Trefftz and Collocation Methods
Author: Z-C. Li
Publisher: WIT Press
Published: 2008-02-22
Total Pages: 433
ISBN-13: 1845641531
DOWNLOAD EBOOK →This title was reviewed in the January 2009 issue of Mathematical Reviews.
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MATLAB and C Programming for Trefftz Finite Element Methods
Author: Qing-Hua Qin
Publisher: CRC Press
Published: 2008-07-21
Total Pages: 464
ISBN-13: 1420072765
DOWNLOAD EBOOK →Although the Trefftz finite element method (FEM) has become a powerful computational tool in the analysis of plane elasticity, thin and thick plate bending, Poisson's equation, heat conduction, and piezoelectric materials, there are few books that offer a comprehensive computer programming treatment of the subject. Collecting results scattered in t
Collocation Trefftz Method for Laplace's Equation on Annular Shaped Domains, Circular and Elliptic Boundaries
Boundary Collocation Techniques and their Application in Engineering
Author: J.A. Kołodziej
Publisher: WIT Press
Published: 2009-10-01
Total Pages: 337
ISBN-13: 1845643941
DOWNLOAD EBOOK →Methods of mathematical modelling applied in contemporary computational mechanics can be divided into purely numerical and analytical-numerical procedures. In this book, the first part is a general presentation of the boundary collocation approach and its numerous variants and in the second part the method is applied to many engineering problems.
Recent Advances in Radial Basis Function Collocation Methods
Author: Wen Chen
Publisher: Springer Science & Business Media
Published: 2013-11-09
Total Pages: 98
ISBN-13: 3642395724
DOWNLOAD EBOOK →This book surveys the latest advances in radial basis function (RBF) meshless collocation methods which emphasis on recent novel kernel RBFs and new numerical schemes for solving partial differential equations. The RBF collocation methods are inherently free of integration and mesh, and avoid tedious mesh generation involved in standard finite element and boundary element methods. This book focuses primarily on the numerical algorithms, engineering applications, and highlights a large class of novel boundary-type RBF meshless collocation methods. These methods have shown a clear edge over the traditional numerical techniques especially for problems involving infinite domain, moving boundary, thin-walled structures, and inverse problems. Due to the rapid development in RBF meshless collocation methods, there is a need to summarize all these new materials so that they are available to scientists, engineers, and graduate students who are interest to apply these newly developed methods for solving real world’s problems. This book is intended to meet this need. Prof. Wen Chen and Dr. Zhuo-Jia Fu work at Hohai University. Prof. C.S. Chen works at the University of Southern Mississippi.
Trefftz and Fundamental Solution-Based Finite Element Methods
Author: Qing-Hua Qin
Publisher: Bentham Science Publishers
Published: 2021-09-07
Total Pages: 357
ISBN-13: 9814998559
DOWNLOAD EBOOK →This reference explains hybrid-Trefftz finite element method (FEM). Readers are introduced to the basic concepts and general element formulations of the method. This is followed by topics on non-homogeneous parabolic problems, thermal analysis of composites, and heat conduction in nonlinear functionally graded materials. A brief summary of the fundamental solution based-FEM is also presented followed by a discussion on axisymmetric potential problems and the rotordynamic response of tapered composites. The book is rounded by chapters that cover the n-sided polygonal hybrid finite elements and analysis of piezoelectric materials. Key Features - Systematic presentation of 9 topics - Covers FEMs in two sections: 1) hybrid-Trefftz method and 2) fundamental FEM solutions - Bibliographic references - Includes solutions to problems in the numerical analysis of different material types - Includes solutions to some problems encountered in civil engineering (seepage, heat transfer, etc). This reference is suitable for scholars involved in advanced courses in mathematics and engineering (civil engineering/materials engineering). Professionals involved in developing analytical tools for materials and construction testing can also benefit from the methods presented in the book.
Advances in Trefftz Methods and Their Applications
Author: Carlos Alves
Publisher: Springer Nature
Published: 2020-09-30
Total Pages: 203
ISBN-13: 3030528049
DOWNLOAD EBOOK →In this book we gather recent mathematical developments and engineering applications of Trefftz methods, with particular emphasis on the Method of Fundamental Solutions (MFS). These are true meshless methods that have the advantage of avoiding the need to set up a mesh altogether, and therefore going beyond the reduction of the mesh to a boundary. These Trefftz methods have advantages in several engineering applications, for instance in inverse problems where the domain is unknown and some numerical methods would require a remeshing approach. Trefftz methods are also known to perform very well with regular domains and regular data in boundary value problems, achieving exponential convergence. On the other hand, they may also under certain conditions, exhibit instabilities and lead to ill-conditioned systems. This book is divided into ten chapters that illustrate recent advances in Trefftz methods and their application to engineering problems. The first eight chapters are devoted to the MFS and variants whereas the last two chapters are devoted to related meshless engineering applications. Part of these selected contributions were presented in the 9th International Conference on Trefftz Methods and 5th International Conference on the MFS, held in 2019, July 29-31, in Lisbon, Portugal.
Numerical Modeling of Coupled Phenomena in Science and Engineering
Author: Mario César Suárez Arriaga
Publisher: CRC Press
Published: 2008-12-01
Total Pages: 496
ISBN-13: 0203886224
DOWNLOAD EBOOK →Mathematics is a universal language. Differential equations, mathematical modeling, numerical methods and computation form the underlying infrastructure of engineering and the sciences. In this context mathematical modeling is a very powerful tool for studying engineering problems, natural systems and human society. This interdisciplinary book cont
Approximate Solution Methods in Engineering Mechanics
Author: Arthur P. Boresi
Publisher: John Wiley & Sons
Published: 2003
Total Pages: 284
ISBN-13: 9780471402428
DOWNLOAD EBOOK →The only complete collection of prevalent approximation methods Unlike any other resource, Approximate Solution Methods in Engineering Mechanics, Second Edition offers in-depth coverage of the most common approximate numerical methods used in the solution of physical problems, including those used in popular computer modeling packages. Descriptions of each approximation method are presented with the latest relevant research and developments, providing thorough, working knowledge of the methods and their principles. Approximation methods covered include: * Boundary element method (BEM) * Weighted residuals method * Finite difference method (FDM) * Finite element method (FEM) * Finite strip/layer/prism methods * Meshless method Approximate Solution Methods in Engineering Mechanics, Second Edition is a valuable reference guide for mechanical, aerospace, and civil engineers, as well as students in these disciplines.
The Trefftz Finite and Boundary Element Method
Author: Qing-Hua Qin
Publisher: Computational Mechanics
Published: 2000
Total Pages: 304
ISBN-13:
DOWNLOAD EBOOK →This text provides an accessible and up-to-date introduction to the Trefftz finite element method. The author's main emphasis is on fundamental concepts and the development of different Trefftz element formulations for stress analysis of various elastic problems. The book is a reference for postgraduate students, researchers, scientists and professional engineers in computational mechanics, structural design, and applied mathematics.
