Magnetic Materials and 3D Finite Element Modeling: 1st Edition (Hardback) book cover

Magnetic Materials and 3D Finite Element Modeling

1st Edition

By João Pedro A. Bastos, Nelson Sadowski

CRC Press

396 pages | 263 B/W Illus.

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Hardback: 9781466592513
pub: 2013-10-16
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pub: 2017-04-28
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Magnetic Materials and 3D Finite Element Modeling explores material characterization and finite element modeling (FEM) applications. This book relates to electromagnetic analysis based on Maxwell’s equations and application of the finite element (FE) method to low frequency devices. A great source for senior undergraduate and graduate students in electromagnetics, it also supports industry professionals working in magnetics, electromagnetics, ferromagnetic materials science and electrical engineering.

The authors present current concepts on ferromagnetic material characterizations and losses. They provide introductory material; highlight basic electromagnetics, present experimental and numerical modeling related to losses and focus on FEM applied to 3D applications. They also explain various formulations, and discuss numerical codes.

• Furnishes algorithms in computational language

• Summarizes concepts related to the FE method

• Uses classical algebra to present the method, making it easily accessible to engineers

Written in an easy-to-understand tutorial format, the text begins with a short presentation of Maxwell’s equations, discusses the generation mechanism of iron losses, and introduces their static and dynamic components. It then demonstrates simplified models for the hysteresis phenomena under alternating magnetic fields. The book also focuses on the Preisach and Jiles–Atherton models, discusses vector hysterisis modeling, introduces the FE technique, and presents nodal and edge elements applied to 3D FE formulation connected to the hysteretic phenomena.

The book discusses the concept of source-field for magnetostatic cases, magnetodynamic fields, eddy currents, and anisotropy. It also explores the need for more sophisticated coding, and presents techniques for solving linear systems generated by the FE cases while considering advantages and drawbacks.


"… an important contribution to the area of numerical design in electromagnetics and in particular in low frequency design, including electric machines and actuators. It is a thorough, balanced presentation of the theory and its application."

—Dr. Nathan Ida, The University of Akron

"Written by specialists in the modeling of electromagnetism …useful for researchers and teachers with experience in the area or for students, wishing to acquire knowledge in the field."

—F. Bouillaultm, Professor at Paris Sud University

"Anyone who wants to learn how to model magnetic cores, especially transformer core materials, in 3D will find this book extremely useful."

IEEE Electrical Insulation Magazine, January/February 2015

Table of Contents

Statics and Quasi-Statics Electromagnetics - Brief Presentation


The Maxwell Equations

The Maxwell Equations: Local Form

The Maxwell Equations: Integral Form

The Maxwell Equations in Low Frequency

The Electrostatics

Magnetostatic Fields

Magnetic Materials

Inductance and Mutual Inductance

Magnetodynamic Fields

Fields Defined by Potentials

Final Considerations


Ferromagnetic Materials and Iron Losses


Basic Concepts

Losses Components

Iron Losses under Alternating, Rotating and DC Biased Inductions

Final Considerations


Scalar Hysteresis Modeling


The Preisach’s Scalar Model

The Jiles-Atherton Scalar Model

Final Considerations


Vector Hysteresis Modeling


Vector Model Obtained with the Superposition of Scalar Models

Vector Generalizations of the Jiles-Atherton Scalar Models

Some Remarks Concerning the Vector Behavior of Hysteresis

Final Considerations


Brief Presentation of the Finite Element Method


The Galerkin Method: Basic Concepts using Real Coordinates

Generalization of the FEM: Using Reference Coordinates

Numerical Integration

Some Finite Elements

Using Edge Elements


Using Nodal Elements with Magnetic Vector Potential


Main Equations

Applying Galerkin Method

Uniqueness of the Solution; the Coulomb’s Gauge


Example and Comparisons

Final Considerations


The Source-Field Method for 3D Magnetostatic Fields


The Magnetostatic Case – Scalar Potential

The Magnetostatic Case – Vector Potential

Implementation Aspects and Conventions

Computational Implementation

Example and Results


The Source-Field Method for 3D Magnetodynamic Fields


Formulation Considering Eddy Currents – Time Stepping

Formulation Considering Eddy Currents – Complex Formulation

Field-Circuit Coupling

Computational Implementation

The Differential Permeability Method

Example and Results


A Matrix-Free Iterative Solution Procedure for Finite Element Problems


The Classical FEM: T-Scheme

The Proposed Technique: N-Scheme



Implementation of N-Scheme with SOR

Applying Non-Stationary Iterative Solver to the N-Scheme

CG Algorithm Implementation

Examples and Results

Results and Discussion


About the Authors

João Pedro A. Bastos completed his doctoral thesis (Docteur d’Etat) at Université Pierre et Marie Curie, Paris VI, in 1984. He then returned to Brazil at the Universidade Federal de Santa Catarina (UFSC) and became a full professor in 1992. He founded GRUCAD in 1985—a group that plays an important role in the development of the area of electromagnetic field analysis in Brazil. Dr. Bastos worked as a visiting professor at the University of Akron, Ohio, in 1992 and 2001. He is also the author of four books and has published several papers in periodic journals and conferences.

Nelson Sadowski received his engineering and master of science degrees from Universidade Federal de Santa Catarina (UFSC) in 1982 and 1985, respectively. In 1993, he received his PhD from the Institut National Polytechnique de Toulouse (INPT). He then returned to Brazil and continued his research and teaching activities at GRUCAD-UFSC and became a full professor in 1996. In 2000, he received his HDR (Habilitation) diploma, also from the INPT. Dr. Sadowski has been active on international agreements with universities in France, Germany, and Belgium. He is also the author of several conference and journal papers. He is also very active on industrial consulting.

Subject Categories

BISAC Subject Codes/Headings:
TECHNOLOGY & ENGINEERING / Electronics / Circuits / General