Über die Autorin bzw. den Autor

Rubin H. Landau is professor of physics and director of the computational physics program at Oregon State University. Manuel José Páez is professor of physics at Universidad de Antioquia in Colombia. Cristian C. Bordeianu, a PhD candidate at University of Bucharest, is vice principal at Technological High School 1 in Suceava, Romania.

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"In addition to being an excellent undergraduate textbook, A Survey of Computational Physics will be useful to scientists wanting a good reference on basic computational modeling methods."--John W. Mintmire, Oklahoma State University

"This book is a welcome addition to the existing literature on the subject. It is needed as much for its pedagogical approach to computational thinking as for its choice of topics in computational physics. Its use of Java as the main programming language brings it up to date with the skills that the new generation of students will bring to class."--Ali Eskandarian, George Washington University

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"In addition to being an excellent undergraduate textbook, A Survey of Computational Physics will be useful to scientists wanting a good reference on basic computational modeling methods."--John W. Mintmire, Oklahoma State University

"This book is a welcome addition to the existing literature on the subject. It is needed as much for its pedagogical approach to computational thinking as for its choice of topics in computational physics. Its use of Java as the main programming language brings it up to date with the skills that the new generation of students will bring to class."--Ali Eskandarian, George Washington University

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A Survey of Computational Physics

Princeton University Press

Chapter One

Some people spend their entire lives reading but never get beyond reading the words on the page; they don't understand that the words are merely stepping stones placed across a fast-flowing river, and the reason they're there is so that we can reach the farther shore; it's the other side that matters. -Jos Saramago

As an introduction to the book to follow, we start this chapter with a description of how computational physics (CP) fits into the broader field of computational science, and what topics we will present as the contents of CP. We then get down to basics and examine computing languages, number representations, and programming. Related topics dealing with hardware basics are found in Chapter 14, "High-Performance Computing Hardware, Tuning, and Parallel Computing."

1.1 Computational Physics and Computational Science

This book adopts the view that CP is a subfield of computational science. This means that CP is a multidisciplinary subject combining aspects of physics, applied mathematics, and computer science (CS) (Figure 1.1), with the aim of solving realistic physics problems. Other computational sciences replace the physics with biology, chemistry, engineering, and so on, and together face grand challenge problems such as

Climate prediction Materials science Structural biology Superconductivity Semiconductor design Drug design Human genome Quantum chromodynamics Turbulence Speech and vision Relativistic astrophysics Vehicle dynamics Nuclear fusion Combustion systems Oil and gas recovery Ocean science Vehicle signature Undersea surveillance

Although related, computational science is not computer science. Computer science studies computing for its own intrinsic interest and develops the hardware and software tools that computational scientists use. Likewise, applied mathematics develops and studies the algorithms that computational scientists use. As much as we too find math and computer science interesting for their own sakes, our focus is on solving physical problems; we need to understand the CS and math tools well enough to be able to solve our problems correctly.

As CP has matured, we have come to realize that it is more than the overlap of physics, computer science, and mathematics (Figure 1.1). It is also a bridge among them (the central region in Figure 1.1) containing core elements of it own, such as computational tools and methods. To us, CP's commonality of tools and a problem-solving mindset draws it toward the other computational sciences and away from the subspecialization found in so much of physics.

In order to emphasize our computational science focus, to the extent possible, we present the subjects in this book in the form of a problem to solve, with the components that constitute the solution separated according to the scientific problem-solving paradigm (Figure 1.2 left). Traditionally, physics employs both experimental and theoretical approaches to discover scientific truth (Figure 1.2 right). Being able to transform a theory into an algorithm requires significant theoretical insight, detailed physical and mathematical understanding, and a mastery of the art of programming. The actual debugging, testing, and organization of scientific programs is analogous to experimentation, with the numerical simulations of nature being essentially virtual experiments. The synthesis of numbers into generalizations, predictions, and conclusions requires the insight and intuition common to both experimental and theoretical science. In fact, the use of computation and simulation has now become so prevalent and essential a part of the scientific process that many people believe that the scientific paradigm has been extended to include simulation as an additional dimension (Figure 1.2 right).

1.2 How to Read and Use This Book

Figure 1.3 maps out the CP concepts we cover in this book and the relations among them. You may think of this concept map as the details left out of Figure 1.1. On the left are the hardware and software components from computer science; in the middle are the algorithms of applied mathematics; on the right are the physics applications. Yet because CP is multidisciplinary, it is easy to argue that certain concepts should be moved someplace else.

A more traditional way to view the materials in this text is in terms of its use in courses. In our classes [CPUG] we use approximately the first third of the text, with its emphasis on computing tools, for a course in scientific computing (after students have acquired familiarity with a compiled language). Typical topics covered in the 10 weeks of such a course are given in Table 1.1. Some options are indicated in the caption, and, depending upon the background of the students, other topics may be included or substituted. The latter two-thirds of the text includes more physics, and, indeed, we use it for a two-quarter (20-week) course in computational physics. Typical topics covered for each term are given in Table 1.2. What with many of the latter topics being research level, we suspect that these materials can easily be used for a full year's course as well.

For these materials to contribute to a successful learning experience, we assume that the reader will work through the problem at the beginning of each chapter or unit. This entails studying the text, writing, debugging and running programs, visualizing the results, and then expressing in words what has been done and what can be concluded. Further exploring is encouraged. Although we recognize that programming is a valuable skill for scientists, we also know that it is incredibly exacting and time-consuming. In order to lighten the workload somewhat, we provide "bare bones" programs in the text and on the CD. We recommend that these be used as guides for the reader's own programs or tested and extended to solve the problem at hand. As part of this approach we suggest that the learner write up a mini lab report for each problem containing

Equations solved Numerical method Code listing Visualization Discussion Critique

The report should be an executive summary of the type given to a boss or manager; make it clear that you understand the materials but do not waste everyone's time.

One of the most rewarding uses of computers is visualizing and analyzing the results of calculations with 2-D and 3-D plots, with color, and with animation. This assists in the debugging process, hastens the development of physical and mathematical intuition, and increases the enjoyment of the work. It is essential that you learn to use visualization tools as soon as possible, and so in Chapter 3, "Visualization Tools," and Appendix C we describe...