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Meshfree methods. Moving beyond the finite element method. 2nd ed. (English) Zbl 1205.74003
Boca Raton, FL: CRC Press (ISBN 978-1-4200-8209-8/hbk; 978-1-4200-8210-4/ebook). xxi, 770 p. (2010).
This book is devoted to description of meshfree methods, and their application for solution of different engineering and scientific problems. It covers comprehensivle meshfree methods: particularly it covers basic and advanced theories, principles, techniques and procedures for solution of problems of mechanics by using a meshfree method. A large number of examples is included. Author presents an Update of a Groundbreaking Work and reflects the significant advances made in the field since the publication of its predecessor. The book “Meshfree Methods: Moving Beyond the Finite Element Method, Second Edition” systematically covers the most widely used meshfree methods. In the second edition there are much more details on fundamental concepts and important theories for numerical methods, the discussions on special properties of meshfree methods, including stability, convergence, accurate, efficiency, and bound property. Further, more detailed discussion on error estimation and adaptive analysis using meshfree methods, the developments on combined meshfree/finite element method (FEM) models and the comparison studies using meshfree and FEM are presented. Based on author’s own research, this book provides a single-source guide to meshfree techniques and theories that can effectively handle a variety of complex engineering problems. It analyzes how the methods work, explains how to use and develop the methods, and explores the problems associated with meshfree method.

MSC:
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76Mxx Basic methods in fluid mechanics
74Sxx Numerical and other methods in solid mechanics
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
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