Lecture Notes in Electrical Engineering

The Cell Method for Electrical Engineering and Multiphysics Problems

An Introduction

Authors: Alotto, P., Freschi, F., Repetto, M., Rosso, C.

  • Introduction to the Cell Method, a numerical method for the solution of a large class of physical problems as an alternative to the classical Finite Element techniques
  • Presents important implementation aspects of the technique as well as a complete fully working computer code for the solution of three‐dimensional stationary thermal problem
  • All chapters include extensive bibliographic references
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About this book

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.

 

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)

Table of contents (6 chapters)

  • Tonti Diagrams

    Alotto, Piergiorgio (et al.)

    Pages 1-9

  • Topological Equations

    Alotto, Piergiorgio (et al.)

    Pages 11-20

  • Constitutive Equations

    Alotto, Piergiorgio (et al.)

    Pages 21-47

  • Classical Physical Problems

    Alotto, Piergiorgio (et al.)

    Pages 49-90

  • Multiphysics Problems

    Alotto, Piergiorgio (et al.)

    Pages 91-114

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-642-36101-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-642-36100-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
The Cell Method for Electrical Engineering and Multiphysics Problems
Book Subtitle
An Introduction
Authors
Series Title
Lecture Notes in Electrical Engineering
Series Volume
230
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-36101-2
DOI
10.1007/978-3-642-36101-2
Hardcover ISBN
978-3-642-36100-5
Series ISSN
1876-1100
Edition Number
1
Number of Pages
XII, 129
Topics