These proceedings contain the introductory and specific scientific papers presented at the international "Conference on Multigrid Methods", which was held at Cologne-Porz from 23rd to 27th November, 1981.
The introductory part describes basic methods, theoretical approaches and practical aspects in a systematic way. Furthermore, some simple applications are discussed, and an exemplary multigrid program for a simple model problem is presented. The four authors of the introductory papers have tried to use a uniform notation. This has been rather difficult since in the meantime several systems of notations have come into general use, and good arguments can be found for all of them. The uniformity reached despite of these difficulties does not concern all occurring quantities but the essential ones.
The specific papers deal with the fields of theory, applications and software development. Most studies concern elliptic problems and their solution by means of difference methods. The conference and the papers reflect an increasing interest in the combination of multigrid techniques with defect correction methods as well as in the solution of singularly perturbed and (indefinite) nonlinear problems. Apart from introductory and specific papers this volume also contains a multigrid bibliography.