2. Linear Multigrid Methods

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Abstract
2.1. Introduction. This chapter is devoted to linear multigrid (MG) methods, by which we mean MG methods especially designed for linear partial differential equations. However, some examples of applications of linear MG to nonlinear problems will be given. The practical aspects of the present state of the art will also be discussed. MG principles have a much wider scope than the class of problems described here; see Brandt [102] for a bird's-eye view. The focus of this chapter is on finite difference and finite volume discretization. For finite elements, see Chapter 5. We restrict ourselves to two-dimensional (2-D) problems because this simplifies our exposition. Most of the concepts and methods discussed here carry over to 3-D. Also, not much work has been done yet on 3-D MG (see, however, Behie and Forsyth [61], Caughey [123], Fuchs and Zhao [181], Gary et al. [189], Kettler and Wesseling [330], Scott [511], Thole and Trottenberg [552], van der Wees [Va2], and van der Wees et al. [Va3]).

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