Every researcher working in the area of the numerical solution of partial differential equations, as well as practitioners in the field of scientific computations, should have at least some familiarity with this powerful technique. Multigrid methods are among the most efficient iterative methods for the solution of linear systems which arise in many large scale scientific calculations. Consequently, the invention of the multigrid method in the 1960's and its subsequent development up until the present is an extremely important area of research with great practical implications. This book presents old and new results concerning the rates of convergence of multigrid iterations. The first part of these notes contains an abstract multigrid theory and its connection with general linear and nonlinear iterative methods.
Several sections are devoted to important, typical applications.
An emphasis is placed on how the latest results can influence the design of effective, robust techniques. We describe a simple one-dimensional multigrid Poisson solver in order to illustrate some of the new features of Fortran90, and how they can be used in multigrid methods. The algorithm is presented based on a heuristic discussion, and the convergence rates obtained with different smoothers are compared. Local mode analysis is used to estimate the smoothing factor and two-level convergence for the method. Copies will be mailed to the participants at the address they provided at the conference.