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Smoothed Point Interpolation Methods: G Space Theory and Weakened Weakforms, by G R Liu, G Y Zhang
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Based on the widely used finite element method (FEM) and the latest Meshfree methods, a next generation of numerical method called Smoothed Point Interpolation Method (S-PIM) has been recently developed. The S-PIM is an innovative and effective combination of the FEM and the meshfree methods, and enables automation in computation, modeling and simulations -- one of the most important features of the next generation methods.
This important book describes the various S-PIM models in a systematic, concise and easy-to-understand manner. The underlying principles for the next generation of computational methods, G space theory, novel weakened weak (W2) formulations, techniques for shape functions, formulation procedures, and implementation strategies are presented in detail. Numerous examples are provided to demonstrate the efficiency and accuracy of the S-PIM solutions in comparison with the FEM and other existing methods. Effective techniques to compute solution bounds employing both S-PIM and FEM are highlighted to obtain certified solutions with both upper and lower bounds.
The book also presents a systematically way to conduct adaptive analysis for solutions of desired accuracy using these bound properties, which is another key feature of the next generation of computational methods. This will benefit researchers, engineers and students who are venturing into new areas of research and computer code development.
Readership: Researchers, practitioners, academics, and graduate students in engineering mechanics, mechanical engineering, aerospace engineering, civil engineering and computational physics.
- Sales Rank: #6032619 in Books
- Published on: 2013-10-20
- Original language: English
- Number of items: 1
- Dimensions: 9.10" h x 1.70" w x 6.20" l, 2.47 pounds
- Binding: Hardcover
- 696 pages
From the Inside Flap
Based on the widely used finite element method (FEM) and the latest Meshfree methods, a next generation of numerical method called Point Interpolation Method (PIM) has been recently developed. The PIM is an innovative and effective combination of the FEM and the meshfree methods, and enables automation in computation, modeling and simulations one of the most important features of the next generation methods.
This important book describes the various PIM models in a systematic, concise and easy-to-understand manner. The underlying principles for the next generation of computational methods, G space theory, novel weakened weak (W2) formulations, techniques for shape functions, formulation procedures, and implementation strategies are presented in detail. Numerous examples are provided to demonstrate the efficiency and accuracy of the PIM solutions in comparison with the FEM and other existing methods. Effective techniques to compute solution bounds employing both PIM and FEM are highlighted to obtain certified solutions with both upper and lower bounds.
The book also presents a systematically way to conduct adaptive analysis for solutions of desired accuracy using these bound properties, which is another key feature of the next generation of computational methods. This will benefit researchers, engineers and students who are venturing into new areas of research and computer code development.
Most helpful customer reviews
0 of 0 people found the following review helpful.
Excellent book on advanced numerical methods for postgraduate level
By Arman Khoshghalb
This book talks about a new group of numerical methods which are very efficient and innovative. The book is well written and comprehensive with lots of examples. The book is of advanced level, so I would recommend it only for post graduate level, although the authors have tried to explain everything in an easy-to-understand language.
The properties of the presented methods are discussed thoroughly and there is solid mathematics behind every statement in this book which makes it very valuable in my opinion.
Another positive aspect of this book is that the authors have released the numerical codes they have developed (in FORTRAN) which makes it attractive for PhD students who can start with the provided codes and then tailor them to their needs.
I think those readers who are already familiar with the finite element methods would benefit from this book the most.
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