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© 2013

The Cell Method for Electrical Engineering and Multiphysics Problems

An Introduction

Book

Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 230)

Table of contents

  1. Front Matter
    Pages 1-9
  2. Piergiorgio Alotto, Fabio Freschi, Maurizio Repetto, Carlo Rosso
    Pages 1-9
  3. Piergiorgio Alotto, Fabio Freschi, Maurizio Repetto, Carlo Rosso
    Pages 11-20
  4. Piergiorgio Alotto, Fabio Freschi, Maurizio Repetto, Carlo Rosso
    Pages 21-47
  5. Piergiorgio Alotto, Fabio Freschi, Maurizio Repetto, Carlo Rosso
    Pages 49-90
  6. Piergiorgio Alotto, Fabio Freschi, Maurizio Repetto, Carlo Rosso
    Pages 91-114
  7. Piergiorgio Alotto, Fabio Freschi, Maurizio Repetto, Carlo Rosso
    Pages 115-129

About this book

Introduction

This book presents a numerical scheme for the solution of field problems governed by partial differential equations: the cell method. The technique lends itself naturally to the solution of multiphysics problems with several interacting phenomena. The Cell Method, based on a space-time tessellation, is intimately related to the work of Tonti and to his ideas of classification diagrams or, as they are nowadays called, Tonti diagrams: a graphical representation of the problem's equations made possible by a suitable selection of a space-time framework relating physical variables to each other. The main features of the cell method are presented and links with many other discrete numerical methods (finite integration techniques, finite difference time domain, finite volumes, mimetic finite differences, etc.) are discussed. After outlining the theoretical basis of the method, a set of physical problems which have been solved with the cell method is described. These single and multiphysics problems stem from the authors' research experience in the fields of electromagnetism, elasticity, thermo-elasticity and others. Finally, 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.

 

Keywords

Computational Electromagnetics Computational Physics Discrete Physics Finite Integration Technique Multiphysics Tonti Diagrams

Authors and affiliations

  1. 1., Dipartimento Ingegneria IndustrialeUniversita’ di PadovaPadovaItaly
  2. 2., Dipartimento EnergiaPolitecnico di TorinoTorinoItaly
  3. 3., Dipartimento EnergiaPolitecnico di TorinoTorinoItaly
  4. 4., Dipartimento di Ingegneria Meccanica ePolitecnico di TorinoTorinoItaly

Bibliographic information

  • Book Title The Cell Method for Electrical Engineering and Multiphysics Problems
  • Book Subtitle An Introduction
  • Authors Piergiorgio Alotto
    Fabio Freschi
    Maurizio Repetto
    Carlo Rosso
  • Series Title Lecture Notes in Electrical Engineering
  • Series Abbreviated Title Lect. Notes Electrical Eng.
  • DOI https://doi.org/10.1007/978-3-642-36101-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering Engineering (R0)
  • Hardcover ISBN 978-3-642-36100-5
  • Softcover ISBN 978-3-642-43450-1
  • eBook ISBN 978-3-642-36101-2
  • Series ISSN 1876-1100
  • Series E-ISSN 1876-1119
  • Edition Number 1
  • Number of Pages XII, 129
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Mathematical and Computational Engineering
    Electrical Engineering
    Numerical and Computational Physics, Simulation
  • Buy this book on publisher's site
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Reviews

From the reviews:

“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 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.” (Teodora-Liliana Rădulescu, zbMATH, Vol. 1280, 2014)

“The book under review introduces the so-called ‘cell method’ (CM) developed by the authors for solving various partial differential equations (PDEs). … authors attempt to introduce the CM without a high level of mathematics and hope that the readers can implement the CM for practical engineering problems. … this book may be interesting to those mathematicians who want to investigate the cell method further and see how it competes with other well-studied numerical methods such as the finite element method and the finite volume method.” (JiChun Li, Mathematical Reviews, October, 2013)