Evaluation of multilevel sequentially semiseparable preconditioners on computational fluid dynamics benchmark problems using Incompressible Flow and Iterative Solver Software

This paper studies a new preconditioning technique for sparse systems arising from discretized partial differential equations in computational fluid dynamics problems. This preconditioning technique exploits the multilevel sequentially semiseparable (MSSS) structure of the system matrix. MSSS matrix computations give a data-sparse way to...

Efficient Preconditioners for PDE-Constrained Optimization Problems with a Multi-level Sequentially Semi-Separable Matrix Structure

In this paper, we consider preconditioning for PDE-constrained optimization problems. The underlying problems yield a linear saddle-point system. We study a class of preconditioners based on multilevel sequentially semiseparable (MSSS) matrix computations. The novel global preconditioner is to make use of the global structure of the saddle-point...

Comparison of some preconditioners for the incompressible Navier-Stokes equations

In this report we explore the performance of the SIMPLER , augmented Lagrangian, ’grad-div’ preconditioners and their variants for the two-by-two block systems arising in the incompressible Navier-Stokes equations. The lid-driven cavity and flow over a finite flat plate are chosen as the benchmark problems. For each problem Reynolds number...

Evaluation of Multilevel Sequentially Semiseparable Preconditioners on CFD Benchmark Problems Using IFISS

This paper studies a new preconditioning technique for sparse systems arising from discretized partial differential equations (PDEs) in computational fluid dynamics (CFD), which exploit the multilevel sequentially semiseparable (MSSS) structure of the system matrix. MSSS matrix computations give a data-sparse way to approximate the LU...

On preconditioning incompressible non-Newtonian flow problems

This paper deals with fast and reliable numerical solution methods for the incompressible non-Newtonian Navier-Stokes equations. To handle the nonlinearity of the governing equations, the Picard and Newton methods are used to linearize these coupled partial differential equations. For space discretization we use the finite element method and...

On the use of rigid body modes in the deflated preconditioned conjugate gradient method

Large discontinuities in material properties, such as those encountered in composite materials, lead to ill-conditioned systems of linear equations. These discontinuities give rise to small eigenvalues that may negatively affect the convergence of iterative solution methods such as the preconditioned conjugate gradient method. This paper...

A comparison of deflation and the balancing Neumann-Neumann preconditioner

In this paper we compare various preconditioners for the numerical solution of partial differential equations. We compare the well-known balancing Neumann Neumann preconditioner used in domain decomposition methods with a so-called deflation preconditioner. We prove that the effective condition number of the deflated preconditioned system is...

A comparison of deflation and coarse grid correction applied to porous media flow

In this paper we compare various preconditioners for the numerical solution of partial dierential equations. We compare a coarse grid correction preconditioner used in domain decomposition methods with a so-called deflation preconditioner. We prove that the effective condition number of the de ated preconditioned system is always, i.e. for all...

On a class of preconditioners for solving the Helmholtz equation