Preface
This monograph is intended as a course textbook for students majoring in physics, en-
gineering, or computer science in the final year of their undergraduate studies, as well
as for graduate students – either those engaged in their first research projects involv-
ing scientific computation, or those who want to really understand the “black box” of
simulation programs for use on their desktop computers. Since this book discusses
both the engineering issues in program design and the mathematical and physical
foundations of scientific computing and because it is supplemented with many end-
of-chapter exercises, it should be well-suited for self-study. The author hopes to con-
vince the readers that a behind-the-scenes look at computer simulations is well worth
the effort and will prove a rewarding and enjoyable experience (compared to e.g. just
learning to click the right buttons of a GUI of a commercial simulation package). It
is by all means an absolute prerequisite for being able to write their own simulation
programs and to adapt existing programs to their specific needs. Thus, the focus of
this book is to put the reader in a position where she is able to design and write her
own scientific programs in a high-level language. What this book does not provide
is a discussion of how to use one of the existing commercial or academic simulation
programs or packages.
The book aims to provide an overview of the basic principles underlying modern
computer simulations as applied to physics and engineering, represented here by the
unit of three disciplines: physics, mathematics, and computer science. As no book
can really discuss all methods currently in use without itself becoming of encyclo-
pedic size, I decided to emphasize the foundations and typical applications of one
of the most important classes of simulation techniques, namely mesh-free, particle
based methods, in particular the Molecular Dynamics (MD) and Monte Carlo (MC)
methods.
This textbook differs from many other books on the subject in that it utilizes a prac-
tical learning-by-doing approach to computational science. It presents the field by
providing not only many algorithms in pseudo code notation, but also many ready-
to-use code examples that show how to actually implement them in a high-level lan-
guage. I will discuss not only the mathematics and physics on which both the outlined
general principles and the presented algorithms are based, but will also show how to
design and write your own scientific computing programs. I will also discuss many
important, real-life, practical issues pertaining to code implementation, which are very
often neglected in textbooks on scientific computing. Becoming an expert in scientific
computing requires above all practice and experience and this book discusses some
