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 discuss several Uzawa-type iterations as smoothers in the context of multigrid schemes
for saddle point problems. A unified framework to analyze the smoothing properties is …

We employ textbook multigrid efficiency (TME), as introduced by Achi Brandt, to construct an
asymptotically optimal monolithic multigrid solver for the Stokes system. The geometric …

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

In this paper, we develop a local Fourier analysis of multigrid methods based on block-
structured relaxation schemes for stable and stabilized mixed finite-element discretizations …

In this work, we propose three novel block-structured multigrid relaxation schemes based on
distributive relaxation, Braess–Sarazin relaxation, and Uzawa relaxation, for solving the …

A fast multigrid solver is presented for high-order accurate Stokes problems discretized by
local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V …

The convection–diffusion equation with dominant convection is considered on a uniform grid
of central difference scheme. The multigrid method is used for solving the strongly …

Saddle point problems arise in a variety of applications, eg, when solving the Stokes
equations. They can be formulated such that the system matrix is symmetric, but indefinite …