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.

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.

Details

Published by: Springer

Publication Date: 2024-10-19

Format: Hardcover

ISBN-13: 9783031593017

DOI: 10.1007/978-3-031-59302-4

Dimensions: 240cm x168cm

Pages: 234