Boundary Integral Equation Method
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Boundary Integral Equation Methods And Numerical Solutions
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Author : Christian Constanda
language : en
Publisher: Springer
Release Date : 2016-03-16
Boundary Integral Equation Methods And Numerical Solutions written by Christian Constanda and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-16 with Mathematics categories.
This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy. The book is intended for graduate students and researchers in the fields of boundary integral equation methods, computational mechanics and, more generally, scientists working in the areas of applied mathematics and engineering. Given its detailed presentation of the material, the book can also be used as a text in a specialized graduate course on the applications of the boundary element method to the numerical computation of solutions in a wide variety of problems.
Boundary Integral Equation Analyses Of Singular Potential And Biharmonic Problems
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Author : D. B. Ingham
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Boundary Integral Equation Analyses Of Singular Potential And Biharmonic Problems written by D. B. Ingham and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
Harmonic and biharmonic boundary value problems (BVP) arising in physical situations in fluid mechanics are, in general, intractable by analytic techniques. In the last decade there has been a rapid increase in the application of integral equation techniques for the numerical solution of such problems [1,2,3]. One such method is the boundary integral equation method (BIE) which is based on Green's Formula [4] and enables one to reformulate certain BVP as integral equations. The reformulation has the effect of reducing the dimension of the problem by one. Because discretisation occurs only on the boundary in the BIE the system of equations generated by a BIE is considerably smaller than that generated by an equivalent finite difference (FD) or finite element (FE) approximation [5]. Application of the BIE in the field of fluid mechanics has in the past been limited almost entirely to the solution of harmonic problems concerning potential flows around selected geometries [3,6,7]. Little work seems to have been done on direct integral equation solution of viscous flow problems. Coleman [8] solves the biharmonic equation describing slow flow between two semi infinite parallel plates using a complex variable approach but does not consider the effects of singularities arising in the solution domain. Since the vorticity at any singularity becomes unbounded then the methods presented in [8] cannot achieve accurate results throughout the entire flow field.
Boundary Integral Equation Methods In Eigenvalue Problems Of Elastodynamics And Thin Plates
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Author : M. Kitahara
language : en
Publisher: Elsevier
Release Date : 2014-12-03
Boundary Integral Equation Methods In Eigenvalue Problems Of Elastodynamics And Thin Plates written by M. Kitahara and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-03 with Mathematics categories.
The boundary integral equation (BIE) method has been used more and more in the last 20 years for solving various engineering problems. It has important advantages over other techniques for numerical treatment of a wide class of boundary value problems and is now regarded as an indispensable tool for potential problems, electromagnetism problems, heat transfer, fluid flow, elastostatics, stress concentration and fracture problems, geomechanical problems, and steady-state and transient electrodynamics.In this book, the author gives a complete, thorough and detailed survey of the method. It provides the only self-contained description of the method and fills a gap in the literature. No-one seriously interested in eigenvalue problems of elasticity or in the boundary integral equation method can afford not to read this book. Research workers, practising engineers and students will all find much of benefit to them.Contents: Introduction. Part I. Applications of Boundary Integral Equation Methods to Eigenvalue Problems of Elastodynamics. Fundamentals of BIE Methods for Elastodynamics. Formulation of BIEs for Steady-State Elastodynamics. Formulation of Eigenvalue Problems by the BIEs. Analytical Treatment of Integral Equations for Circular and Annular Domains. Numerical Procedures for Eigenvalue Problems. Numerical Analysis of Eigenvalue Problems in Antiplane Elastodynamics. Numerical Analysis of Eigenvalue Problems in Elastodynamics. Appendix: Dominant mode analysis around caverns in a semi-infinite domain. Part II. Applications of BIE Methods to Eigenvalue Problems of Thin Plates. Fundamentals of BIE Methods for Thin Plates. Formulation of BIEs for Thin Plates and Eigenvalue Problems. Numerical Analysis of Eigenvalue Problems in Plate Problems. Indexes.
Direct And Indirect Boundary Integral Equation Methods
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Author : Christian Constanda
language : en
Publisher: CRC Press
Release Date : 2020-01-16
Direct And Indirect Boundary Integral Equation Methods written by Christian Constanda and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-16 with Mathematics categories.
The computational power currently available means that practitioners can find extremely accurate approximations to the solutions of more and more sophisticated mathematical models-providing they know the right analytical techniques. In relatively simple terms, this book describes a class of techniques that fulfill this need by providing closed-form solutions to many boundary value problems that arise in science and engineering. Boundary integral equation methods (BIEM's) have certain advantages over other procedures for solving such problems: BIEM's are powerful, applicable to a wide variety of situations, elegant, and ideal for numerical treatment. Certain fundamental constructs in BIEM's are also essential ingredients in boundary element methods, often used by scientists and engineers. However, BIEM's are also sometimes more difficult to use in plane cases than in their three-dimensional counterparts. Consequently, the full, detailed BIEM treatment of two-dimensional problems has been largely neglected in the literature-even when it is more than marginally different from that applied to the corresponding three-dimensional versions. This volume discusses three typical cases where such differences are clear: the Laplace equation (one unknown function), plane strain (two unknown functions), and the bending of plates with transverse shear deformation (three unknown functions). The author considers each of these with Dirichlet, Neumann, and Robin boundary conditions. He subjects each to a thorough investigation-with respect to the existence and uniqueness of regular solutions-through several BIEM's. He proposes suitable generalizations of the concept of logarithmic capacity for plane strain and bending of plates, then uses these to identify contours where non-uniqueness may occur. In the final section, the author compares and contrasts the various solution representations, links them by means of boundary operators, and evaluates them for their suitability for
Mathematical And Computational Aspects
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Author : C. A. Brebbia
language : en
Publisher: Springer
Release Date : 1987-09
Mathematical And Computational Aspects written by C. A. Brebbia and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-09 with Mathematics categories.
This book contains the edited versions of most of the papers presented at the 9th International Conference on Boundary Elements held at the University of Stuttgart, Germany from August 31st to September 4th, 1987, which was organized in co-operation with the Computational Mechanics Institute and GAMM (Society for Applied Mathematics and Mechanics). This Conference, as the previous ones, aimed to review the latest developments in technique and theory and point out new advanced future trends. The emphasis of the meeting was on the engineering advances versus mathematical formulations, in an effort to consolidate the basis of many new applications. Recently engineers have proposed different techniques to solve non-linear and time dependent problems and many of these formulations needed a better mathematical understanding. Furthermore, new approximate formulations have been proposed for boundary elements which appeared to work in engineering practice, but did not have a proper theoretical background. The Conference also discussed the engineering applications of the method and concentrated on a link between BEM practitioners, industrial users and researchers working on the latest development of the method. The editors would like to express their appreciation and thanks to Ms. Liz Newman and Mr. H. Schmitz for their unstinting work in the preparation of the Conference.
The Fast Solution Of Boundary Integral Equations
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Author : Sergej Rjasanow
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-17
The Fast Solution Of Boundary Integral Equations written by Sergej Rjasanow and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-17 with Mathematics categories.
Boundary Element Methods (BEM) play an important role in modern numerical computations in the applied and engineering sciences. These methods turn out to be powerful tools for numerical studies of various physical phenomena which can be described mathematically by partial differential equations. The most prominent example is the potential equation (Laplace equation), which is used to model physical phenomena in electromagnetism, gravitation theory, and in perfect fluids. A further application leading to the Laplace equation is the model of steady state heat flow. One of the most popular applications of the BEM is the system of linear elastostatics, which can be considered in both bounded and unbounded domains. A simple model for a fluid flow, the Stokes system, can also be solved by the use of the BEM. The most important examples for the Helmholtz equation are the acoustic scattering and the sound radiation. The Fast Solution of Boundary Integral Equations provides a detailed description of fast boundary element methods which are based on rigorous mathematical analysis. In particular, a symmetric formulation of boundary integral equations is used, Galerkin discretisation is discussed, and the necessary related stability and error estimates are derived. For the practical use of boundary integral methods, efficient algorithms together with their implementation are needed. The authors therefore describe the Adaptive Cross Approximation Algorithm, starting from the basic ideas and proceeding to their practical realization. Numerous examples representing standard problems are given which underline both theoretical results and the practical relevance of boundary element methods in typical computations.
Mathematical Foundation Of The Boundary Integro Differential Equation Method
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Author : Houde Han
language : en
Publisher: Springer Nature
Release Date : 2026-01-13
Mathematical Foundation Of The Boundary Integro Differential Equation Method written by Houde Han and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2026-01-13 with Mathematics categories.
The book focuses on the mathematical foundations of boundary integro-differential equation method, with a primary focus on reducing the hypersingular integrals in traditional boundary integral equations into boundary integro-differential equations with weak singularities. It briefly introduces the theory of distributions, while the boundary integral equations method is grounded in the fundamental solutions of linear partial differential equations, hence a relatively detailed exposition of the fundamental solutions of differential equations is also provided. In the subsequent chapters, the authors sequentially discuss the boundary integro-differential equation methods and theories for Laplace equation, Helmholtz equation, Navier equations, Stokes equations, among others. Furthermore, the book addresses the boundary integro-differential equation method for certain nonlinear problems, such as thermal radiation, variational inequalities, and Steklov eigenvalue problems. Lastly, it explores the symmetric coupling issues between finite element and boundary element methods.
Boundary Integral And Singularity Methods For Linearized Viscous Flow
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Author : C. Pozrikidis
language : en
Publisher: Cambridge University Press
Release Date : 1992-02-28
Boundary Integral And Singularity Methods For Linearized Viscous Flow written by C. Pozrikidis and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-02-28 with Mathematics categories.
In addition to theory, this study focuses on practical application and computer implementation in a coherent introduction to boundary integrals, boundary element and singularity methods for steady and unsteady flow at zero Reynolds numbers.
Boundary Element Methods
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Author : Carlos A. Brebbia
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Boundary Element Methods written by Carlos A. Brebbia and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
The Boundary Integral Equation Method In Axisymmetric Stress Analysis Problems
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Author : A. A. Bakr
language : en
Publisher: Springer Verlag
Release Date : 1986
The Boundary Integral Equation Method In Axisymmetric Stress Analysis Problems written by A. A. Bakr and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Technology & Engineering categories.