Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
A parallel block multi-level preconditioner for the 3D incompressible Navier--Stokes equations
Journal of Computational Physics
A parallel solver for PDE systems and application to the incompressible Navier-Stokes equations
Applied Numerical Mathematics - Numerical algorithms, parallelism and applications
Block Preconditioners for LDG Discretizations of Linear Incompressible Flow Problems
Journal of Scientific Computing
Finite Element Simulation of Three-Dimensional Free-Surface Flow Problems
Journal of Scientific Computing
An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Preconditioning Strategies for Models of Incompressible Flow
Journal of Scientific Computing
Block preconditioners for LDG discretizations of linear incompressible flow problems
Journal of Scientific Computing
Algorithm 866: IFISS, a Matlab toolbox for modelling incompressible flow
ACM Transactions on Mathematical Software (TOMS)
An iterative matrix-free method in implicit immersed boundary/continuum methods
Computers and Structures
Journal of Computational Physics
On computational issues of immersed finite element methods
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
A non-conforming monolithic finite element method for problems of coupled mechanics
Journal of Computational Physics
Applied Numerical Mathematics
Adaptive Time-Stepping for Incompressible Flow Part II: Navier-Stokes Equations
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
On HSS-based constraint preconditioners for generalized saddle-point problems
Numerical Algorithms
An agglomerate multilevel preconditioner for linear isostasy saddle point problems
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
A Robust Two-Level Incomplete Factorization for (Navier-)Stokes Saddle Point Matrices
SIAM Journal on Matrix Analysis and Applications
Playa: High-performance programmable linear algebra
Scientific Programming
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We present a new method for solving the sparse linear system of equations arising from the discretization of the linearized steady-state Navier--Stokes equations (also known as the Oseen equations). The solver is an iterative method of Krylov subspace type for which we devise a preconditioner through a heuristic argument based on the fundamental solution tensor for the Oseen operator. The preconditioner may also be conceived through a weaker heuristic argument involving differential operators. Computations indicate that convergence for the preconditioned discrete Oseen problem is only mildly dependent on the viscosity (inverse Reynolds number) and, most importantly, that the number of iterations does not grow as the mesh size is reduced. Indeed, since the preconditioner is motivated through analysis of continuous operators, the number of iterations decreases for smaller mesh size which accords with better approximation of these operators.