Preliminaries

Abstract

The numerical solution of boundary value problems is indispensable in almost all fields of physics and engineering sciences. The recent development, e.g. the study of three-dimensional problems, leads to systems of a larger and larger number of equations. Although the computers have become faster and vector computers are available, new numerical methods are required. A step in this direction was the development of fast Poisson solvers in the late sixties. At that time it seemed that there exist faster numerical methods the simpler the discrete elliptic problem. The first multi-grid methods have also been applied to Poisson's equation and show an efficiency similar to that of the direct solvers. But differently from other numerical methods, the efficiency is not lost when more involved problems are to be solved.