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Programming finite elements in Java
Nikishkov G., Springer Publishing Company, Incorporated, New York, NY, 2010. 402 pp. Type: Book (978-1-848829-71-8)
Date Reviewed: Jan 30 2013

Finite element analysis is a technique from applied mathematics that is widely used to model stress forces, fluid dynamics, and other mechanical processes. The best thing about this book is that it is good for computer scientists as well as mechanical engineers. The author uses a Java implementation of solid mechanics software, which was developed by him and is freely available for download from the publisher. It may take the casual Java programmer some time to get it up and running, but it works, it is portable, and it pays back.

Throughout the book, the author provides, in an object-oriented paradigm, clear and compact Java code snippets extracted from his own software application.

The finite element method (FEM) has three main steps: preprocessing, processing, and post-processing. This could have been better emphasized in the book. Preprocessing deals with geometry, mesh generation, and preparing the test case. The processing step produces an equation system and uses numerical algorithms to compute a solution. Post-processing is used to visualize and interpret the results.

The book has four parts. The first covers the general formulation of the FEM. It is clear and well written, and is one of the strong points for recommending this book as an introductory finite element text for computer scientists. Chapter 1 introduces the FEM formulation. Chapter 2 presents finite element equations for heat transfer. Chapter 3 introduces the FEM for solid mechanics problems, and chapter 4 briefly reviews the FEM program structure using object-oriented concepts.

Part 2 covers the algorithms and implementations used for the finite element solution of solid mechanics problems. The class structure is described in chapters 5 to 9, assembly of the finite element equation system is explained in chapters 14 to 17, and the solution is discussed in chapters 18 and 19. Chapters 10 to 13 cover 2D and 3D isoparametric and quadratic elements.

Part 3 explores computational geometry and mesh generation problems using 2D and 3D examples. In my opinion, this part should have been presented before the assembly of the global equation system, because it falls under FEM pre-processing. That would have made Part 2 on FEM processing easier to follow. As it stands, this part comprises chapters 20 to 25.

The last part deals with scientific visualization of the results, which requires the Java 3D package. Fortunately, the author shows how visualization techniques are implemented. Most other books use closed-source or highly complex visualization tools for the post-processing step, so this is a plus for clarity. This part spans chapters 26 to 32 and does not require a background in computer graphics.

The book has four appendices on using the solid mechanics software. Appendix D has a complete step-by-step example of a solid mechanics 3D test case using the software from the book.

The intended audience includes advanced undergraduate students in finite element analysis courses and graduate students in introductory FEM courses. Scientists and engineers who are familiar with FEM techniques can benefit from the book’s discussion of object-oriented implementation. Although not specifically declared as such, this book would also be highly valuable for computer scientists who want to learn about computational science and engineering and the FEM. It goes well with the books by Tveito and Winther [1] and Bærentzen et al. [2].

Reviewer:  Alin Anton Review #: CR140888 (1305-0349)
1) Tveito, A.; Winther, R. Introduction to partial differential equations: a computational approach. Springer, New York, NY, 1998.
2) Bærentzen, J. A.; Gravesen, J.; Anton, F.; Aanæs, H. Guide to computational geometry processing: foundations, algorithms, and methods. Springer, New York, NY, 2012.
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