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Educational value of the algebraic numerical methods in electromagnetism

Educational value of the algebraic numerical methods in electromagnetism Purpose – The aim of this paper is to highlight the educational value of algebraic numerical methods with respect to traditional numerical techniques based on differential formulation. Design/methodology/approach – Algebraic formulations of electromagnetic fields are gaining a new interest in the research community. One common characteristic of these methods is that they impose field equations, for instance charge or mass conservation, directly in algebraic form as a sum of partial contributes, without using differential operators like the divergence one. This feature leads directly to a system of linear equations without requiring any intermediate differential formulation as in finite element method. In addition, these systems of linear equations can be efficiently expressed as a product of matrices related to problem topology and material characteristics. Findings – Owing to these features, a MATLAB implementation of these theoretical frameworks is particularly efficient and simple and can be used by electrical engineering students which, even if with a basic mathematical background, have a good practice with network theory and its computer implementation. Following this way of thinking, a MATLAB based environment has been created and here it is presented and discussed. Originality/value – The implementation of the algebraic formulation can be done by using very basic mathematical tools, therefore the algebraic method becomes also a good way to introduce the numerical field analysis to undergraduate students. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

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Publisher
Emerald Publishing
Copyright
Copyright © 2008 Emerald Group Publishing Limited. All rights reserved.
ISSN
0332-1649
DOI
10.1108/03321640810905828
Publisher site
See Article on Publisher Site

Abstract

Purpose – The aim of this paper is to highlight the educational value of algebraic numerical methods with respect to traditional numerical techniques based on differential formulation. Design/methodology/approach – Algebraic formulations of electromagnetic fields are gaining a new interest in the research community. One common characteristic of these methods is that they impose field equations, for instance charge or mass conservation, directly in algebraic form as a sum of partial contributes, without using differential operators like the divergence one. This feature leads directly to a system of linear equations without requiring any intermediate differential formulation as in finite element method. In addition, these systems of linear equations can be efficiently expressed as a product of matrices related to problem topology and material characteristics. Findings – Owing to these features, a MATLAB implementation of these theoretical frameworks is particularly efficient and simple and can be used by electrical engineering students which, even if with a basic mathematical background, have a good practice with network theory and its computer implementation. Following this way of thinking, a MATLAB based environment has been created and here it is presented and discussed. Originality/value – The implementation of the algebraic formulation can be done by using very basic mathematical tools, therefore the algebraic method becomes also a good way to introduce the numerical field analysis to undergraduate students.

Journal

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic EngineeringEmerald Publishing

Published: Nov 14, 2008

Keywords: Numerical analysis; Electromagnetism; Finite element analysis

References

  • Symmetric positive‐definite constitutive matrices for discrete eddy‐current problems
    Codecasa, L.; Specogna, R.; Trevisan, F.

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