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 Franz J. Vesely: Computational Physics - An Introduction Second Edition Kluwer Academic / Plenum Publishers, New York-London 2001. ISBN 0-306-46631-7

# Preface: What is Computational Physics?

Computational physics is physics done by means of computational methods. Computers do not enter into this tentative definition. A number of fundamental techniques of our craft were introduced by Newton, Gauss, Jacobi, and other pioneers who lived quite some time before the invention of workable calculating machines. To be sure, nobody in his right state of mind would apply stochastic methods by throwing dice, and the iterative solution of differential equations is feasible only in conjunction with the high computing speed of electronic calculators. Nevertheless, computational physics is much more than ``Physics Using Computers.''

The essential point in computational physics is not the use of machines, but the systematic application of numerical techniques in place of, and in addition to, analytical methods, in order to render accessible to computation as large a part of physical reality as possible.

In all quantifying sciences the advent of computers rapidly extended the applicability of such numerical methods. In the case of physics, however, it triggered the evolution of an entirely new field with its own goals, its own problems, and its own heroes. Since the late forties, computational physicists have developed new numerical techniques (Monte Carlo and molecular dynamics simulation, fast Fourier transformation), discovered unexpected physical phenomena (Alder vortices, shear thinning), and posed new questions to theory and experiment (chaos, strange attractors, cellular automata, neural nets, spin glasses, ...).

An introductory text on computational physics must first of all provide the basic numerical/computational techniques. This will be done in Parts I and II. These chapters differ from the respective treatments in textbooks on numerical mathematics in that they are less comprehensive - only those methods that are of importance in physics will be described - and in focusing more on ``recipes'' than on stringent proofs.

Having laid out the tools, we may then go on to explain specific problems of computational physics. Part III provides a - quite subjective - selection of modern fields of research. A systematic classification of applied computational physics is not possible, and probably not even necessary. In fact, all areas of physics have been fertilized, and to some extent transformed, by the massive (and intelligent) use of numerical methods. Any more advanced sequels to this introductory book would therefore have to be either collections of contributions by several authors, or else monographs on various subfields of computational physics.

Appendix A is devoted to a short description of some properties of computing machines. In addition to those inaccuracies and instabilities that are inherent in the numerical methods themselves, we have always to keep in mind the sources of error that stem from the finite accuracy of the internal representation of numbers in a computer.

In Appendix Ban outline of the technique of ``Fast Fourier Transformation'' (FFT)   is given. The basic properties and the general usefulness of the Fourier transform need no explanation, and its discretized version is easy to understand. But what about the practical implementation? By simply ``coding along'' we would end up at an impasse. The expense in computing time would increase as the square of the number N of tabulated values of the function to be transformed, and things would get sticky above N=500 or so. A trick that is usually ascribed to the authors Cooley and Tukey leads to a substantial acceleration that only renders the procedure practicable. In this fast method, the computing time increases as N log2 N only, so that table lengths of the order N=10.000 are no problem at all.

When pregnant with a book, one should avoid people. If, however, one has to seek them, be it to ask for advice, to request support or to beg for the taking over of teaching loads, they should be such patient and helpful people like Renato Lukac, Martin Neumann, Harald Posch, Georg Reischl or Konrad Singer.

What one is doing to one's family cannot be made good by words alone.

Franz J. Vesely
March 1993

# Preface to Second Edition 2001

In a rapidly evolving field such as computational physics, six years is an eternity. Even though many of the elementary techniques described here are of venerable age, their assembly into sophisticated combined methods and their intensive application to ever new problems is an ongoing and exciting process. After six years, a new edition of this textbook must therefore take into account some of the new vistas that have opened up recently.

Apart from these additions and some didactic improvements, the general structure of the book holds good. The first three chapters are devoted to a thorough, if concise, treatment of the main ingredients from numerical mathematics: finite differences, linear algebra, and stochastics. This exercise will prove valuable when we proceed, in chapters 4 and 5, to combine these elementary tools into powerful instruments for the integration of differential equations. The final chapters are devoted to a number of applications in selected fields: statistical physics, quantum mechanics, and hydrodynamics.

I will gradually augment this text by web-resident sample programs. These will be written in JAVA and will be accompanied by short explanations and references to this text. Thus it may prove worthwhile to pay an occasional visit to my web-site

homepage.univie.ac.at/Franz.Vesely/cp0102/

to see if any new applets have sprung up.

August 2000