This book is an excellent reference for those who are already familiar with the concept and the objectives of numerical grid generation (NGG). NGG is a computer-oriented tool for the solution of partial differential equations within geometrically complex boundaries. NGG is in a rapidly developing stage and, for this reason, no reference book can remain a reference for a long time. However, there are certain derivations and formulas that will always remain of fundamental importance in any NGG technique, and about three-quarters of the book is devoted to these derivations. Of particular interest to the NGG researcher is an elaborate list of available publications (as of 1985), which is provided at the end of the book.
The book, as a whole, is written in a lucid, comprehensive style; however, a graduate-level background in numerical analysis, partial differential equations of physics, and applied mathematics is required.
The 11 chapters of the book cover the following subjects:
:9N(1) Introductory material (6 pp.)
(2) A top-level presentation of boundary-conforming transformations dealing with one-, two-, and three-dimensional regions, simply- and multiply- connected regions, branch-cut discontinuity, and embedded regions (88 pp.)
(3) Transformation Relations (141 pp.)
(4) Numerical Implementation (34 pp.)
(5) Truncation Error (16 pp.)
(6) Elliptic Generation Systems (84 pp.)
(7) Parabolic and Hyperbolic Generation Systems (6 pp.)
(8) Algebraic Generation Systems (52 pp.)
(9) Orthogonal Systems (19 pp.)
(10) Conformal Mapping (17 pp.)
(11) Adaptive Grids (55 pp.)
Three appendices (40 pp.) at the end of the book provide:9N(1) Differential-Geometric Concepts on Space Curves and Surfaces
(2) Euler Equations: Variational Principle in Transformed Space and Variational Principle in Physical Space
(3) Code Development and Computer Exercises
To make this book equally useful for newcomers to the field of NGG and as a possible text in a graduate-level course, the following suggestions are presented::9N(1) Add a chapter, preferably at the beginning of the book, where a physical example (e.g., a steady-state temperature distribution in a two-dimensional region) is solved by the NGG method. If the region and the boundary conditions are chosen with care, and the steps (from the physical model to the mathematical model to the numerical computations) are explained in detail, the reader will grasp the fundamental concept and will be able to appreciate the top-level discussions of chapter 2 and the rest of the book.
(2) Provide flow diagrams of the digital programs and the codes themselves if they are not too lengthy.
(3) Show the application of each code by presenting at least one complete case from the input to the output.
(4) After each major derivation or formulation, include a worked-out example to show the application.
(5) To keep the book size manageable, refer to references for some of the top-level discussions.
