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Automatic mesh generation. Application to finite element methods. (English) Zbl 0808.65122

Chichester: John Wiley & Sons Ltd.. Paris: Masson. x, 333 p. (1991).
This book is a valuable addition to the vast finite element literature. It is devoted exclusively to an important part of practical implementation of the finite element method: mesh generation. After a general description of meshes and a general discussion of the methodology, various approaches for mesh generation are presented. The reader will get a rough idea of what methods are covered by looking at the following list of titles of relevant chapters: Manual and semi- automatic methods, transport-mapping methods, mesh creation by solving a partial differential equation, grid superposition-deformation, multiblock methods, advancing front methods, Voronoĭ methods and extensions, creation of surface meshes, mesh transformations. In addition, one chapter gives a brief overview of available codes for mesh generation. The last chapter is on some specific applications and possible extensions for further development.
The book was translated from its French version (1991; Zbl 0709.73093). When reading the book, one needs to be aware that some of the terminology is not in the most conventional of forms, e.g., “partial derivative equation” is used for “partial differential equation”. It is impossible to cover everything in one book. Thus, for instance, efficient mesh refinements around re-entrant corners are not discussed.
The book is highly accessible. It is especially useful for those who use the finite element method to solve physical problems imposed on complicated domains.

MSC:

65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S05 Finite element methods applied to problems in solid mechanics
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis

Citations:

Zbl 0709.73093
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