the compressible Euler and Navier-Stokes equations
Finite element analysis of the compressible Euler and Navier-Stokes equations
Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Preconditioning for the Steady-State Navier--Stokes Equations with Low Viscosity
SIAM Journal on Scientific Computing
A multigrid tutorial: second edition
A multigrid tutorial: second edition
A Note on Preconditioning for Indefinite Linear Systems
SIAM Journal on Scientific Computing
Parallel multilevel k-way partitioning scheme for irregular graphs
Supercomputing '96 Proceedings of the 1996 ACM/IEEE conference on Supercomputing
Multigrid
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A parallel block multi-level preconditioner for the 3D incompressible Navier--Stokes equations
Journal of Computational Physics
Journal of Computational Physics
An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
An Improved Convergence Bound for Aggregation-Based Domain Decomposition Preconditioners
SIAM Journal on Matrix Analysis and Applications
Block Preconditioners Based on Approximate Commutators
SIAM Journal on Scientific Computing
Stabilization of Low-order Mixed Finite Elements for the Stokes Equations
SIAM Journal on Numerical Analysis
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Principles of Computational Fluid Dynamics
Principles of Computational Fluid Dynamics
Journal of Computational Physics
An Augmented Lagrangian-Based Approach to the Oseen Problem
SIAM Journal on Scientific Computing
Least Squares Preconditioners for Stabilized Discretizations of the Navier-Stokes Equations
SIAM Journal on Scientific Computing
A New Petrov-Galerkin Smoothed Aggregation Preconditioner for Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods
Journal of Computational Physics
Hi-index | 31.45 |
This study compares several block-oriented preconditioners for the stabilized finite element discretization of the incompressible Navier-Stokes equations. This includes standard additive Schwarz domain decomposition methods, aggressive coarsening multigrid, and three preconditioners based on an approximate block LU factorization, specifically SIMPLEC, LSC, and PCD. Robustness is considered with a particular focus on the impact that different stabilization methods have on preconditioner performance. Additionally, parallel scaling studies are undertaken. The numerical results indicate that aggressive coarsening multigrid, LSC and PCD all have good algorithmic scalability. Coupling this with the fact that block methods can be applied to systems arising from stable mixed discretizations implies that these techniques are a promising direction for developing scalable methods for Navier-Stokes.