Local Fourier analysis is a useful tool for predicting and analyzing the performance of many
efficient algorithms for the solution of discretized PDEs, such as multigrid and domain …

Multigrid methods are popular solution algorithms for many discretized PDEs, either as
standalone iterative solvers or as preconditioners, due to their high efficiency. However, the …

We consider an additive Vanka‐type smoother for the Poisson equation discretized by the
standard finite difference centered scheme. Using local Fourier analysis, we derive …

A well‐known strategy for building effective preconditioners for higher‐order discretizations
of some PDEs, such as Poisson's equation, is to leverage effective preconditioners for their …

Advanced finite-element discretizations and preconditioners for models of poroelasticity
have attracted significant attention in recent years. The equations of poroelasticity offer …

We derive optimal complex relaxation parameters minimizing smoothing factors associated
with multigrid using red-black successive overrelaxation or damped Jacobi smoothing …

Multigrid methods are popular for solving linear systems derived from discretizing PDEs.
Local Fourier analysis (LFA) is a technique for investigating and tuning multigrid methods. P …

In recent years, solvers for finite-element discretizations of linear or linearized saddle-point
problems, like the Stokes and Oseen equations, have become well established. There are …

Overlapping block smoothers efficiently damp the error contributions from highly oscillatory
components within multigrid methods for the Stokes equations but they are computationally …

In this paper we propose and analyze new efficient sparse approximate inverse (SAI)
smoothers for solving the two-dimensional (2D) and three-dimensional (3D) Laplacian linear …