Udo F. 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

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Verlag: Springer / Springer Nature Switzerland / Springer, Berlin
• Artikelnr. des Verlages: 978-3-031-59301-7
• Seitenzahl: 244
• Erscheinungstermin: 19. Oktober 2024
• Englisch
• Abmessung: 246mm x 173mm x 19mm
• Gewicht: 529g
• ISBN-13: 9783031593017
• ISBN-10: 3031593014
• Artikelnr.: 70248987

Autorenporträt

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

Inhaltsangabe

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.