Meissner 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
Erscheinungsjahr 2024
ISBN: 978-3-031-59302-4
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 234 Seiten, Web PDF

Reihe: Engineering (R0)

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.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Meissner, Udo F.

Inhaltsverzeichnis

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.

Über Autor(innen)

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