Computational grids. Generation, adaption, and solution strategies. (English) Zbl 0955.74001

Series in Computational and Physical Processes in Mechanics and Thermal Sciences. Washington, DC: Taylor & Francis. xiv, 496 p. (1997).
This book provides a comprehensive introduction to mesh generation and mesh based methods in computational mechanics. Since mesh updating in response to the solution is important, mesh generation is integrated with solution methods, which are covered in somehow less detail. The book provides a thorough treatment of algorithmic issues and touches software development, computer graphics, and mathematical foundations. Focus is on presentation of ideas, examples, and algorithms. The style is informal, lively and clear, more lecture style than a monograph. There are very few theorems and proofs. Additional material is presented as exercises at the end of every chapter. The bibliography is comprehensive (33 pages), but there are few citations in the text and no remarks on the history of the subject.
From author’s introduction: “Chapter 1 introduces ideas related to structured grid generation including such topics as mapping techniques, smoothing, PDE grid generators, renumbering, and geometric modeling. Unstructured grids and Delaunay triangulations are discussed in Chapter 2. This leads to a treatment of point insertion as a strategy for generating or refining a grid. Supporting data structures also are introduced here. A brief description of finite elements, domain error, and partitioning concludes Chapter 2. In Chapter 3, error estimators and error indicators are introduced to guide the refinement and redistribution process. For example, approaches based on residuals, a priori estimates, superconvergent projections, and extrapolations are developed. Further details of the refinement algorithms are provided in Chapter 4, which also covers transition element constraints, data structures, and refinement criteria. The idea of interweaving grid refinement with solution iterations is the main topic of Chapter 5, and this topic leads naturally to the question of acceleration by projection between grids. This subject is then treated in more detail in Chapter 6, which covers both multilevel schemes and domain decomposition. Finally, Chapters 7 and 8 concern grid redistribution and moving grid strategies, respectively.”
The book is suitable for a course for engineering, computational mathematics, or computer science graduate students. It will be also of interest to researchers in the area of computational mechanics and finite element software as an easily accessible and timely introduction.
Reviewer: J.Mandel (Denver)


74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74Sxx Numerical and other methods in solid mechanics
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis