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Author: Weifeng Tang Publisher: Springer Science & Business Media ISBN: 3642834655 Category : Technology & Engineering Languages : en Pages : 216
Book Description
CHAPTER 1 1-1 NUMERICAL METHODS For the last two or three decades, scientists and engineers have used numerical methods as an important tool in many different areas. This significant fact has its inexorable historical trend and it is the inevitable outcome of the recent developments in science, technology and industry. Analytical methods have been developed for a long period and have produced a great amount of successful results, but they failed to solve most practical engineering problems with complicated boundary conditions or irregular geometry. It is also very difficult to solve non-linear or time-dependent problems using analytical approaches, even if they are very simple. On the other hand, research on analytical methods has provided a solid foundation for different types of numerical methods. Because of the rapid developments of science and technology it is now necessary to solve complicated problems using more efficient and accurate approaches than before. Not only problems with complicated boundary conditions or irregular configurations require solutions but also non-linear or time-dependent problems must be solved. Computer hardware and software have developed at an unexpected high speed. During the last thirty years, ithaz become possible for scientists and engineers to use numerical methods with computers easily. This has 2 stimulated scientists and engineers to improve some classical numerical methods (such as finite difference method) and to establish new numerical methods (such as the finite element method and boundary element method). For all these reasons, numerical methods have rapidly developed in the areas of mechanics and engineering.
Author: Weifeng Tang Publisher: Springer Science & Business Media ISBN: 3642834655 Category : Technology & Engineering Languages : en Pages : 216
Book Description
CHAPTER 1 1-1 NUMERICAL METHODS For the last two or three decades, scientists and engineers have used numerical methods as an important tool in many different areas. This significant fact has its inexorable historical trend and it is the inevitable outcome of the recent developments in science, technology and industry. Analytical methods have been developed for a long period and have produced a great amount of successful results, but they failed to solve most practical engineering problems with complicated boundary conditions or irregular geometry. It is also very difficult to solve non-linear or time-dependent problems using analytical approaches, even if they are very simple. On the other hand, research on analytical methods has provided a solid foundation for different types of numerical methods. Because of the rapid developments of science and technology it is now necessary to solve complicated problems using more efficient and accurate approaches than before. Not only problems with complicated boundary conditions or irregular configurations require solutions but also non-linear or time-dependent problems must be solved. Computer hardware and software have developed at an unexpected high speed. During the last thirty years, ithaz become possible for scientists and engineers to use numerical methods with computers easily. This has 2 stimulated scientists and engineers to improve some classical numerical methods (such as finite difference method) and to establish new numerical methods (such as the finite element method and boundary element method). For all these reasons, numerical methods have rapidly developed in the areas of mechanics and engineering.
Author: L. Škerget Publisher: WIT Press ISBN: 1845641000 Category : Mathematics Languages : en Pages : 321
Book Description
The sub-domain techniques in the BEM are nowadays finding its place in the toolbox of numerical modellers, especially when dealing with complex 3D problems. We see their main application in conjunction with the classical BEM approach, which is based on a single domain, when part of the domain needs to be solved using a single domain approach, the classical BEM, and part needs to be solved using a domain approach. This has usually been done in the past by coupling the BEM with the FEM, however, it is much more efficient to use a combination of the BEM and a BEM sub-domain technique. The advantage arises from the simplicity of coupling the single domain and multi-domain solutions, and from the fact that only one formulation needs to be developed, rather than two separate formulations based on different techniques. There are still possibilities for improving the BEM sub-domain techniques. However, considering the increased interest and research in this approach we believe that BEM sub-domain techniques will become a logical choice in the future substituting the FEM whenever an efficient solution requires coupling of the BEM with a domain technique.
Author: Vladimír Sládek Publisher: Computational Mechanics ISBN: Category : Mathematics Languages : en Pages : 456
Book Description
A text in singular integrals in boundary element methods. Topics covered include: treatment in crack problems; regularization of boundary integral equations by the derivative transfer method; regularization and evaluation of singular domain integrals in boundary element methods and others.
Author: Youssef F. Rashed Publisher: Witpress ISBN: Category : Mathematics Languages : en Pages : 272
Book Description
Describing the most up-to-date methods for the transformation of the domain integrals to the boundary, this book includes both analytical and numerical techniques.
Author: Steffen Marburg Publisher: Springer Science & Business Media ISBN: 3540774483 Category : Science Languages : en Pages : 584
Book Description
The book provides a survey of numerical methods for acoustics, namely the finite element method (FEM) and the boundary element method (BEM). It is the first book summarizing FEM and BEM (and optimization) for acoustics. The book shows that both methods can be effectively used for many other cases, FEM even for open domains and BEM for closed ones. Emphasis of the book is put on numerical aspects and on treatment of the exterior problem in acoustics, i.e. noise radiation.
Author: Athanasios S. Fokas Publisher: SIAM ISBN: 1611973821 Category : Mathematics Languages : en Pages : 290
Book Description
This book describes state-of-the-art advances and applications of the unified transform and its relation to the boundary element method. The authors present the solution of boundary value problems from several different perspectives, in particular the type of problems modeled by partial differential equations (PDEs). They discuss recent applications of the unified transform to the analysis and numerical modeling of boundary value problems for linear and integrable nonlinear PDEs and the closely related boundary element method, a well-established numerical approach for solving linear elliptic PDEs. The text is divided into three parts. Part I contains new theoretical results on linear and nonlinear evolutionary and elliptic problems. New explicit solution representations for several classes of boundary value problems are constructed and rigorously analyzed. Part II is a detailed overview of variational formulations for elliptic problems. It places the unified transform approach in a classic context alongside the boundary element method and stresses its novelty. Part III presents recent numerical applications based on the boundary element method and on the unified transform.
Author: Levon G. Petrosian Publisher: CRC Press ISBN: 1000585697 Category : Technology & Engineering Languages : en Pages : 571
Book Description
- Introduces a general approach to the method of integral transforms based on the spectral theory of the linear differential operators. - Presents a new, versatile foundation model with a number of advantages over the ground-based models currently used in practical calculations. - Provides new transforms which will aid in solving various problems relevant to bars, beams, plates, and shells in particular for the structures on elastic foundation. - Examines the methods of solving boundary-value problems typical for structural mechanics and related fields.
Author: Weifeng Tang
Author: Weifeng Tang
Author: L. Škerget
Author: Vladimír Sládek
Author: Youssef F. Rashed
Author: Steffen Marburg
Author: Friedel Hartmann
Author: 
Author: Zhixiong Gong
Author: Athanasios S. Fokas
Author: Levon G. Petrosian