Vizimag: Innovative software for visualizing magnetic fields. Field lines and flux density can be simulated and measured. A free trial download is available.
The
book, "Visualising Magnetic Fields," gives a complete
description of the theory behind the technique and a detailed (but
simple to understand) description of the two major ways of solving the
equations - the Gaussian Elimination and the conjugate gradient methods.
In addition there is the
full source code for Vizimag version 1.0, together with a plain English
description of each procedure in the code. A
second computer application, "Showalg", provides a visualization
of the Gaussian and conjugate gradient equation solvers in
action.
Book chapters: The book covers all these topics:
Chapter 1: Introduction
Magnetic lines of force.
What is visualization?
Chapter 2: Physics of the magnetic field
Fields and field lines
Gauss's Law
The Biot-Savart law
Ampere's Law
Magnetic force on a conductor
Magnetic materials and permanent magnets
The magnetization curve
Hysteresis
Maxwell's equations
The magnetic circuit
The first step in visualization
Chapter 3: The basic technique
Overview
Characteristics of the technique
Generating the equations
The matrix form
Making use of the technique
Chapter 4: Numerical algorithm theory
Gaussian elimination
The conjugate gradient method
Double versus single precision arithmetic
Theory of the conjugate gradient method
The equations being solved
The quadratic form
The method of Steepest Descent
The method of Conjugate Gradients
Comparing the two algorithms
Preconditioning
Timing and storage results
Indirect Addressing for arrays
Choice of analysis method and mesh size
16 and 32 bit operating systems
Progress indicator
Error level setting
Understanding the matrix solving algorithms
Chapter 5: Visualizing the algorithms
Conjugate Gradient visualization
Gaussian elimination visualization
Chapter 6: The boundary region, smoothing and external fields
Why a boundary region is needed
Using the boundary for external field simulation
Chapter 7: The magnetic flux density function
Magnetic flux density filter and log scale
Putting the theory to work
Chapter 8: Model creation
Model functions provided
Data structure
Model generation
Equation generation
Editing
Running the program
Chapter 9: Version 1.0 program installation and use
Installation
Using
On-line help
The Source code
Hints and tips
Chapter 10: Sample results
Chapter 11: Version 1.0 source code
Architecture
Code flow descriptions
General Program Procedures.
Order
details
The book and release 1.0 software: "Visualising Magnetic Fields - Numerical equation solvers in action" by John Stuart Beeteson, is published by Academic Press, ISBN 0-12-084731-0. Available from your High Street or On-line bookstore, or direct from Elsevier (Academic Press).
To order from Elsevier click here
To order on-line from Amazon the US click here
To order on-line from Amazon in the UK, click here
Some reviews
Dr
Tony Lowe of Hampshire, England writes:
Electromagnetism
CAN be fun!
This book is a delight! If only it had been available during those less than interesting lectures on electromagnetic theory..........
Here, the reader can simulate almost any combination of magnets, conductors and external fields and visualize the result in a number of different ways. So this book and its accompanying software will find use in grade school, universities and industry. The visual impact of the approach used by John Beeteson should prove inspirational to younger students. I would recommend that any teacher involved in this subject should buy this book and try it out.
I have used the software on a W98 notebook computer and on a powerful dual processor NT machine. It works just fine in both cases.
Professor
Andrew R. Knox of Ayrshire, Scotland writes:
This book provides a no-nonsense introduction to the ideas and concepts of magnetic field visualization. Electromagnetism is a large and complex field and, as such, can be difficult to obtain an intuitive grasp of. This book presents the basic ideas of magnetic field analysis in a simple and orderly manner with examples to demonstrate the important fundamental concepts. This makes it an ideal companion for more rigorous texts on the subject that go into greater detail where necessary.
The use of numerical analysis tools is widely regarded as essential for more than the simplest of geometries. Frequently these tools require a substantial knowledge in order to be able to apply them to the problem at hand. With the use of the author's visualization of numerical solvers in action the user is able to understand how the computation process develops in solving in 2D a mathematical representation of the field problem. This understanding is essential if the reader wishes to progress to the more challenging 3D simulation environment, especially for those creating rather than just applying the simulation software.
Overall I found the book useful as a means of introducing the subject and would recommend it to students in their last year of school or as an introductory text in undergraduate studies. In addition to students of Physics and Electrical Engineering, the underlying concepts covered are similar to those for mechanical analysis (stress, strain, distortion) and computational fluid dynamics, including heat flow problems. Thus students in the other Engineering disciplines will find something useful in the book and especially the accompanying software.
Magnetic field software. Vizimag modelling software gives visualization of field lines and flux density.