Numerical Methods IV: Interpolation and Shape Functions

 
9781511594882: Numerical Methods IV: Interpolation and Shape Functions
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An amazingly economical version of an excellent textbook prepared for those students which prefer light books.

Format: B&W on White Paper, 8,5"x11" (216x279 mm), Paperback, 96 pages. A complete content of the parent edition (270 pgs) is scaled and rearranged to fit in the two column layout. However, the reader should take into consideration if applied 7pt font is the best choice for him. If not, the usual B&W or colour versions of this textbook are recommended.

About the book:

An excellent textbook established at several universities. Primarily written for students at technical universities, it is also a very useful handbook for engineers, PhD students and scientists. Now available in several forms at all continents.

This textbook introduces the reader into various interpolation methods. The interpolation domain is usually divided into interpolation elements, such as finite elements and boundary elements. Interpolation on these elements is provided by shape functions, which are systematically defined in global and local coordinates by using null-points, null-lines or null-planes.

Why the interpolation and shape functions are so important? Simply, because various various numerical methods (such as FEM and BEM) are based on them.

The book is divided into seven chapters. The first chapter briefly explaines a background of interpolation. There is explained a difference between simple interpolation methods and higher level interpolation methods, as well as two kinds of interpolation formulas which uses coordinate and shape functions. In the second chapter are described various polynomial interpolation methods. It is also shown how Chebyshev polynomial interpolation my suppress Runge’s phenomenon and reduce interpolation error. In the third chapter non-polynomial methods (exponential, logarithmic, and rational) are discussed. These methods are important if the interpolation is performed over the semi-infinite or infinite domain, while described Fourier interpolations should be used if the interpolation function is periodic. Piecewise interpolation with one dimensional interpolation elements and splines are described in the fourth chapter. Interpolation on triangular and rectangular elements, as well as construction of their shape functions are described in the fifth and sixth chapter. Finally, volume interpolation elements (tetrahedral, prismatic and cube elements) are described in seventh chapter.

Practical application is supported by 10 algorithms and 43 examples. Described interpolation elements can be easily used in finite and boundary element methods. Besides its practical usage, the given text with 131 figures and 26 tables, represents a valuable background for understanding, developing and applying various numerical methods.

Reviewed by:

Prof. Maja Fosner, D.Sc., University of Maribor, Slovenia

Prof. Damir Jelaska, D.Sc., University of Split, Croatia

Prof. Valery Lysenko, D.Sc., Academic of the Russian Metrological Academy, Russian Research Institute for Metrological Service, Russia

Prof. Iztok Potrc, D.Sc., University of Maribor. Slovenia

Prof. Evgeny Pushkar, D.Sc., Member correspondent of the Russian Academy of Natural Sciences, Moscow State Industrial University, Russia

Proof reading by:

Senior Lecturer, Ksenija Mance, prof., University of Rijeka, Croatia

"synopsis" may belong to another edition of this title.

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