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# Why Do Electromagnetic Finite Element Analysis?

**The main objective of this book is to provide some background information on performing electromagnetic analyses using the finite element (FE) method. Although the FE method is an established technique, particularly in structural and thermal applications, the development and deployment of electromagnetic FE codes are still continuing in both industrial and academic worlds. As such there are comparatively fewer practical guides that have been published on the subject of electromagnetic analysis using the FE method than its mechanical counterpart****.**

This book is aimed at **readers who have interest and some appreciation of electromagnetic phenomena.** Although knowledge and previous experience in FE analysis will be useful, they do not need to be familiar with the numerical implementation of the Finite Element method in electromagnetism. As a useful background to solving electromagnetic problems the principles of Maxwell’s equations, which are commonly used in electromagnetic Finite Element software, are briefly introduced in Chapter 2. From the treatise it is hoped that one can readily appreciate the various forms of electromagnetic solution present in modern electromagnetic FE software, their assumptions and specific applications.

The book continues to discuss the promise and benefits of using the FE method to solve electromagnetic problems in Chapter 3. The pre-requisites and considerations for investing in the technology are then appraised in Chapter 4. These two chapters would be of interest to managers or heads of engineering department who are in a position to consider forming or expanding their in-house Finite Element team.

Technical and practical aspects of electromagnetic modelling using the FE method are then reviewed. These aspects include model dimensionality, element types, material properties, boundary conditions, excitation, meshing considerations, solution types, post-processing and evaluation of the results. The discussion is then extended to multi-physics interaction involving electromagnetism and multiphysics material behaviours.

The book also includes some examples of how the FE method can be used to solve the different types of electromagnetic problems. It is the object of the book to provide a comprehensive overview of why FE technology can be a viable tool for design engineers and researchers in the field, and to provide a practical framework for potential users to make the Finite Element modelling as efficient and accurate as possible.

## Contents

**1. Introduction**

**2. A Brief Introduction to the Principles of Electromagnetism**

2.1 A Walk through History

2.2 Electricity and Magnetism are Related and Interdependent

2.3 Maxwell’s Unified Theory of Electricity and Magnetism

2.4 What If Time Varying Effects Are Negligible?

2.5 What If the Time Varying Effects Are Significant? Different Types of Electromagnetic Solutions

2.6 Can We Decouple Electric and Magnetic Phenomena in a Harmonic or Transient Electromagnetic Solution?

**3. The Promise and Benefits of Electrostatic, Electric Field and Electromagnetic Analysis**

3.1 Why Finite Element Analysis for Electromagnetic Problems?

3.2 Benefits of Utilising Finite Element Analysis

3.3 Examples of Electromagnetic Problems Solved Using the Finite Element Analysis

3.4 What are the Alternatives?

**4. The Preparation and Investment in the Technology**

4.1 Right Software for the Right Job

4.2 Hardware Considerations

4.3 Experience, Experimental Data and a Vigilant Mind

4.4 Are You Investing for the Future?

**5. The Basic Considerations for Electrostatic, Electric Field and Electromagnetic Analyses**

5.1 Model Dimensionality

5.2 What Element Types

5.3 Material Properties

5.4 Boundary Conditions and Excitations

5.5 Meshing Considerations

5.6 Solver Capabilities

5.7 Post-processing and Results Evaluation

**6. Further Considerations – Multi-physics Solutions**

6.1 Temperature Dependent Electric and Magnetic Properties

6.2 Structurally Coupled Solutions – Fields in Motion

6.3 Other Complex Material Responses

**7. Examples of Electromagnetic Analyses**

7.1 Electrostatic Analysis of a Current Transformer Bushing

7.2 Multilayer Capacitor with a Lossy Dielectric Material Subjected to an AC Voltage at Different Frequencies

7.3 Actuation Force of a DC Actuator

7.4 Characteristics of a 6/4 Switched Reluctance Motor

7.5 Eddy Current in Steel Base Plate

7.6 Propagation of Electromagnetic Waves from an Antenna

### Appendix A - Relevant Formulae

References

# About

K. Cheong & D. Ellis

Published December 2009

Softback, 100 Pages