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Although the aim of this book is to give a unified introduction into finite and boundary element methods, the main focus is on the numerical analysis of boundary integral and boundary element methods. Starting from the variational formulation of elliptic boundary value problems boundary integral operators and associated boundary integral equations are introduced and analyzed. By using finite and boundary elements corresponding numerical approximation schemes are considered. This textbook may serve as a basis for an introductory course in particular for boundary element methods including modern trends such as fast boundary element methods and efficient solution methods, as well as the coupling of finite and boundary element methods.

Boundary value problems --- Finite element method. --- Boundary element methods. --- Numerical solutions. --- BEM (Engineering analysis) --- BIE analysis --- BIE methods --- Boundary element analysis --- Boundary elements methods --- Boundary integral equation analysis --- Boundary integral equation methods --- Boundary integral methods --- Numerical analysis --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Isogeometric analysis --- Numerical analysis. --- Mathematics. --- Engineering mathematics. --- Numerical Analysis. --- Applications of Mathematics. --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- Math --- Science --- Mathematics --- Applied mathematics.

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This book is devoted to the basic mathematical properties of solutions to boundary integral equations and presents a systematic approach to the variational methods for the boundary integral equations arising in elasticity, fluid mechanics, and acoustic scattering theory. It may also serve as the mathematical foundation of the boundary element methods. The latter have recently become extremely popular and efficient computational tools in applications. The authors are well known for their fundamental work on boundary integral equations and related topics. This book is a major scholarly contribution to the modern theory of boundary integral equations and should be accessible and useful to a large community of mathematical analysts, applied mathematicians, engineers and scientists.

Boundary element methods. --- Integral equations. --- Equations, Integral --- Functional equations --- Functional analysis --- BEM (Engineering analysis) --- BIE analysis --- BIE methods --- Boundary element analysis --- Boundary elements methods --- Boundary integral equation analysis --- Boundary integral equation methods --- Boundary integral methods --- Numerical analysis --- Computer science --- Numerical analysis. --- Engineering mathematics. --- Differential equations, partial. --- Computational Mathematics and Numerical Analysis. --- Numerical Analysis. --- Mathematical and Computational Engineering. --- Partial Differential Equations. --- Mathematics. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Mathematical analysis --- Partial differential equations --- Engineering --- Engineering analysis --- Mathematics --- Computer mathematics. --- Applied mathematics. --- Partial differential equations. --- Boundary element methods --- Integral equations

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Symmetric Galerkin Boundary Element Method presents an introduction as well as recent developments of this accurate, powerful, and versatile method. The formulation possesses the attractive feature of producing a symmetric coefficient matrix. In addition, the Galerkin approximation allows standard continuous elements to be used for evaluation of hypersingular integrals. FEATURES • Written in a form suitable for a graduate level textbook as well as a self-learning tutorial in the field. • Covers applications in two-dimensional and three-dimensional problems of potential theory and elasticity. Additional basic topics involve axisymmetry, multi-zone and interface formulations. More advanced topics include fluid flow (wave breaking over a sloping beach), non-homogeneous media, functionally graded materials (FGMs), anisotropic elasticity, error estimation, adaptivity, and fracture mechanics. • Presents integral equations as a basis for the formulation of general symmetric Galerkin boundary element methods and their corresponding numerical implementation. • Designed to convey effective unified procedures for the treatment of singular and hypersingular integrals that naturally arise in the method. Symbolic codes using Maple® for singular-type integrations are provided and discussed in detail. • The user-friendly adaptive computer code BEAN (Boundary Element ANalysis), fully written in Matlab®, is available as a companion to the text. The complete source code, including the graphical user-interface (GUI), can be downloaded from the web site http://www.ghpaulino.com/SGBEM_book. The source code can be used as the basis for building new applications, and should also function as an effective teaching tool. To facilitate the use of BEAN, a video tutorial and a library of practical examples are provided.

Engineering. --- Numerical analysis. --- Applied mathematics. --- Engineering mathematics. --- Computational intelligence. --- Continuum mechanics. --- Structural mechanics. --- Fluid mechanics. --- Appl.Mathematics/Computational Methods of Engineering. --- Computational Intelligence. --- Numerical Analysis. --- Continuum Mechanics and Mechanics of Materials. --- Structural Mechanics. --- Engineering Fluid Dynamics. --- Hydromechanics --- Continuum mechanics --- Architectural engineering --- Engineering, Architectural --- Structural mechanics --- Structures, Theory of --- Structural engineering --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Engineering --- Engineering analysis --- Mathematical analysis --- Construction --- Industrial arts --- Technology --- Mathematics --- Galerkin methods. --- Boundary element methods. --- BEM (Engineering analysis) --- BIE analysis --- BIE methods --- Boundary element analysis --- Boundary elements methods --- Boundary integral equation analysis --- Boundary integral equation methods --- Boundary integral methods --- Numerical analysis --- Sinc-Galerkin methods --- Sinc methods --- Mechanics. --- Mechanics, Applied. --- Hydraulic engineering. --- Mathematical and Computational Engineering. --- Solid Mechanics. --- Engineering, Hydraulic --- Fluid mechanics --- Hydraulics --- Shore protection --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory