The Finite Element Method for Electromagnetic Modeling (PDF)

Written by specialists of modeling in electromagnetism, this book
provides a comprehensive review of the finite element method for
low frequency applications. Fundamentals of the method as well as
new advances in the field are described in detail.

Chapters 1 to 4 present general 2D and 3D static and dynamic
formulations by the use of scalar and vector unknowns and adapted
interpolations for the fields (nodal, edge, face or volume).

Chapter 5 is dedicated to the presentation of different macroscopic
behavior laws of materials and their implementation in a finite
element context: anisotropy and hysteretic properties for magnetic
sheets, iron losses, non-linear permanent magnets and
superconductors.

More specific formulations are then proposed: the modeling of thin
regions when finite elements become misfit (Chapter 6), infinite
domains by using geometrical transformations (Chapter 7), the
coupling of 2D and 3D formulations with circuit equations (Chapter
8), taking into account the movement, particularly in the presence
of Eddy currents (Chapter 9) and an original approach for the
treatment of geometrical symmetries when the sources are not
symmetric (Chapter 10).

Chapters 11 to 13 are devoted to coupled problems: magneto-thermal
coupling for induction heating, magneto-mechanical coupling by
introducing the notion of strong and weak coupling and
magneto-hydrodynamical coupling focusing on electromagnetic
instabilities in fluid conductors.

Chapter 14 presents different meshing methods in the context of
electromagnetism (presence of air) and introduces self-adaptive
mesh refinement procedures. Optimization techniques are then
covered in Chapter 15, with the adaptation of deterministic and
probabilistic methods to the numerical finite element
environment.

Chapter 16 presents a variational approach of electromagnetism,
showing how Maxwell equations are derived from thermodynamic
principles.