Computational Partial Differential Equations: Numerical Methods and Diffpack Programming, Second Edition

Abstract

11R1. Computational Partial Differential Equations: Numerical Methods and Diffpack Programming, Second Edition. - HP Langtangen (Simula Res Lab, Martin Linges vei 17, Fornebu, PO Box 134, Lysaker, 1325, Norway). Springer-Verlag, Berlin. 2003. 855 pp. ISBN 3-540-43416-X. $69.95.Reviewed by RL Huston (Dept of Mech, Indust, and Nucl Eng, Univ of Cincinnati, PO Box 210072, Cincinnati OH 45221-0072).This is the second edition of a popular tutorial on the numerical solution of partial differential equations (PDEs). It is intended for students, researchers, and practitioners interested in developing computer codes for the solution of the equations. The stated aim of the book is to equip the reader with skills for developing simulation software for physical phenomena (particularly, solid and fluid mechanics) governed by PDEs. The flow and style of the book are numeric together with listed computer codes. The software tools are based upon Diffpack–a numerical library using C++ and object oriented modules. Prior familiarity with C++ and Diffpack is thus obviously an advantage for potential readers. However, the book is written so that readers can learn both C++ and the use of Diffpack through a series of simple introductory examples and illustrations. The book is directed toward application in the various areas of solid and fluid mechanics. The book itself is divided into seven large chapters (or sections) together with four appendices spanning over 800 pages. Chapter 1 introduces the concepts of PDE solution using Diffpack. Elements of C++ programming are included. The chapter presents several illustrations of finite difference solution of the Poisson equation and the wave equation. Chapter 2 provides an introduction to the finite-element method starting with a discussion of weighted-residual methods and concluding with the mathematics of variational formulations. The third chapter presents a discussion of the use of Diffpack’s finite element software tools. Applications in heat transfer and the solution of the wave equation are given. Chapter 4 is devoted to nonlinear problems. It discusses discretation and the solution of nonlinear PDEs using both finite-difference and finite-element methods. Chapter 5, 6, and 7 present applications in solid mechanics, fluid mechanics, and coupled solid/fluid and fluid/heat transfer problems. The book concludes with four appendices providing extensive discussions of the underlying mathematics, Diffpack topics, linear systems, and software tools for solving linear systems. In the spirit of being a tutorial and text, Computational Partial Differential Equations: Numerical Methods and Diffpack Programming has over 150 exercises and a comparable number of worked-out examples together with computational code. There is an extensive bibliography of 156 references for further reading. The book is clearly very specialized but still devoted to an important aspect of applied mechanics. Therefore, it should be of interest and use to researchers and practitioners working in computational mechanics and to students aspiring to enter that field. It should make a good text for graduate-level numeric courses. Purchase by libraries is recommended.