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Symmetric Galerkin boundary element method. (English) Zbl 1156.65101

Berlin: Springer (ISBN 978-3-540-68770-2/hbk). xviii, 276 p. (2008).
The rough contents of this book are as follows: Chapter 1: Introduction; Chapter 2: Boundary integral equations; Chapter 3: Two dimensional analysis; Chapter 4: Three dimensional analysis; Chapter 5: Surface gradient; Chapter 6: Axisymmetry; Chapter 7: Interface and multizone; Chapter 8: Error estimation and adaptivity; Chapter 9: Fracture mechanics; Chapter 10: Nonhomogeneous media: and Chapter 11: BEAN: Boundary Element ANalysis program. The book also contains three appendices covering some mathematical preliminaries.
It is oriented to engineering applications of boundary element methods (BEM). The authors do not get involved into formal mathematical subtleties of BEM (operator theory, fractional Sobolev spaces, etc.) but pay a tremenduous attention to the computational aspects of the Galerkin variant of BEM. They successively consider a large number of engineering problems and thoroughly comment on the mesh issue (adaptivity, reduction, etc.), accurate integration of the singular and hypersingular integrals, various types of elements, as well as on the solutions of the resulting algebraic systems. The numerical solutions are displayed in suggestive figures, most of them colored! The authors invite the readers to download the educational computer code BEAN from their site. The code possesses some post-processing capabilities.

MSC:

65N38 Boundary element methods for boundary value problems involving PDEs
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
74S15 Boundary element methods applied to problems in solid mechanics
74Rxx Fracture and damage
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J40 Boundary value problems for higher-order elliptic equations
68W30 Symbolic computation and algebraic computation
65Y15 Packaged methods for numerical algorithms

Software:

Matlab; BEAN; Maple
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