Magnetic materials and 3D finite element modeling
Statics and Quasi Statics Electromagnetics Brief Presentation Introduction 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 References Ferromagnetic Materials and Iron Losses Introduction Basic Concepts Losses Components Iron Losses under Alternating, Rotating and DC Biased Inductions Final Considerations References Scalar Hysteresis Modeling Introduction The Preisach's Scalar Model The Jiles Atherton Scalar Model Final Considerations References Vector Hysteresis Modeling Introduction 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 References Brief Presentation of the Finite Element Method Introduction The Galerkin Method: Basic Concepts using Real Coordinates Generalization of the FEM: Using Reference Coordinates Numerical Integration Some Finite Elements Using Edge Elements References Using Nodal Elements with Magnetic Vector Potential Introduction Main Equations Applying Galerkin Method Uniqueness of the Solution the Coulomb's Gauge Implementation Example and Comparisons Final Considerations References The Source Field Method for 3D Magnetostatic Fields Introduction The Magnetostatic Case Scalar Potential The Magnetostatic Case Vector Potential Implementation Aspects and Conventions Computational Implementation Example and Results References The Source Field Method for 3D Magnetodynamic Fields Introduction Formulation Considering Eddy Currents Time Stepping Formulation Considering Eddy Currents Complex Formulation Field Circuit Coupling Computational Implementation The Differential Permeability Method Example and Results References A Matrix Free Iterative Solution Procedure for Finite Element Problems Introduction The Classical FEM: T Scheme The Proposed Technique: N Scheme Implementation Convergence Implementation of N Scheme with SOR Applying Non Stationary Iterative Solver to the N Scheme CG Algorithm Implementation Examples and Results Results and Discussion References