Tensor Calculus With Object Oriented Matrices For Numerical Methods In Mechanics And Engineering
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Tensor Calculus with Object-Oriented Matrices for Numerical Methods in Mechanics and Engineering
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.
Tensorkalkül mit objektorientierten Matrizen für numerische Methoden in Mechanik und Ingenieurwissenschaften
Die Intention des Buches ist es, für numerische Algorithmen zur Analyse von Tragstrukturen eine Synthese von klassischen Matrizen- und Tensor-Methoden einerseits und von moderner Software-Technologie andererseits auf der Basis von objektorientierten Methoden zu vollziehen. Dafür wird ein durchgängiges Methodenkonzept bereitgestellt, mit dem die theoretischen Modellierungsgrundlagen nahtlos in numerische Berechnungen umgesetzt werden können, um methodische Brüche in Teilbereichen zu überwinden. Der Schlüssel dazu liegt in der Umsetzung des objektorientierten Paradigmas bei der Modellierung der mechanisch/numerischen Strukturen und beim Entwurf von Klassen, welches inzwischen im Ingenieurwesen hinlänglich untersucht und in der Software-Entwicklung weit verbreitet ist. Als innovativer Ansatz wird den entworfenen Methoden die indexbasierte Tensor- und Matrizen-Notation zugrunde gelegt, um gleichartige Operationen mit überladenen Standardoperatoren in C++ für Tensoren und Matrizen höherer Stufe ausführen zu können. Exemplarische Anwendungen und prototypische Programme zeigen den Vorteil dieser integrativen Vorgehensweise.
Multiphysics Modeling: Numerical Methods and Engineering Applications
Multiphysics Modeling: Numerical Methods and Engineering Applications: Tsinghua University Press Computational Mechanics Series describes the basic principles and methods for multiphysics modeling, covering related areas of physics such as structure mechanics, fluid dynamics, heat transfer, electromagnetic field, and noise. The book provides the latest information on basic numerical methods, also considering coupled problems spanning fluid-solid interaction, thermal-stress coupling, fluid-solid-thermal coupling, electromagnetic solid thermal fluid coupling, and structure-noise coupling. Users will find a comprehensive book that covers background theory, algorithms, key technologies, and applications for each coupling method. - Presents a wealth of multiphysics modeling methods, issues, and worked examples in a single volume - Provides a go-to resource for coupling and multiphysics problems - Covers the multiphysics details not touched upon in broader numerical methods references, including load transfer between physics, element level strong coupling, and interface strong coupling, amongst others - Discusses practical applications throughout and tackles real-life multiphysics problems across areas such as automotive, aerospace, and biomedical engineering