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Boundary Integral Equation Method
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Book Synopsis Boundary Integral Equations by : George C. Hsiao
Download or read book Boundary Integral Equations written by George C. Hsiao and published by Springer Nature. This book was released on 2021-03-26 with total page 783 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of the book which has two additional new chapters on Maxwell’s equations as well as a section on properties of solution spaces of Maxwell’s equations and their trace spaces. These two new chapters, which summarize the most up-to-date results in the literature for the Maxwell’s equations, are sufficient enough to serve as a self-contained introductory book on the modern mathematical theory of boundary integral equations in electromagnetics. The book now contains 12 chapters and is divided into two parts. The first six chapters present modern mathematical theory of boundary integral equations that arise in fundamental problems in continuum mechanics and electromagnetics based on the approach of variational formulations of the equations. The second six chapters present an introduction to basic classical theory of the pseudo-differential operators. The aforementioned corresponding boundary integral operators can now be recast as pseudo-differential operators. These serve as concrete examples that illustrate the basic ideas of how one may apply the theory of pseudo-differential operators and their calculus to obtain additional properties for the corresponding boundary integral operators. These two different approaches are complementary to each other. Both serve as the mathematical foundation of the boundary element methods, which have become extremely popular and efficient computational tools for boundary problems in applications. This book contains a wide spectrum of boundary integral equations arising in fundamental problems in continuum mechanics and electromagnetics. The book is a major scholarly contribution to the modern approaches of boundary integral equations, and should be accessible and useful to a large community of advanced graduate students and researchers in mathematics, physics, and engineering.
Book Synopsis Direct and Indirect Boundary Integral Equation Methods by : Christian Constanda
Download or read book Direct and Indirect Boundary Integral Equation Methods written by Christian Constanda and published by CRC Press. This book was released on 2020-01-16 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Boundary Integral Equation Methods for Solids and Fluids by : Marc Bonnet
Download or read book Boundary Integral Equation Methods for Solids and Fluids written by Marc Bonnet and published by Wiley. This book was released on 1999-07-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The boundary element method is more appropriate than the finite element method to tackle linear, wave propagation, infinite domain, mobile boundaries and unknown boundaries problems. In some engineering applications, both methods are combined. This book presents the mathematical basis of this method and its computer implementation. Numerous applications to fluid mechanics, mechanics of solids, acoustics and electromagnetism are developed.
Book Synopsis The Fast Solution of Boundary Integral Equations by : Sergej Rjasanow
Download or read book The Fast Solution of Boundary Integral Equations written by Sergej Rjasanow and published by Springer Science & Business Media. This book was released on 2007-04-17 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed description of fast boundary element methods, all based on rigorous mathematical analysis. In particular, the authors use a symmetric formulation of boundary integral equations as well as discussing Galerkin discretisation. All the necessary related stability and error estimates are derived. 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.
Book Synopsis Linear Integral Equations by : Rainer Kress
Download or read book Linear Integral Equations written by Rainer Kress and published by Springer Science & Business Media. This book was released on 2013-12-04 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers alike, the author has made it as self-contained as possible, requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equations is developed within the book itself. Problems are included at the end of each chapter. For this third edition in order to make the introduction to the basic functional analytic tools more complete the Hahn–Banach extension theorem and the Banach open mapping theorem are now included in the text. The treatment of boundary value problems in potential theory has been extended by a more complete discussion of integral equations of the first kind in the classical Holder space setting and of both integral equations of the first and second kind in the contemporary Sobolev space setting. In the numerical solution part of the book, the author included a new collocation method for two-dimensional hypersingular boundary integral equations and a collocation method for the three-dimensional Lippmann-Schwinger equation. The final chapter of the book on inverse boundary value problems for the Laplace equation has been largely rewritten with special attention to the trilogy of decomposition, iterative and sampling methods Reviews of earlier editions: "This book is an excellent introductory text for students, scientists, and engineers who want to learn the basic theory of linear integral equations and their numerical solution." (Math. Reviews, 2000) "This is a good introductory text book on linear integral equations. It contains almost all the topics necessary for a student. The presentation of the subject matter is lucid, clear and in the proper modern framework without being too abstract." (ZbMath, 1999)
Book Synopsis Boundary Integral Equations in Elasticity Theory by : A.M. Linkov
Download or read book Boundary Integral Equations in Elasticity Theory written by A.M. Linkov and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: by the author to the English edition The book aims to present a powerful new tool of computational mechanics, complex variable boundary integral equations (CV-BIE). The book is conceived as a continuation of the classical monograph by N. I. Muskhelishvili into the computer era. Two years have passed since the Russian edition of the present book. We have seen growing interest in numerical simulation of media with internal structure, and have evidence of the potential of the new methods. The evidence was especially clear in problems relating to multiple grains, blocks, cracks, inclusions and voids. This prompted me, when preparing the English edition, to place more emphasis on such topics. The other change was inspired by Professor Graham Gladwell. It was he who urged me to abridge the chain of formulae and to increase the number of examples. Now the reader will find more examples showing the potential and advantages of the analysis. The first chapter of the book contains a simple exposition of the theory of real variable potentials, including the hypersingular potential and the hypersingular equations. This makes up for the absence of such exposition in current textbooks, and reveals important links between the real variable BIE and the complex variable counterparts. The chapter may also help readers who are learning or lecturing on the boundary element method.
Book Synopsis Boundary Integral Methods by : IABEM (Organization). Symposium
Download or read book Boundary Integral Methods written by IABEM (Organization). Symposium and published by Springer. This book was released on 1991 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Boundary Integral Equation Methods and Numerical Solutions by : Christian Constanda
Download or read book Boundary Integral Equation Methods and Numerical Solutions written by Christian Constanda and published by Springer. This book was released on 2016-04-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Integral Equation Methods in Scattering Theory by : David Colton
Download or read book Integral Equation Methods in Scattering Theory written by David Colton and published by SIAM. This book was released on 2013-11-15 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic book provides a rigorous treatment of the Riesz?Fredholm theory of compact operators in dual systems, followed by a derivation of the jump relations and mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions. These results are then used to study scattering problems for the Helmholtz and Maxwell equations. Readers will benefit from a full discussion of the mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions, an in-depth treatment of the use of boundary integral equations to solve scattering problems for acoustic and electromagnetic waves, and an introduction to inverse scattering theory with an emphasis on the ill-posedness and nonlinearity of the inverse scattering problem.
Book Synopsis The Boundary Element Method for Engineers and Scientists by : John T. Katsikadelis
Download or read book The Boundary Element Method for Engineers and Scientists written by John T. Katsikadelis and published by Academic Press. This book was released on 2016-10-10 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Boundary Element Method for Engineers and Scientists: Theory and Applications is a detailed introduction to the principles and use of boundary element method (BEM), enabling this versatile and powerful computational tool to be employed for engineering analysis and design. In this book, Dr. Katsikadelis presents the underlying principles and explains how the BEM equations are formed and numerically solved using only the mathematics and mechanics to which readers will have been exposed during undergraduate studies. All concepts are illustrated with worked examples and problems, helping to put theory into practice and to familiarize the reader with BEM programming through the use of code and programs listed in the book and also available in electronic form on the book’s companion website. Offers an accessible guide to BEM principles and numerical implementation, with worked examples and detailed discussion of practical applications This second edition features three new chapters, including coverage of the dual reciprocity method (DRM) and analog equation method (AEM), with their application to complicated problems, including time dependent and non-linear problems, as well as problems described by fractional differential equations Companion website includes source code of all computer programs developed in the book for the solution of a broad range of real-life engineering problems
Book Synopsis Integral Equations by : Wolfgang Hackbusch
Download or read book Integral Equations written by Wolfgang Hackbusch and published by Birkhäuser. This book was released on 2012-12-06 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis. On the other hand, integral equations are of practical interest because of the «boundary integral equation method», which transforms partial differential equations on a domain into integral equations over its boundary. This book grew out of a series of lectures given by the author at the Ruhr-Universitat Bochum and the Christian-Albrecht-Universitat zu Kiel to students of mathematics. The contents of the first six chapters correspond to an intensive lecture course of four hours per week for a semester. Readers of the book require background from analysis and the foundations of numeri cal mathematics. Knowledge of functional analysis is helpful, but to begin with some basic facts about Banach and Hilbert spaces are sufficient. The theoretical part of this book is reduced to a minimum; in Chapters 2, 4, and 5 more importance is attached to the numerical treatment of the integral equations than to their theory. Important parts of functional analysis (e. g. , the Riesz-Schauder theory) are presented without proof. We expect the reader either to be already familiar with functional analysis or to become motivated by the practical examples given here to read a book about this topic. We recall that also from a historical point of view, functional analysis was initially stimulated by the investigation of integral equations.
Book Synopsis Boundary Integral and Singularity Methods for Linearized Viscous Flow by : C. Pozrikidis
Download or read book Boundary Integral and Singularity Methods for Linearized Viscous Flow written by C. Pozrikidis and published by Cambridge University Press. This book was released on 1992-02-28 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Boundary Element Methods by : Stefan A. Sauter
Download or read book Boundary Element Methods written by Stefan A. Sauter and published by Springer Science & Business Media. This book was released on 2010-11-01 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a thorough treatment of boundary element methods (BEM) for solving strongly elliptic boundary integral equations obtained from boundary reduction of elliptic boundary value problems in $\mathbb{R}^3$. The book is self-contained, the prerequisites on elliptic partial differential and integral equations being presented in Chapters 2 and 3. The main focus is on the development, analysis, and implementation of Galerkin boundary element methods, which is one of the most flexible and robust numerical discretization methods for integral equations. For the efficient realization of the Galerkin BEM, it is essential to replace time-consuming steps in the numerical solution process with fast algorithms. In Chapters 5-9 these methods are developed, analyzed, and formulated in an algorithmic way.
Book Synopsis Integral Methods in Science and Engineering by : Barbara S Bertram
Download or read book Integral Methods in Science and Engineering written by Barbara S Bertram and published by CRC Press. This book was released on 2019-05-20 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on proceedings of the International Conference on Integral Methods in Science and Engineering, this collection of papers addresses the solution of mathematical problems by integral methods in conjunction with approximation schemes from various physical domains. Topics and applications include: wavelet expansions, reaction-diffusion systems, variational methods , fracture theory, boundary value problems at resonance, micromechanics, fluid mechanics, combustion problems, nonlinear problems, elasticity theory, and plates and shells.
Book Synopsis A Beginner's Course in Boundary Element Methods by : Whye-Teong Ang
Download or read book A Beginner's Course in Boundary Element Methods written by Whye-Teong Ang and published by Universal-Publishers. This book was released on 2007 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a course in boundary element methods for the absolute beginners. Basic concepts are carefully explained through the use of progressively more complicated boundary value problems in engineering and physical sciences. The readers are assumed to have prior basic knowledge of vector calculus (covering topics such as line, surface and volume integrals and the various integral theorems), ordinary and partial differential equations, complex variables, and computer programming. Electronic ebook edition available at Powells.com. Click on Powells logo to the left.
Book Synopsis Boundary Element Methods by : Carlos A. Brebbia
Download or read book Boundary Element Methods written by Carlos A. Brebbia and published by Springer. This book was released on 2013-10-03 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Boundary Element Method with Programming by : Gernot Beer
Download or read book The Boundary Element Method with Programming written by Gernot Beer and published by Springer Science & Business Media. This book was released on 2008-09-03 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thorough yet understandable introduction to the boundary element method presents an attractive alternative to the finite element method. It not only explains the theory but also presents the implementation of the theory into computer code, the code in FORTRAN 95 can be freely downloaded. The book also addresses the issue of efficiently using parallel processing hardware in order to considerably speed up the computations for large systems. The applications range from problems of heat and fluid flow to static and dynamic elasto-plastic problems in continuum mechanics.
