The Finite Element Method for Electromagnetic Modeling

Written by specialists of modeling in electromagnetism, this bookprovides a comprehensive review of the finite element method forlow frequency applications. Fundamentals of the method as well asnew advances in the field are described in detail.
Chapters 1 to 4 present general 2D and 3D static and dynamicformulations by the use of scalar and vector unknowns and adaptedinterpolations for the fields (nodal, edge, face or volume).
Chapter 5 is dedicated to the presentation of different macroscopicbehavior laws of materials and their implementation in a finiteelement context: anisotropy and hysteretic properties for magneticsheets, iron losses, non-linear permanent magnets andsuperconductors.
More specific formulations are then proposed: the modeling of thinregions when finite elements become misfit (Chapter 6), infinitedomains by using geometrical transformations (Chapter 7), thecoupling of 2D and 3D formulations with circuit equations (Chapter8), taking into account the movement, particularly in the presenceof Eddy currents (Chapter 9) and an original approach for thetreatment of geometrical symmetries when the sources are notsymmetric (Chapter 10).
Chapters 11 to 13 are devoted to coupled problems: magneto-thermalcoupling for induction heating, magneto-mechanical coupling byintroducing the notion of strong and weak coupling andmagneto-hydrodynamical coupling focusing on electromagneticinstabilities in fluid conductors.
Chapter 14 presents different meshing methods in the context ofelectromagnetism (presence of air) and introduces self-adaptivemesh refinement procedures. Optimization techniques are thencovered in Chapter 15, with the adaptation of deterministic andprobabilistic methods to the numerical finite elementenvironment.
Chapter 16 presents a variational approach of electromagnetism,showing how Maxwell equations are derived from thermodynamicprinciples.