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
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Beschreibung
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.
Content
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
About the author
Prof. Dr.-Ing. Dr.-Ing. E. h. Udo F. Meissner read for his Dipl.-Ing., Dr.-Ing. and Habilitation at the University of Hannover, where he was a Professor of Mechanics. In 1990 he was appointed as a Professor of Numerical Methods and Informatics in Civil and Structural Engineering by the Technical University of Darmstadt. During 1974/75 and 1985/86 he gained visiting professorships at the UC Berkeley and at the Chuo University in Tokyo. The award as Dr.-Ing. E. h., he received from the Bauhaus-University of Weimar in 2004.
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.
Fundamentals for the integration of tensor notation, matrix calculus and object-oriented numeric Presentation of a hierarchy of basic and derived tensor/matrix classes with specific declarations Conversion of traditional matrix algebra by overloaded operators for multidimensional matrices
Autor*in
Udo F. Meissner
Themen in »Tensor Calculus with Object-Oriented Matrices for Numerical Methods in Mechanics and Engineering«
Fundamentals of Matrix Calculus Object-Oriented Matrices Fundamentals of Tensor Calculus Three-dimensional Visualization of Vector Objects Tensor Analysis for Finite Elements