Many software systems in the field of scientific computing, in particular in the area of computational simulations, require the user to provide a decomposition of the geometrical domain of interest into a (typically very large) set of small subregions, the archetypal examples for such cases being the now classical finite-element and finite-volume methods. The construction of such a grid is a very challenging task in itself that can only be solved with the help of highly sophisticated algorithms. Liseikin’s book provides a comprehensive description of possible approaches to construct these algorithms for generating such grids.

Written in a traditional textbook style, the book starts with an introductory section outlining the problem and a section that recalls some fundamental geometrical concepts needed later on. This is followed by a survey of the commonly used quality measures for grids. The remaining ten chapters are then devoted to a detailed discussion of a large variety of different grid generation techniques. This includes methods constructed for many different specific application scenarios; in particular, the book covers structured, unstructured, and hybrid grids; uniform grids; grids whose element sizes are adapted to the properties of the simulated process; 2D and 3D grids; triangular/tetrahedral and quadrangular/hexahedral grids; and many other facets. Indeed, I do not think that any particularly relevant aspect is missing.

Each chapter provides a thorough description of the background of the method under consideration, explains its properties, and makes clear for which type of problem it is suitable. Plenty of carefully designed instructive figures provide examples illustrating the methods’ features.

The book’s main weakness is that, due to its textbook character, it cannot really be used as a handbook by someone needing to derive a grid for a special problem. This is due to the facts that (1) the construction of the subject index does not immediately allow finding the right approach from the large number of possibilities contained in the book, and (2) the grid generation techniques are mainly described in a language that, although it is precise, needs some work to be translated into (pseudo-)code. In spite of these drawbacks, I think the text provides excellent reading for novices who want to obtain a general overview of grid generation methods, and also for experienced researchers who know which algorithm to use and who want to be reminded about certain details of their favorite approach. It is also likely to form an excellent foundation for designing a semester’s set of lectures for a course addressing graduate students.

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