Relaxation schemes for spectral multigrid methods

Relaxation Schemes for Chebyshev Spectral Multigrid Methods

SUMMARY Two relaxation schemes for Chebyshev spectral multigrid methods are presented for elliptic equations with Dirichlet boundary conditions. The rst scheme is a pointwise-preconditioned Richardson relaxation scheme and the second is a line relaxation scheme. The line relaxation scheme provides an eecient and relatively simple approach for solving two-dimensional spectral equations. Numerica...

Spectral Multigrid Methods for Elliptic Equations Ii

A Note on Multi-block Relaxation Schemes for Multigrid Solvers

E cient and robust multigrid solvers for anisotropic problems typically use either semi-coarsened grids or implicit smoothers line relaxation in 2D and plane relaxation in 3D. However, both of these may be di cult to implement in codes using multiblock structured grids where there may be no natural de nition of a global `line' or `plane'. These multi-block structured grids are often used in uid...

Local Fourier Analysis of Space-Time Relaxation and Multigrid Schemes

We consider numerical methods for generalized diffusion equations that are motivated by the transport problems arising in electron beam radiation therapy planning. While Monte Carlo methods are typically used for simulations of the forward-peaked scattering behavior of electron beams, rough calculations suggest that grid-based discretizations can provide more efficient simulations if the discre...

Multigrid relaxation methods for systems of saddle point type ✩

In this paper, we give an overview of multigrid methods for two systems of equations, namely the Stokes equations and the incompressible poroelasticity equations. We emphasize the saddle point type aspect in these two systems and discuss their discretization on staggered and collocated grids. The basic problem is that of smoothing a system of equations that has a zero (or almost zero) block in ...