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Boundary elements. An introductory course. (English) Zbl 0691.73033
Southampton etc.: Computational Mechanics Publications; New York etc.: McGraw-Hill Book Company. 293 p. (1989).
This book is essentially an updated version of the first boundary element book written by the first author [Boundary element method for engineers (1978; Zbl 0414.65060)]. Rather than presenting the latest developments and the now available different applications of the method to various engineering problems, it concentrates on basic potential (Laplace or Poisson) equations and the standard elastostatic implementation. The numerical discretization is discussed in detail for 2-D problems, including a range from constant to quadratic elements and a series of well documented FORTRAN subroutines, which permits the student to build up standard BE codes. Chapter 1 discusses some of the fundamental concepts of approximate solutions and weighted residual techniques, Chapter 2 introduces potential problems. Chapter 3 concentrates on the general elastostatic formulation and Chapter 4 includes details of the 2- D implementation. The combination of the technique with finite elements and other topics (such as fracture mechanics) is left to Chapter 5.
The book is ideally suited as a first reading introduction to the subject, but lacks a comprehensive updated reference list to classical and further state-of-the-art applications.
Reviewer: J.C.F.Telles

74S30 Other numerical methods in solid mechanics (MSC2010)
65R20 Numerical methods for integral equations
74-04 Software, source code, etc. for problems pertaining to mechanics of deformable solids
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs