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The Finite Element Method for Electromagnetic Modeling 1st Edition by Gerard Meunier ISBN 1905209649 9781905209644

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The Finite Element Method for Electromagnetic Modeling 1st Edition Gerard Meunier Digital Instant Download

Author(s): Gerard Meunier
ISBN(s): 9781848210301, 1848210302
Edition: 1
File Details: PDF, 5.43 MB
Year: 2008
Language: english
SKU: EB-1801078 Category: Tag:

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ISBN 10:    1905209649
ISBN 13: 978-1905209644
Author:   Gerard Meunier

Written by specialists of modeling in electromagnetism, this resource provides a comprehensive review of the finite element method for low frequency applications. The fundamentals of this method and latest advances in the field are described in detail through topics such as macroscopic behavior laws of materials, magneto-thermal coupling for induction heating, and how Maxwell equations are derived from thermodynamic principles.
 

The Finite Element Method for Electromagnetic Modeling 1st Table of contents:

Chapter 1. Introduction to Nodal Finite Elements
Jean-Louis COULOMB

  • 1.1. Introduction

    • Overview of the finite element method (FEM)

  • 1.1.1. The Finite Element Method

    • Basic principles and applications of FEM in solving physical problems.

  • 1.2. The 1D Finite Element Method

    • 1.2.1. A Simple Electrostatics Problem
      • Introduction to electrostatics using the 1D finite element method.
    • 1.2.2. Differential Approach
      • Solving the electrostatics problem using differential equations.
    • 1.2.3. Variational Approach
      • Alternative approach using variational principles.
    • 1.2.4. First-Order Finite Elements
      • Application of first-order finite elements in 1D problems.
    • 1.2.5. Second-Order Finite Elements
      • Use of second-order finite elements for better accuracy.

  • 1.3. The Finite Element Method in Two Dimensions

    • 1.3.1. The Problem of the Condenser with Square Section
      • Solving a problem involving a condenser using FEM.
    • 1.3.2. Differential Approach
      • Application of differential methods in two-dimensional problems.
    • 1.3.3. Variational Approach
      • Variational approach for solving two-dimensional FEM problems.
    • 1.3.4. Meshing in First-Order Triangular Finite Elements
      • Generating a mesh for FEM using triangular elements.
    • 1.3.5. Finite Element Interpolation
      • Interpolation techniques for finite element analysis.
    • 1.3.6. Construction of the System of Equations by the Ritz Method
      • Building the system of equations using the Ritz method.
    • 1.3.7. Calculation of the Matrix Coefficients
      • Computation of matrix coefficients in finite element problems.
    • 1.3.8. Analysis of the Results
      • Techniques for analyzing FEM results.
    • 1.3.9. Dual Formations, Framing and Convergence
      • Discussing dual formulations and convergence issues.
    • 1.3.10. Resolution of Nonlinear Problems
      • Solving nonlinear problems using FEM.
    • 1.3.11. Alternative to the Variational Method: The Weighted Residues Method
      • Alternative methods to variational approaches, focusing on weighted residues.

  • 1.4. The Reference Elements

    • 1.4.1. Linear Reference Elements
      • Use of linear reference elements in FEM.
    • 1.4.2. Surface Reference Elements
      • Surface elements for 2D problems in FEM.
    • 1.4.3. Volume Reference Elements
      • Volume elements for 3D FEM problems.
    • 1.4.4. Properties of the Shape Functions
      • Discussing shape functions and their properties.
    • 1.4.5. Transformation from Reference Coordinates to Domain Coordinates
      • Coordinate transformations in FEM.
    • 1.4.6. Approximation of the Physical Variable
      • Approximating physical variables in finite element analysis.
    • 1.4.7. Numerical Integrations on the Reference Elements
      • Methods for numerical integration in FEM.
    • 1.4.8. Local Jacobian Derivative Method
      • Using the Jacobian derivative for local computations in FEM.

  • 1.5. Conclusion

    • Summary and conclusion of FEM concepts.

  • 1.6. References

    • List of references for further reading.

Chapter 2. Static Formulations: Electrostatic, Electrokinetic, Magnetostatics
Patrick DULAR and Francis PIRIOU

  • 2.1. Problems to Solve

    • 2.1.1. Maxwell’s Equations
      • Overview of Maxwell’s equations in static problems.
    • 2.1.2. Behavior Laws of Materials
      • Understanding material properties and their behavior in static fields.
    • 2.1.3. Boundary Conditions
      • Importance and types of boundary conditions in static problems.
    • 2.1.4. Complete Static Models
      • Building complete static models for solving electromagnetic problems.
    • 2.1.5. The Formulations in Potentials
      • Using potentials to formulate static problems.

  • 2.2. Function Spaces in the Fields and Weak Formulations

    • 2.2.1. Integral Expressions: Introduction
      • Introduction to integral expressions in the context of weak formulations.
    • 2.2.2. Definitions of Function Spaces
      • Defining function spaces for the formulation of electromagnetic problems.
    • 2.2.3. Tonti Diagram: Synthesis Scheme of a Problem
      • A diagrammatic approach for problem synthesis.
    • 2.2.4. Weak Formulations
      • Developing weak formulations for solving static problems.

  • 2.3. Discretization of Function Spaces and Weak Formulations

    • 2.3.1. Finite Elements
      • Discretizing function spaces using finite element methods.
    • 2.3.2. Sequence of Discrete Spaces
      • Creating a sequence of discrete spaces for approximation.
    • 2.3.3. Gauge Conditions and Source Terms in Discrete Spaces
      • Incorporating gauge conditions and source terms in discrete formulations.
    • 2.3.4. Weak Discrete Formulations
      • Developing weak discrete formulations for solving problems.
    • 2.3.5. Expression of Global Variables
      • Expression of global variables in discretized form.

  • 2.4. References

    • List of references for further study.

Chapter 3. Magnetodynamic Formulations
Zhuoxiang REN and Frédéric BOUILLAULT

  • 3.1. Introduction

    • Overview of magnetodynamic formulations.

  • 3.2. Electric Formulations

    • 3.2.1. Formulation in Electric Field
      • Formulating problems in the electric field.
    • 3.2.2. Formulation in Combined Potentials
      • Using combined potentials for electric field problems.
    • 3.2.3. Comparison of the Formulations in Field and in Combined Potentials
      • Comparing formulations using different approaches.

  • 3.3. Magnetic Formulations

    • 3.3.1. Formulation in Magnetic Field
      • Magnetic field formulations for magnetodynamic problems.
    • 3.3.2. Formulation in Combined Potentials
      • Magnetic formulations using combined potentials.
    • 3.3.3. Numerical Example
      • A numerical example to illustrate the magnetic formulations.

  • 3.4. Hybrid Formulation

    • Hybrid formulations for magnetodynamics.

  • 3.5. Electric and Magnetic Formulation Complementarities

    • 3.5.1. Complementary Features
      • Exploring complementary features in electric and magnetic formulations.
    • 3.5.2. Concerning the Energy Bounds
      • Energy bounds in magnetodynamic problems.
    • 3.5.3. Numerical Example
      • Numerical example demonstrating the complementarity of formulations.

  • 3.6. Conclusion

    • Summary of magnetodynamic formulations.

  • 3.7. References

    • List of references for further study.

Chapter 4. Mixed Finite Element Methods in Electromagnetism
Bernard BANDELIER and Françoise RIOUX-DAMIDAU

  • 4.1. Introduction

    • Introduction to mixed finite element methods in electromagnetism.

  • 4.2. Mixed Formulations in Magnetostatics

    • 4.2.1. Magnetic Induction Oriented Formulation
      • Mixed formulations using magnetic induction.
    • 4.2.2. Formulation Oriented Magnetic Field
      • Using magnetic field-oriented formulations in magnetostatics.
    • 4.2.3. Formulation in Induction and Field
      • Combining induction and field formulations.

  • 4.3. Energy Approach: Minimization Problems, Searching for a Saddle-Point

    • 4.3.1. Minimization of a Functional Calculus Related to Energy
      • Minimizing energy-related functionals.
    • 4.3.2. Variational Principle of Magnetic Energy
      • Variational principles applied to magnetic energy.
    • 4.3.3. Searching for a Saddle-Point
      • Techniques for searching for saddle-points in magnetostatic problems.

  • 4.4. Hybrid Formulations

    • 4.4.1. Magnetic Induction Oriented Hybrid Formulation
      • Hybrid formulations based on magnetic induction.
    • 4.4.2. Hybrid Formulation Oriented Magnetic Field
      • Hybrid formulations based on magnetic field.
    • 4.4.3. Mixed Hybrid Method
      • Mixed hybrid methods for electromagnetism.

  • 4.5. Compatibility of Approximation Spaces – Inf-Sup Condition

    • Conditions for the compatibility of approximation spaces in mixed formulations.

  • 4.6. Mixed Finite Elements, Whitney Elements

    • Use of Whitney elements in mixed finite element methods.

  • 4.7. Mixed Formulations in Magnetodynamics

    • 4.7.1. Magnetic Field Oriented Formulation
      • Magnetodynamic formulations using magnetic field.
    • 4.7.2. Formulation Oriented Electric Field
      • Electric field-based formulations in magnetodynamics.

  • 4.8. Solving Techniques

    • 4.8.1. Penalization Methods
      • Techniques for penalizing solutions in magnetodynamics.
    • 4.8.2. Algorithm Using the Schur Complement
      • Numerical methods based on the Schur complement.

  • 4.9. References

    • List of references for further study.

Chapter 5. Behavior Laws of Materials
Frédéric BOUILLAULT, Afef KEDOUS-LEBOUC, Gérard MEUNIER, Florence OSSART and Francis PIRIOU

  • 5.1. Introduction

    • Introduction to the behavior laws of materials in electromagnetism.

  • 5.2. Behavior Law of Ferromagnetic Materials

    • 5.2.1. Definitions
      • Basic definitions related to ferromagnetic materials.
    • 5.2.2. Hysteresis and Anisotropy
      • Hysteresis and anisotropy in magnetic materials.
    • 5.2.3. Classification of Models Dealing with the Behavior Law
      • Classification of models used for material behavior laws.

  • 5.3. Implementation of Nonlinear Behavior Models

    • 5.3.1. Newton Method
      • Implementing nonlinear models using the Newton method.
    • 5.3.2. Fixed Point Method
      • Fixed point methods for solving nonlinear problems.
    • 5.3.3. Particular Case of a Behavior with Hysteresis
      • Modeling behavior with hysteresis in materials.

  • 5.4. Modeling of Magnetic Sheets

    • 5.4.1. Some Words About Magnetic Sheets
      • Introduction to magnetic sheets and their use in engineering.
    • 5.4.2. Example of Stress in Electric Machines
      • Example of modeling stress in electric machines.
    • 5.4.3. Anisotropy of Sheets with Oriented Grains
      • Modeling anisotropic behavior of magnetic sheets.

  • 5.5. Modeling of Permanent Magnets

    • 5.5.1. Introduction
      • Overview of permanent magnets and their use in finite element analysis.
    • 5.5.2. Magnets Obtained by Powder Metallurgy
      • Study of permanent magnets made through powder metallurgy.

  • 5.6. Modeling of Superconductors

    • 5.6.1. Introduction
      • Understanding superconductors and their behavior in finite element models.

  • 5.7. Conclusion

    • Summary of modeling approaches for various materials.

  • 5.8. References

    • List of references for further study.

Chapter 6. Modeling on Thin and Line Regions
Christophe GUÉRIN

  • 6.1. Introduction

    • Overview of modeling methods for thin and line regions.

  • 6.2. Different Special Elements and Their Interest

    • Specialized elements for modeling thin regions.

  • 6.3. Method for Taking into Account Thin Regions Without Potential Jump

    • Techniques for modeling thin regions without potential discontinuities.

  • 6.4. Method for Taking into Account Thin Regions with Potential Jump

    • Handling thin regions where potential jumps occur.

  • 6.5. Method for Taking Thin Regions into Account

    • General methods for modeling thin regions.

  • 6.6. Thin and Line Regions in Magnetostatics

    • Modeling thin regions in magnetostatics.

  • 6.7. Thin and Line Regions in Magnetoharmonics

    • Addressing thin regions in magnetoharmonic problems.

  • 6.8. Thin Regions in Electrostatic Problems

    • Modeling thin regions in electrostatic and electric conduction problems.

  • 6.9. Thin Thermal Regions

    • Handling thin regions in thermal analysis.

  • 6.10. References

    • References for further study.

Chapter 7. Coupling with Circuit Equations
Gérard MEUNIER, Yvan LEFEVRE, Patrick LOMBARD, and Yann LE FLOCH

  • Introduction
  • Review of the various methods of setting up electric circuit equations
    • Circuit equations with nodal potentials
    • Circuit equations with mesh currents
    • Circuit equations with time integrated nodal potentials
    • Formulation of circuit equations in the form of state equations
    • Conclusion on the methods of setting up electric equations
  • Different types of coupling
    • Indirect coupling
    • Integro-differential formulation
    • Simultaneous resolution
    • Conclusion
  • Establishment of the “current-voltage” relations
    • Insulated massive conductor with two ends: basic assumptions and preliminary relations
    • Current-voltage relations using the magnetic vector potential
    • Current-voltage relations using magnetic induction
    • Wound conductors
    • Losses in the wound conductors
  • Establishment of the coupled field and circuit equations
    • Coupling with a vector potential formulation in 2D
    • Coupling with a vector potential formulation in 3D
    • Coupling with a scalar potential formulation in 3D
  • General conclusion
  • References

Chapter 8. Modeling of Motion: Accounting for Movement in the Modeling of Magnetic Phenomena
Vincent LECONTE

  • Introduction
  • Formulation of an electromagnetic problem with motion
    • Definition of motion
    • Maxwell equations and motion
    • Formulations in potentials
    • Eulerian approach
    • Lagrangian approach
    • Example application
  • Methods for taking the movement into account
    • Introduction
    • Methods for rotating machines
    • Coupling methods without meshing and with the finite element method
    • Coupling of boundary integrals with the finite element method
    • Automatic remeshing methods for large distortions
  • Conclusion
  • References

Chapter 9. Symmetric Components and Numerical Modeling
Jacques LOBRY, Eric NENS, and Christian BROCHE

  • Introduction
  • Representation of group theory
    • Finite groups
    • Symmetric functions and irreducible representations
    • Orthogonal decomposition of a function
    • Symmetries and vector fields
  • Poisson’s problem and geometric symmetries
    • Differential and integral formulations
    • Numerical processing
  • Applications
    • 2D magnetostatics
    • 3D magnetodynamics
  • Conclusions and future work
  • References

Chapter 10. Magneto-thermal Coupling
Mouloud FÉLIACHI and Javad FOULADGAR

  • Introduction
  • Magneto-thermal phenomena and fundamental equations
    • Electromagnetism
    • Thermal
    • Flow
  • Behavior laws and couplings
    • Electromagnetic phenomena
    • Thermal phenomena
    • Flow phenomena
  • Resolution methods
    • Numerical methods
    • Semi-analytical methods
    • Analytical-numerical methods
    • Magneto-thermal coupling models
  • Heating of a moving work piece
  • Induction plasma
    • Introduction
    • Inductive plasma installation
    • Mathematical models
    • Results
    • Conclusion
  • References

Chapter 11. Magneto-mechanical Modeling
Yvan LEFEVRE and Gilbert REYNE

  • Introduction
  • Modeling of coupled magneto-mechanical phenomena
    • Modeling of mechanical structure
    • Coupled magneto-mechanical modeling
    • Conclusion
  • Numerical modeling of electromechanical conversion in conventional actuators
    • General simulation procedure
    • Global magnetic force calculation method
    • Conclusion
  • Numerical modeling of electromagnetic vibrations
    • Magnetostriction vs. magnetic forces
    • Procedure for simulating vibrations of magnetic origin
    • Magnetic forces density
    • Case of rotating machine teeth
    • Magnetic response modeling
    • Model superposition method
    • Conclusion
  • Modeling strongly coupled phenomena
    • Weak coupling and strong coupling from a physical viewpoint
    • Weak coupling or strong coupling problem from a numerical modeling analysis
    • Weak coupling and intelligent use of software tools
    • Displacement and deformation of a magnetic system
    • Structural modeling based on magnetostrictive materials
    • Electromagnetic induction launchers
  • Conclusion
  • References

Chapter 12. Magnetohydrodynamics: Modeling of a Kinematic Dynamo
Franck PLUNIAN and Philippe MASSÉ

  • Introduction
    • Generalities
    • Maxwell’s equations and Ohm’s law
    • The induction equation
    • The dimensionless equation
  • Modeling the induction equation using finite elements
    • Potential (A,ɸ) quadric-vector formulation
    • 2D1/2 quadri-vector potential formulation
  • Some simulation examples
    • Screw dynamo (Ponomarenko dynamo)
    • Two-scale dynamo without walls (Roberts dynamo)
    • Two-scale dynamo with walls
    • A dynamo at the industrial scale
  • Modeling of the dynamic problem
  • References

Chapter 13. Mesh Generation
Yves DU TERRAIL COUVAT, François-Xavier ZGAINSKI, and Yves MARÉCHAL

  • Introduction
  • General definition
  • A short history
  • Mesh algorithms
    • The basic algorithms
    • General mesh algorithms
  • Mesh regularization
    • Regularization by displacement of nodes
    • Regularization by bubbles
    • Adaptation of nodes population
    • Insertion in meshing algorithms
    • Value of bubble regularization
  • Mesh processor and modeling environment
    • Some typical criteria
    • Electromagnetism and meshing constraints
  • Conclusion
  • References

Chapter 14. Optimization
Jean-Louis COULOMB

  • Introduction
    • Optimization: who, why, how?
    • Optimization by numerical simulation: is this reasonable?
    • Optimization by numerical simulation: difficulties
    • Numerical design of experiments (DOE) method: an elegant solution
    • Sensitivity analysis: an “added value” accessible by simulation
    • Organization of this chapter
  • Optimization methods
    • Optimization problems: some definitions
    • Optimization problems without constraints
    • Constrained optimization problems
    • Multi-objective optimization
  • Design of experiments (DOE) method
    • The direct control of the simulation tool by an optimization algorithm: principle and disadvantages
    • The response surface: an approximation enabling indirect optimization
    • DOE method: a short history
    • DOE method: a simple example
  • Response surfaces
    • Basic principles
    • Polynomial surfaces of degree 1 without interaction: simple but sometimes useful
    • Polynomial surfaces of degree 1 with interactions: quite useful for screening
    • Polynomial surfaces of degree 2: a first approach for nonlinearities
    • Response surfaces of degrees 1 and 2: interests and limits
    • Response surfaces by combination of radial functions
    • Response surfaces using diffuse elements
    • Adaptive response surfaces
  • Sensitivity analysis
    • Finite difference method
    • Method for local derivation of the Jacobian matrix
    • Steadiness of state variables: steadiness of state equations
    • Sensitivity of the objective function: the adjoint state method
    • Higher order derivative
  • A complete example of optimization
    • The problem of optimization
    • Determination of the influential parameters by the DOE method
    • Approximation of the objective function by a response surface
    • Search for the optimum on the response surface
    • Verification of the solution by simulation
  • Conclusion

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