We consider the iterative solution of large sparse linear systems arising from the upwind
finite difference discretization of convection-diffusion equations. The system matrix is then an …

Before applying multigrid methods to a project, mathematicians, scientists, and engineers
need to answer questions related to the quality of convergence, whether a development will …

We consider a boundary value problem in weak form of a steady-state Riesz space-
fractional diffusion equation (FDE) of order 2-α with 0<α<1. By using a finite volume …

Parallel‐in‐time methods, such as multigrid reduction‐in‐time (MGRIT) and Parareal,
provide an attractive option for increasing concurrency when simulating time‐dependent …

In this chapter, we describe the various kinds of multigrid methods for the solution of large
sparse linear systems arising from the discretization of elliptic PDEs. We highlight an …

Applying smoothed aggregation (SA) multigrid to solve a nonsymmetric linear system, Ax=b,
is often impeded by the lack of a minimization principle that can be used as a basis for the …

In this paper, we propose a novel nonstandard local Fourier analysis (LFA) variant for
accurately predicting the multigrid convergence of problems with random and jum** …

This paper introduces a nonlinear multigrid solution approach for the discrete Boltzmann
equation discretized by an implicit second-order Finite Difference scheme. For simplicity we …

In this paper, we present three-grid Fourier analysis for multigrid methods. Due to the
recursive structure of a multigrid iteration, this analysis can be deduced from the well-known …

Parallel-in-time methods for partial differential equations (PDEs) have been the subject of
intense development over recent decades, particularly for diffusion-dominated problems. It …