5. Multigrid method

To explain the principle of the multigrid method as simply as possible, we begin by presenting the 2-Grid method, which combines two poorly performing methods to produce a highly efficient method. We consider a fine grid with step size h and a coarse grid with step size H = 2h, and the solution of a one-dimensional Poisson problem with homogeneous Dirichlet boundary conditions.

A 2-Grid cycle consists of two phases:

• a smoothing method, corresponding to two or three iterations of a relaxation method,...