Tensor Calculus with Object-Oriented Matrices for Numerical Methods in Mechanics and Engineering
Springer International Publishing (Verlag)
978-3-031-59301-7 (ISBN)
The intension of the book is to synthesize classical matrix and tensor methods with object-oriented software techniques and efficient matrix methods for numerical algorithms. The aim is to establish a coherent methodological framework through which the tensor-based modeling of physical phenomena can be seamlessly applied in numerical algorithms without encountering methodological inconsistencies across different sub-areas, like indexed notation of tensors and two- dimensional matrix algebra in symbolic notation.
The key to an effective solution lies in object-oriented numerical structures and software design. The author presents a coherent integration of tensor-based theory through multi-dimensional matrix calculus to object-oriented numeric classes and methods for adequate simulations.
The index-based tensor and matrix notation and the object-oriented overloading of standard operators in C++ offers an innovative means to define comparable matrix operations for processing matrix objects of higher order. Typical applications demonstrate the advantages of this unique integration.
Prof. Dr.-Ing. Dr.-Ing. E.h. Udo F. Meißner (em. TU Darmstadt)
Fundamentals of tensor and matrix calculus.- Object-oriented matrix methods.- Tensor basis and metrics.- Three-dimensional visualization.- Tensor analysis for Finite Elements.- Object-oriented numeric.
| Erscheinungsdatum | 19.10.2024 |
|---|---|
| Zusatzinfo | X, 234 p. 1 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 168 x 240 mm |
| Themenwelt | Technik ► Bauwesen |
| Weitere Fachgebiete ► Handwerk | |
| Schlagworte | Fundamentals of Matrix Calculus • Fundamentals of Tensor Calculus • Object-Oriented Matrices • Tensor Analysis for Finite Elements • Three-dimensional Visualization of Vector Objects |
| ISBN-10 | 3-031-59301-4 / 3031593014 |
| ISBN-13 | 978-3-031-59301-7 / 9783031593017 |
| Zustand | Neuware |
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