The cell method for electrical engineering and multiphysics problems. An introduction
The book under review introduces the cell method, which is a numerical scheme for the solution of field problems governed by partial differential equations. This method is based on a space-time tessellation and it is strongly related with the work of Tonti on classification diagrams, namely, the Tonti diagrams. The content of the volume is divided into the following six chapters: 1. Tonti diagrams; 2. Topological equations; 3. Constitutive equations; 4. Classical physical problems; 5. Multiphysics problems; 6. Implementation. The first chapter deals with an explanation of the main concepts and it forms the basis of the development of the cell method. Chapter 2 is devoted to the explanation of how Tonti diagrams can be translated into a numerical procedure, how topological operators are translated into matrices and how constitutive equations can be expressed in terms of global variables. Some common characteristics of the computation of constitutive equations are presented in Chapter 3. Two basic problems studied in this chapter are the thermal problem and the magneto-static problem. The cell method developed in the first three chapters is then applied to different classes of physical problems. The aim of Chapter 5 is to show that the Tonti diagrams are of a natural structure that can be used to develop multiphysics numerical formulations. In the final chapter of this volume, the implementation of the numerical technique is described in all its main components: space-time discretization, problem formulation, solution and representation of the resulting physical fields. This book may be of interest to engineers and mathematicians who want to investigate the cell method further and see how it can interplay with other numerical methods, including the finite element method and the finite volume method.
computational intelligence and complexity
theoretical, mathematical and computational physics
scientific article; zbMATH DE number 6147066