The Boundary-Domain Integral Method for Elliptic Systems
The Boundary-Domain Integral Method for Elliptic Systems

Author: Andreas Pomp

Publisher: Springer

Published: 2006-11-14

Total Pages: 175

ISBN-13: 3540696970

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This monograph gives a description of all algorithmic steps and a mathematical foundation for a special numerical method, namely the boundary-domain integral method (BDIM). This method is a generalization of the well-known boundary element method, but it is also applicable to linear elliptic systems with variable coefficients, especially to shell equations. The text should be understandable at the beginning graduate-level. It is addressed to researchers in the fields of numerical analysis and computational mechanics, and will be of interest to everyone looking at serious alternatives to the well-established finite element methods.

Strongly Elliptic Systems and Boundary Integral Equations
Strongly Elliptic Systems and Boundary Integral Equations

Author: William Charles Hector McLean

Publisher: Cambridge University Press

Published: 2000-01-28

Total Pages: 376

ISBN-13: 9780521663755

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This 2000 book provided the first detailed exposition of the mathematical theory of boundary integral equations of the first kind on non-smooth domains.

Boundary Element Methods in Engineering and Sciences
Boundary Element Methods in Engineering and Sciences

Author: M. H. Aliabadi

Publisher: World Scientific

Published: 2011

Total Pages: 412

ISBN-13: 184816579X

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The boundary element method (BEM), also known as the boundary integral equation method (BIEM), is a modern numerical technique. It is an established alternative to traditional computational methods of engineering analysis. This book provides a comprehensive account of the method and its application to problems in engineering and science.

Integral Methods in Science and Engineering
Integral Methods in Science and Engineering

Author: Christian Constanda

Publisher: Springer

Published: 2019-07-18

Total Pages: 476

ISBN-13: 3030160777

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This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. The chapters in this book are based on talks given at the Fifteenth International Conference on Integral Methods in Science and Engineering, held July 16-20, 2018 at the University of Brighton, UK, and are written by internationally recognized researchers. The topics addressed are wide ranging, and include: Asymptotic analysis Boundary-domain integral equations Viscoplastic fluid flow Stationary waves Interior Neumann shape optimization Self-configuring neural networks This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential tool.

Boundary Element Methods
Boundary Element Methods

Author: Stefan A. Sauter

Publisher: Springer Science & Business Media

Published: 2010-11-01

Total Pages: 575

ISBN-13: 3540680934

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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.

Integral Methods in Science and Engineering, Volume 1
Integral Methods in Science and Engineering, Volume 1

Author: Christian Constanda

Publisher: Birkhäuser

Published: 2017-09-08

Total Pages: 342

ISBN-13: 3319593846

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This contributed volume contains a collection of articles on the most recent advances in integral methods. The first of two volumes, this work focuses on the construction of theoretical integral methods. Written by internationally recognized researchers, the chapters in this book are based on talks given at the Fourteenth International Conference on Integral Methods in Science and Engineering, held July 25-29, 2016, in Padova, Italy. A broad range of topics is addressed, such as:• Integral equations• Homogenization• Duality methods• Optimal design• Conformal techniques This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines, and to other professionals who use integration as an essential tool in their work.

The Fast Solution of Boundary Integral Equations
The Fast Solution of Boundary Integral Equations

Author: Sergej Rjasanow

Publisher: Springer Science & Business Media

Published: 2007-04-17

Total Pages: 285

ISBN-13: 0387340424

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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.

Integral Methods in Science and Engineering
Integral Methods in Science and Engineering

Author: M. Zuhair Nashed

Publisher: Springer Science & Business Media

Published: 2006-11-24

Total Pages: 311

ISBN-13: 0817644504

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The quantitative and qualitative study of the physical world makes use of many mathematical models governed by a great diversity of ordinary, partial differential, integral, and integro-differential equations. An essential step in such investigations is the solution of these types of equations, which sometimes can be performed analytically, while at other times only numerically. This edited, self-contained volume presents a series of state-of-the-art analytic and numerical methods of solution constructed for important problems arising in science and engineering, all based on the powerful operation of (exact or approximate) integration. The volume may be used as a reference guide and a practical resource. It is suitable for researchers and practitioners in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines.

Open Quantum Systems I
Open Quantum Systems I

Author: Stéphane Attal

Publisher: Springer

Published: 2006-08-18

Total Pages: 347

ISBN-13: 3540339221

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Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.