Numerical Approximation Methods For Elliptic Boundary Value Problems

Author: Olaf Steinbach
Publisher: Springer Science & Business Media
ISBN: 0387313125
File Size: 19,34 MB
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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.

Numerical Approximation Methods For Elliptic Boundary Value Problems

Author: Olaf Steinbach
Publisher: Springer Science & Business Media
ISBN: 0387688056
File Size: 70,71 MB
Format: PDF, ePub
Read: 9286
Download or Read Book

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.

Numerical Approximation Methods For Elliptic Boundary Value Problems

Author: Olaf Steinbach
Publisher: Springer
ISBN: 9781441921734
File Size: 45,20 MB
Format: PDF, ePub
Read: 2675
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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.

Hierarchical Matrices

Author: Mario Bebendorf
Publisher: Springer Science & Business Media
ISBN: 3540771476
File Size: 62,84 MB
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Hierarchical matrices are an efficient framework for large-scale fully populated matrices arising, e.g., from the finite element discretization of solution operators of elliptic boundary value problems. In addition to storing such matrices, approximations of the usual matrix operations can be computed with logarithmic-linear complexity, which can be exploited to setup approximate preconditioners in an efficient and convenient way. Besides the algorithmic aspects of hierarchical matrices, the main aim of this book is to present their theoretical background. The book contains the existing approximation theory for elliptic problems including partial differential operators with nonsmooth coefficients. Furthermore, it presents in full detail the adaptive cross approximation method for the efficient treatment of integral operators with non-local kernel functions. The theory is supported by many numerical experiments from real applications.

Finite Element And Boundary Element Techniques From Mathematical And Engineering Point Of View

Author: E. Stein
Publisher: Springer
ISBN: 3709128269
File Size: 22,43 MB
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Traditional FEM and the more recent BEM underlie many engineering computational methods and corresponding software. Both methods have their merits and also their limitations. The combination of both methods will provide an improved numerical tool in the future. The aim of this book is to present significant basic formulations of FEM and BEM and to show their common practical and mathematical foundations, their differences and possibilities for their combination. These include variational foundations, FEM and BEM for linear and non-linear elasticity and potential problems, the combination of FEM-BEM asymptotic error analysis, modifications due to corner and crack singularities and corresponding improvement of convergence, plastic analysis, numerical algorithms and engineering applications.

A Beginner S Course In Boundary Element Methods

Author: Whye-Teong Ang
Publisher: Universal-Publishers
ISBN: 1581129742
File Size: 50,73 MB
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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.

Boundary Element Methods For Engineers And Scientists

Author: Lothar Gaul
Publisher: Springer Science & Business Media
ISBN: 9783540004639
File Size: 41,65 MB
Format: PDF, ePub, Docs
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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.

Boundary Element Methods

Author: Stefan Sauter
Publisher: Springer Science & Business Media
ISBN: 9783540680932
File Size: 48,73 MB
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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.

Elliptic Problems In Nonsmooth Domains

Author: Pierre Grisvard
Publisher: SIAM
ISBN: 1611972027
File Size: 31,10 MB
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Originally published: Boston: Pitman Advanced Pub. Program, 1985.

The Finite Element Method For Elliptic Problems

Author: Philippe G. Ciarlet
Publisher: SIAM
ISBN: 0898715148
File Size: 23,89 MB
Format: PDF, ePub, Mobi
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This is the only book available that fully analyzes the mathematical foundations of the finite element method. Not only is it valuable reference and introduction to current research, it is also a working textbook for graduate courses in numerical analysis, including useful figures and exercises of varying difficulty.