Author: W.L. Wendland Publisher: Springer Science & Business Media ISBN: 3642607918 Category : Technology & Engineering Languages : en Pages : 506
Book Description
The so-called boundary element methods BEM, i.e. finite element approxima tions of boundary integral equations have been improved recently even more vividly then ever before and found some remarkable support by the German Research Foundation DFG in the just finished Priority Research Program "boundary element methods" . When this program began, we could start from several already existing particular activities which then during the six years initiated many new re sults and decisive new developments in theory and algorithms. The program was started due to encouragement by E. Stein, when most of the later par ticipants met in Stuttgart at a Boundary Element Conference 1987. Then W. Hackbusch, G. Kuhn, S. Wagner and W. Wendland were entrusted with writing the proposal which was 1988 presented at the German Research Foun dation and started in 1989 with 14 projects at 11 different universities. After German unification, the program was heavily extended by six more projects, four of which located in Eastern Germany. When we started, we were longing for the following goals: 1. Mathematicians and engineers should do joint research. 2. Methods and computational algorithms should be streamlined with re spect to the new computer architectures of vector and parallel computers. 3. The asymptotic error analysis of boundary element methods should be further developed. 4. Non-linear material laws should be taken care of by boundary element methods for crack-mechanics. 5. The coupling of finite boundary elements should be improved.
Author: Lothar Gaul Publisher: Springer Science & Business Media ISBN: 9783540004639 Category : Computers Languages : en Pages : 896
Book Description
This introductory course on the classical Boundary Element Method also contains advanced topics such as the Dual Reciprocity and the Hybrid Boundary Element Methods. The latter methods are extensions that permit the application of BME to anisotropic materials, as well as multi-field problems and fluid-structure interaction. The class-tested textbook offers a clear and easy-to-understand introduction to the subject, including worked-out examples that describe all the basic features of the method. The first two chapters not only establish the mathematical basis for BEM but also review the basics of continuum mechanics for field problems, perhaps a unique feature for a text on numerical methods. This helps the reader to understand the physical principles of the field problems, to apply the method judiciously, and toe critically evaluate the results.
Author: Joachim Gwinner Publisher: Springer ISBN: 3319920014 Category : Mathematics Languages : en Pages : 661
Book Description
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.
Author: C. A. Brebbia Publisher: Springer ISBN: 1489928774 Category : Technology & Engineering Languages : en Pages : 268
Book Description
As the Boundary Element Method develops into a tool of engineering analysis more effort is dedicated to studying new applications and solving different problems. This book contains chapters on the basic principles of the technique, time dependent problems, fluid mechanics, hydraulics, geomechanics and plate bending. The number of non-linear and time dependent problems which have become amenable to solution using boundary elements have induced many researchers to investigate in depth the basis of the method. Chapter 0 of this book presents an ap proach based on weighted residual and error approximations, which permits easy construction of the governing boundary integral equations. Chapter I reviews the theoretical aspects of integral equation formulations with emphasis in their mathematical aspects. The analysis of time dependent problems is presented in Chap. 2 which describes the time and space dependent integral formulation of heat conduction problems and then proposes a numerical procedure and time marching algorithm. Chapter 3 reviews the application of boundary elements for fracture mechanics analysis in the presence of thermal stresses. The chapter presents numerical results and the considerations on numerical accuracy are of interest to analysts as well as practising engineers.
Author: Carlos A. Brebbia Publisher: Springer ISBN: 3662296519 Category : Science Languages : en Pages : 273
Book Description
This series has been developed in response to the interest shown in boundary ele ments by scientists and engineers. Whilst Volume I was dedicated to basic principles and applications, this book is concerned with the state of the art in the solution of time-dependent problems. Since papers have recently been published on this im portant topic it is time to produce a work ofa morepermanent nature. The volume begins with a chapter on the Fundamentals of Boundary Integral Equation Methods in Elastodynamics. After reviewing the basic equations of elasto dynamics, the wave equation and dynamic reciprocal theorems are stated and the direct and indirect boundary element formulations are presented. Eigenvalue problems are discussed together with the case of the Fourier transformations. Several applications illustrate the etfectiveness ofthe technique for engineering. Chapter 2 examines some ofthe various boundary integral equation formulations available for elastodynamic problems. In particular the displacement-traction for mulation is compared with the displacement-potential case. The special character istics ofthe elastodynamics fundamental solutions are discussed in detail and a criti cal comparison with the elastostatics case is presented. While the chapter is not meant to be a complete review of the work in the field, the original presentation of the problern and the suggestions for further work make an important contribu tion to the development ofthe method.
Author: C. A. Brebbia Publisher: Springer Science & Business Media ISBN: 3642488609 Category : Technology & Engineering Languages : en Pages : 479
Book Description
VI SOCRATES: I think that we ought to stress that we will write only about things that we have first hand experience in, in a coherent way that will be useful to engineers and other scientists and stressing the formulation without being too mathematical. We should write with integrity and honesty, giving reference to other authors where reference is due, but avoiding mentioning everybody just to be certain that our book is widely advertised. Above all, the book should be clear and useful. PLATO: I think we should include a good discussion of fundamental ideas, of how integral equations are formed, pointing out that they are like two dimensional shadows of three dimensional objects, ... SOCRATES: Stop there! Remember you are not 'the' Plato! PLATO: Sorry, I was carried away. ARISTOTLE: I think that the book should have many applications so that the reader can learn by looking at them how to use the method. SOCRATES: I agree. But we should be careful. It is easy to include many illustra tions and examples in a book in order to disguise its meagre contents. All examples should be relevant. ARISTOTLE: And we should also include a full computer program to give the reader if so he wishes, a working experience of the technique.
Author: S. Kobayashi Publisher: Springer Science & Business Media ISBN: 3662061538 Category : Technology & Engineering Languages : en Pages : 422
Book Description
The Boundary Element Methods (BEM) has become one of the most efficient tools for solving various kinds of problems in engineering science. The International Association for Boundary Element Methods (IABEM) was established in order to promote and facilitate the exchange of scientific ideas related to the theory and applications of boundary element methods. The aim of this symposium is to provide a forum for researchers in boundary element methods and boundary-integral formulations in general to present contemporary concepts and techniques leading to the advancement of capabilities and understanding of this com putational methodology. The topics covered in this symposium include mathematical and computational aspects, applications to solid mechanics, fluid mechanics, acoustics, electromagnetics, heat transfer, optimization, control, inverse problems and other interdisciplinary problems. Papers deal ing with the coupling of the boundary element method with other computational methods are also included. The editors hope that this volume presents some innovative techniques and useful knowl edge for the development of the boundary element methods. February, 1992 S. Kobayashi N. Nishimura Contents Abe, K.
Author: Gernot Beer Publisher: Springer Science & Business Media ISBN: 3211715762 Category : Technology & Engineering Languages : en Pages : 496
Book Description
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.
Author: Ulrich Langer Publisher: Springer Science & Business Media ISBN: 3642256708 Category : Technology & Engineering Languages : en Pages : 278
Book Description
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.
Author: W.L. Wendland
Author: Lothar Gaul
Author: Joachim Gwinner
Author: C. A. Brebbia
Author: Carlos A. Brebbia
Author: C. A. Brebbia
Author: S. Kobayashi
Author: Gernot Beer
Author: Goong Chen
Author: Ulrich Langer