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

By: Udo F. Meissner

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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.