Tensor Calculus with Object-Oriented Matrices for Numerical Methods in Mechanics and Engineering: Fundamentals and Functions for Tensor/Matrix Algorithms of the Finite Element Method

Meissner, Udo F.

ISBN 10: 3031593014 / ISBN 13: 9783031593017

Published by Springer, 2024

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Bibliographic Details

• Title: Tensor Calculus with Object-Oriented Matrices for Numerical Methods in Mechanics and Engineering: Fundamentals and Functions for Tensor/Matrix Algorithms of the Finite Element Method
• Publisher: Springer
• Publication Date: 2024
• Language: English
• ISBN 10: 3031593014
• ISBN 13: 9783031593017
• Binding: Hardcover
• Condition: New

About this title

Synopsis

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.

About the Author

Prof. Dr.-Ing. Dr.-Ing. E.h. Udo F. Meissner (em. TU Darmstadt)