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The Fast Solution Of Boundary Integral Equations
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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 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. This book was released on 2008-11-01 with total page 0 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 Wavelets for the Fast Solution of Boundary Integral Equations by : Helmut Harbrecht
Download or read book Wavelets for the Fast Solution of Boundary Integral Equations written by Helmut Harbrecht and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fast Boundary Element Methods in Engineering and Industrial Applications by : Ulrich Langer
Download or read book Fast Boundary Element Methods in Engineering and Industrial Applications written by Ulrich Langer and published by Springer Science & Business Media. This book was released on 2012-02-02 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains eight state of the art contributions on mathematical aspects and applications of fast boundary element methods in engineering and industry. This covers the analysis and numerics of boundary integral equations by using differential forms, preconditioning of hp boundary element methods, the application of fast boundary element methods for solving challenging problems in magnetostatics, the simulation of micro electro mechanical systems, and for contact problems in solid mechanics. Other contributions are on recent results on boundary element methods for the solution of transient problems. This book is addressed to researchers, graduate students and practitioners working on and using boundary element methods. All contributions also show the great achievements of interdisciplinary research between mathematicians and engineers, with direct applications in engineering and industry.
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 Wavelet Based Fast Solution of Boundary Integral Equations by : Helmut Harbrecht
Download or read book Wavelet Based Fast Solution of Boundary Integral Equations written by Helmut Harbrecht and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 2016-03-16 with total page 242 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 Boundary Integral Equation Analyses of Singular, Potential, and Biharmonic Problems by : D. B. Ingham
Download or read book Boundary Integral Equation Analyses of Singular, Potential, and Biharmonic Problems written by D. B. Ingham and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Solution of Integral Equations by : Michael A. Golberg
Download or read book Numerical Solution of Integral Equations written by Michael A. Golberg and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1979, I edited Volume 18 in this series: Solution Methods for Integral Equations: Theory and Applications. Since that time, there has been an explosive growth in all aspects of the numerical solution of integral equations. By my estimate over 2000 papers on this subject have been published in the last decade, and more than 60 books on theory and applications have appeared. In particular, as can be seen in many of the chapters in this book, integral equation techniques are playing an increas ingly important role in the solution of many scientific and engineering problems. For instance, the boundary element method discussed by Atkinson in Chapter 1 is becoming an equal partner with finite element and finite difference techniques for solving many types of partial differential equations. Obviously, in one volume it would be impossible to present a complete picture of what has taken place in this area during the past ten years. Consequently, we have chosen a number of subjects in which significant advances have been made that we feel have not been covered in depth in other books. For instance, ten years ago the theory of the numerical solution of Cauchy singular equations was in its infancy. Today, as shown by Golberg and Elliott in Chapters 5 and 6, the theory of polynomial approximations is essentially complete, although many details of practical implementation remain to be worked out.
Book Synopsis Integral Equations and Boundary Value Problems by : MD Raisinghania
Download or read book Integral Equations and Boundary Value Problems written by MD Raisinghania and published by S. Chand Publishing. This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The tenth edition of Integral Equations and Boundary Value Problems continues to offer an in-depth presentation of integral equations for the solution of boundary value problems. The book provides a plethora of examples and step-by-step presentation of definitions, proofs of the standard results and theorems which enhance students' problem-solving skills. Solved examples and numerous problems with hints and answers have been carefully chosen, classified in various types and methods, and presented to illustrate the concepts discussed. With the author's vast experience of teaching mathematics, his approach of providing a one-stop solution to the students' problems is engaging which goes a long way for the reader to retain the knowledge gained.
Book Synopsis The Numerical Solution of Integral Equations of the Second Kind by : Kendall E. Atkinson
Download or read book The Numerical Solution of Integral Equations of the Second Kind written by Kendall E. Atkinson and published by Cambridge University Press. This book was released on 1997-06-28 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive introduction to the numerical solution of a large class of integral equations.
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 2020-03-31 with total page 111 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 Advanced Boundary Element Methods by : Joachim Gwinner
Download or read book Advanced Boundary Element Methods written by Joachim Gwinner and published by Springer. This book was released on 2018-07-28 with total page 661 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the mathematical analysis of the numerical solution of boundary integral equations treating boundary value, transmission and contact problems arising in elasticity, acoustic and electromagnetic scattering. It serves as the mathematical foundation of the boundary element methods (BEM) both for static and dynamic problems. The book presents a systematic approach to the variational methods for boundary integral equations including the treatment with variational inequalities for contact problems. It also features adaptive BEM, hp-version BEM, coupling of finite and boundary element methods – efficient computational tools that have become extremely popular in applications. Familiarizing readers with tools like Mellin transformation and pseudodifferential operators as well as convex and nonsmooth analysis for variational inequalities, it concisely presents efficient, state-of-the-art boundary element approximations and points to up-to-date research. The authors are well known for their fundamental work on boundary elements and related topics, and this book is a major contribution to the modern theory of the BEM (especially for error controlled adaptive methods and for unilateral contact and dynamic problems) and is a valuable resource for applied mathematicians, engineers, scientists and graduate students.
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 Numerical Approximation Methods for Elliptic Boundary Value Problems by : Olaf Steinbach
Download or read book Numerical Approximation Methods for Elliptic Boundary Value Problems written by Olaf Steinbach and published by Springer Science & Business Media. This book was released on 2007-12-22 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified theory of the Finite Element Method and the Boundary Element Method for a numerical solution of second order elliptic boundary value problems. This includes the solvability, stability, and error analysis as well as efficient methods to solve the resulting linear systems. Applications are the potential equation, the system of linear elastostatics and the Stokes system. While there are textbooks on the finite element method, this is one of the first books on Theory of Boundary Element Methods. It is suitable for self study and exercises are included.
Book Synopsis Rapid Solution of First Kind Boundary Integral Equations in R3* by : G. Schmidlin
Download or read book Rapid Solution of First Kind Boundary Integral Equations in R3* written by G. Schmidlin and published by . This book was released on 2002 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
