Technical book of Prof. Dr.-Ing. Udo F. Meißner published

New publication “Tensor Calculus with Object-Oriented Matrices for Numerical Methods in Mechanics and Engineering” published by Springer Vieweg

2023/03/06 by

Prof. Dr.-Ing. Udo F. Meißner, former professor at the IIB, is the author of the book “Tensor Calculus with Object-Oriented Matrices for Numerical Methods in Mechanics and Engineering Sciences” recently published by Springer Vieweg.

The Institute of Numerical Methods and Informatics in Civil Engineering (IIB) and the Support Association of the IIB congratulate Prof. Dr.-Ing. Udo F. Meißner on the publication of his new textbook, with which he further thinks the classical tensor calculus with the help of the object-oriented paradigm. Meißner himself states:

“The central concern was to synoptically elaborate the classical tensor calculus in symbolic and index notation in such a way that it can be directly implemented in numerical algorithms. The object-oriented paradigm offers the possibility of systematically dividing tensors and matrices into class structures and assigning corresponding functional and arithmetic processing methods to their objects.

What is new here is the object-oriented notation of tensor/matrix operations, which allows arithmetic operations with tensors and matrices and their management to be carried out in the same way as we are used to for scalar quantities. The programming language C++ opens up this possibility by overloading the corresponding operators. Key here is the general matrix multiplication, which also covers the various combinations with transposed matrices. For the resolution of linear systems of equations with a quadratic coefficient matrix, a matrix division can also be declared in this way.

We have tested the presented methodology in teaching at the IIB in Darmstadt and have had the best experience with it. The tensor calculation, which has so far been presented mainly theoretically, acquires through the published teachware the elegant ability to implement numerical and also graphical methods synonymously. This new methodology is exemplified by means of corresponding algorithms.

The book presents the associated software methods and shows corresponding applications of the finite element method.”

Link to the book (Springer Vieweg)

eBook ISBN: 978-3-658-39881-1

Textbuch ISBN: 978-3-658-39880-4