11R2. Numerical Modeling in Materials Science and Engineering. Series in Computational Math, Vol 32. - M Rappaz (Lab of Phys Metall, Swiss Fed Inst of Tech, Lausanne, 1015, Switzerland), M Bellet (Ecole des Mines de Paris, CEMEF, Sophia Antipolis, 06904, France), M Deville (Lab of Comput Eng, Swiss Fed Inst of Tech, Lausanne, 1015, Switzerland). Springer-Verlag, Berlin. 2003. 540 pp. ISBN 3-540-42676-0. $89.95.

Reviewed by HM Srivastava (Dept of Math and Stat, Univ of Victoria, PO Box 3045, Victoria V8W 3P4, BC, Canada).

The past two decades have witnessed an increasingly diversified account of the various numerical methods and their applications in the fields of materials science and engineering; in particular, the Monte Carlo methods, cellular automata, random walkers, atomistic methods related to molecular dynamics, boundary element methods, homogenization techniques based upon average conservation laws, and so on. The book under review is devoted to the numerical simulation and modeling in (especially) materials science and engineering. It aims at familiarizing the materials scientists and engineers with the numerical methods and techniques that are state-of-the-art in this subject.

There are ten chapters in this book. Chapter 1 (Continuous Media) introduces the equations of conservation of mass, momentum, energy and solute, initiates an investigation of the principal equations for materials behavior (which are developed in depth in Chapters 5, 6, and 7), and provides the definitions of the boundary conditions and the initial conditions. And the last chapter (Chapter 10, Appendices) consists of the sections Table of Symbols, Vector Calculus, Gauss Integration Method, Non-Dimensional Numbers, and Interpretation of the Terms of the Elementary Stiffness Matrix for a Diffusion Problem on a Triangular Linear Finite Element.

Chapter 2 (The Finite Difference Method), Chapter 3 (The Finite Element Method), and Chapter 4 (Elements of Numerical Algorithms) present lucid and more-or-less self-contained accounts of the subjects titled and also indicate the possibility of extending some of these methods to sundry more complicated cases which are not dealt with in detail in this book.

Chapter 5 (Phase Transformations), Chapter 6 (Deformations of Solids), and Chapter 7 (Incompressible Fluid Flow) provide further in-depth developments of the aforementioned principal equations for materials behavior (which were introduced in Chapter 1 itself).

The remaining chapters of this book, Chapter 8 (Inverse Methods) and Chapter 9 (Stochastic Methods) describe and illustrate the underlying general principles of each of these additional methods.

With the natural exception of Chapter 10, each chapter of this book contains a bibliography for further reading. And, more importantly, Numerical Modeling in Materials Science and Engineering is full of useful computer-generated pictures and diagrams for illustrative purposes.

In summary, this is a well written and well-organized reference book that will hopefully prove to be indispensable, especially for those materials scientists and engineers whose investigations make use of the various numerical methods and techniques developed in this book.