Electromagnetics and Calculation of Fields（2nd ed）

Contents
Preface
Part1.TheElectromagneticFieldandMaxwell'sEquations
1.MathematicalPreliminaries
1.1.Introduction
1.2.TheVectorNotation
1.3.VectorDerivation
1.3.1.TheNabla(V)Operator
1.3.2.DefinitionoftheGradient,Divrgence,andCurl
1.4.TheGradient
1.4.1.ExampleofGradient
1.5.TheDivergence
1.5.1.DefmitionofFlux
1.5.2.TheDivergenceTheorem
1.5.3.ConservativeFlux
1.5.4.ExampleofDivergence
1.6.TheCurl
1.6.1.CirculationofaVector
1.6.2.Stokes'Theorem
1.6.3.ExampleofCurl
1.7.SecondOrderOperators
1.8.ApplicationofOperatorstoMorethanOneFunction
1.9.ExpressionsinCylindricalandSphericalCoordinates
2.TheElectromagneticFieldandMaxwell'sEquations
2.1.Introduction
2.2.Maxwell'sEquations
2.2.1.FundamentalPhysicalPrinciplesoftheElectromagneticPield
2.2.2.PointFormoftheEquations
2.2.3.TheEquationsinVacuum
2.2.4.TheEquationsinMediawithand
2.2.5.TheEquationsinGeneralMedia
2.2.6.TheIntegralFormofMaxwell'sEquations
2.3.ApproximationstoMaxwell'sEquations
2.4.Units
3ElectrostaticFields
3.1.Introduction
3.2.TheElectrostaticCharge
3.2.1.TheElectricField
3.2.2.ForceonanElectricCharge
3.2.3.TheElectricScalarPotentialV
3.3.NonconservativeFields:ElectromotiveForce
3.4.RefractionoftheElectricField
3.5.DielectricStrength
3.6.TheCapacitor
3.6.1.DefmitionofCapacitance
3.6.2.EnergyStoredinaCapacitor
3.6.3.EnergyinaStatic,ConservativeFie1
3.7.Laplace'sandPoisson'sEquationsinTemoftheElectricField
3.8.Examples
3.8.1.TheInfmiteChargedLine
3.8.2.TheChargedSphericalHalf-Shell
3.8.3.TheSphericalCapacitor
3.8.4.TheSphericalCapacitorwithTwoDielectricLayers
3.9.ABriefIntroductiontotheFiniteElementMethod:SolutionoftH
Two-DimensionalLaplaceEquation
3.9.1.TheFiniteElementTechniqueforDivisionofaDomain
3.9.2.TheVariationalMethod
3.9.3.AFiniteElementProgram
3.9.4.ExampleforUseoftheFiniteElementProgram
3.10.TablesofPermittivities,DielectricStrength,andConductivities
4.MagnetostaticFields
4.1.Introduction
4.2.Maxwell'sEquationsinMagnetostatics
4.2.1.TheEquation
4.2.2.TheEquation
4.2.3.TheEquation
4.3.TheBiot-SavartLaw
4.4.BoundaryConditionsfortheMagneticField
4.5.MagneticMaterials
4.5.1.DiamagneticMaterials
4.5.2.ParamagneticMaterials
4.5.3.FerromagneticMaterials
4.5.4.PennanentMagnets
4.6.TheAnalogybetweenMagneticandElectricCircuits
4.7.InductanceandMutualInductance
4.7.1.DefinitionofInductance
4.7.2.EnergyinaLinearSystem
4.7.3.TheEnergyStoredintheMagneticField
4.8.Examples
4.8.1.CalculationofFieldIntensityandInducianceofaLong
Solenoid
4.8.2.CalculationofHforaCircularLoop
4.8.3.FieldofaRectangularLoop
4.8.4.CalculationofInductanceofaCoaxilCable
4.8.5.CalculationoftheFieldInsideaCy)hdricalConductor
4.8.6.CalculationoftheMagneticFieldHoensityinaMagnetic
Circuit
4.8.7.CalculationoftheMagneticFieldhtensityofaSaturated
MagneticCircuit
4.8.8.MagneticCircuitIncorporatingPrmanentMagnets
4.9.Laplace'sEquationinTermsoftheMagneticScalarPotential
4.10.PropertiesofSoftMagneticMaterials
MagnetodynamicFields
5.1.Introduction
5.2.Maxwell'sEquationsfortheMagnetodynamicField
5.3.PenetrationofTimeDependentFieldsinConductingMaterials
5.3.1.TheEquationforH
5.3.2.TheEquationforB
5.3.3.TheEquationforE
5.3.4.TheEquationforJ
5.3.5.SolutionoftheEquations
5.4.EddyCurrentLossesinPlates
5.5.HysteresisLosses
5.6.Examples
5.6.1.InducedCurrentsDuetoChangeinInduction
5.6.2.InducedCurrentsDuetoChangesinGeometry
5.6.3.InductiveHeatingofaConductingBlock
5.6.4.EffectofMovementofaMagnetRelativetoaFlat
Conductor
5.6.5.VisualizationofPenetrationofFieldsasaFunctionof
Frequency
5.6.6.TheVoltageTransformer
6.InteractionbetweenElectromagneticandMechanicalForces
6.1.Introduction
6.2.ForceonaConductor
6.3.ForceonMovingCharges:TheLorentzForce
6.4.EnergyintheMagneticField
6.5.ForceasVariationofEnergy(VirtualWork)
6.6.ThePoyntingVector
6.7.Maxwell'sForceTensor
6.8.Examples
6.8.1.ForcebetweenTwoConductingSegments
6.8.2.TorqueonaLoop
6.8.3.TheHallEffect
6.8.4.TheLinearMotorandGenerator
6.8.5.AttractionofaFerromagneticBody
6.8.6.RepulsionofaDiamagneticBody
6.8.7.MagneticLevitation
6.8.8.TheMagneticBrake
7.WavePropagationandHigh-FrequencyElectromagneticFields
7.1.Introduction
7.2.TheWaveEquationandItsSolutioB
7.2.1.TheTimeDependentEquations
7.2.2.TheTimeHarmonicWaveEquations
7.2.3.SolutionoftheWaveEquation
7.2.4.SolutionforPlaneWaves
7.2.5.TheOne-DimensionalWaveEquationinFreeSpaceand
LosslessDielectrics
7.3.PropagationofWavesinMaterials
7.31.PropagationofWavesinLossyDielectrics
7.3.2.PropagationofPlaneWavesinLow-LossDielectrics
7.3.3.PropagationofPlaneWavesinConductors
7.3.4.PropagationinaConductor:DefinitionoftheSkinDepth
7.4.PolarizationofPlaneWaves
7.5.Reflection,Refraction,andTransmissionofPlaneWaves
7.5.1.ReflectionandTransmissionataLossyDielectricInterface:
NormalIncidence
7.5.2.ReflectionandTransmissionataConductorInterface:
NormalIncidence
7.5.3.ReflectionandTransmissionataFiniteConductivity
ConductorInterface
7.5.4.ReflectionandTransmissionatanInterface:
ObliqueIncidence
7.5.5.ObliqueIncidenceonaConductingInterface:
PerpendicularPolarization
7.5.6.ObliqueIncidenceonaConductingInterface:
ParallelPolarization
7.5.7.ObliqueIncidenceonaDielectricInterface:
PerpendicularPolarization
7.5.8.ObliqueIncidenceonaDielectricInterfare:
ParallelPolarization
7.6.Waveguides
7.6.1.TEM,TE,andTMWaves
7.6.2.TEMWaves
7.6.3.TEWaves
7.6.4.TMWaves
7.6.5.RectangularWaveguides
7.6.6.TMModesinWaveguides
7.6.7.TEModesinWaveguides
7.7.CavityResonators
7.7.1.TMandTEModesinCavityResonators
7.7.2.TEModesinaCavity
7.7.3.EnergyinaCavity
7.7.4.QualityFactorofaCavityResonator
7.7.5.CouplingtoCavities
PartII.IntroductiontotheFiniteElementMethodinElectromagnetics
8.IntroductiontotheFiniteElementMethod
8.1.Introduction
8.2.TheGalerkinMethod-BasicConcepts
8.3.TheGalerkinMethod-Extensionto2D
8.3.1.TheBoundaryConditions
8.3.2.Calculationofthe2DElementalMatrix
8.4.TheVariationalMethod-BasicConcepts
8.5.TheVariationalMethod-Extensionto2D
8.5.1.TheVariationalFormulation
8.5.2.Calculationofthe2DElementalMatrix
8.6.GeneralizationoftheFiniteElementMethod
8.6.1.High-OrderFiniteElements:General
8.6.2.High-OrderFiniteElements:Notation
8.6.3.High-OrderFiniteElements:Implementation
8.6.4.ContinuityofFiniteElements
8.6.5.PolynomialBasis
8.6.6.TransformationofQuantities-theJacobian
8.6.7.EvaluationoftheIntegrals
8.7.NumericalIntegration
8.7.1.EvaluationoftheIntegrals
8.7.2.BasicPrinciplesofNumericalIntegration
8.7.3.AccuracyandErrorsinNumericalIntegration
8.8.SomeSpecificFiniteElements
8.8.1.IDElements
8.8.2.2DElements
8.8.3.3DElements
8.9.CouplingDifferentFiniteElements;Infinite3lements
8.9.1.CouplingDifferentTypesofFiniteFements
8.9.2.InfiniteEIements
8.10.CalculationofSomeTermsinPoisson'Equation
8.10.1.TheStiffnessMatrix
8.10.2.EvaluationoftheSecondTerminEq.(8.130)
8.10.3.EvaluationoftheThirdTerminEq.(8.130)
8.10.4.EvaluationoftheSourceTerm
8.11.ASimplified2DSecond-OrderFiniteElementProgram
8.11.1.TheProblemtoBeSolved
8.11.2.TheDiscretizedDomain
8.11.3.TheFiniteElementProgram
TheVariationalFiniteElementMethod:
SomeStaticApplications
9.1.Introduction
9.2.SomeStaticApplications
9.2.1.ElectrostaticFields:DielectricMaterials
9.2.2.StationaryCurrents:ConductingMaterials
9.2.3.MagneticFields:ScalarPotential
9.2.4.TheMagneticField:VectorPotential
9.2.5.TheElectricVectorPotential
9.3.TheVariationalMethod
9.3.1.TheVariationalFormulation
9.3.2.FunctionalsInvolvingScalarPotentials
9.3.3.TheVectorPotentialFunctionals
9.4.TheFiniteElementMethod
9.5.ApplicationofFiniteElementswiththeVariationalMethod
9.5.1.ApplicationtotheElectrostaticField
9.5.2.ApplicationtotheCaseofStationaryCurrents
9.5.3.ApplicationtotheMagneticField:ScalarPotential
9.5.4.ApplicationtotheMagneticField:VectorPotential
9.5.5.ApplicationtotheElectricVectorPotential
9.6.AssemblyoftheMatrixSystem
9.7.Axi-SymmetricApplications
9.8.NonlinearApplications
9.8.1.MethodofSuccessiveApproximation
9.8.2.TheNewton-RaphsonMethod
9.9.TheThree-DimensionalScalarPotential
9.9.1.TheFirst-OrderTetrahedralElement
9.9.2.ApplicationoftheVariationalMethod
9.9.3.Modelingof3DPermanentMagnets
9.10.Examples
9.10.1.CalculationofElectrostaticFields
9.10.2.CalculationofStaticCurrents
9.10.3.CalculationoftheMagneticField:SalarPotential
9.10.4.CalculationoftheMagneticField:VectorPotential
9.10.5.Three-DimensionalCalculationofFieldsofPermanent
Magnets
Galerkin'sResidualMethod:ApplicationstoDynamicFields
10.1.Introduction
10.2.ApplicationtoMagneticFieldsinAnisotropicMedia
10.3.Applicationto2DEddyCurrentProblems
10.3.1.First-OrderElementinLocalCoordinates
10.3.2.TheVectorPotentialEquationUsingTime
Discretization
10.3.3.TheComplexVectorPotentialEquation
10.3.4.StructureswithMovingParts
10.3.5.TheAxi-SymmetricFormulation
10.3.6.AModifiedComplexVectorPotentialFormulationfor
WavePropagation
10.3.7.FormulationofHelmholtz'sEquation
10.3.8.AdvantagesandLimitationsof2DFonnulations
10.4.ApplicationoftheNewton-RaphsonMethod
10.5.Examples
10.5.1.EddyCurrents:TimeDiscretization
10.5.2.MovingConductingPieceinFrontofan
Electromagnet
10.5.3.ModesandFieldsinaWaveguide
10.5.4.ResonantFrequenciesofaMicrowaveCavity
11.HexahedralEdgeElements-Some3DApplications
11.1.Introduction
11.2.TheHexahedralEdgeElementShapeFunctions
11.3.ConstructionoftheShapeFunctions
11.4.ApplicationofEdgeElementstoLow-Frequency
Maxwell'sEquations
11.4.1.StaticCases
11.4.2.ListingoftheMatrixConstructionCode
11.4.3.ModelingofPermanentMagnets
11.4.4.EddyCurrents-theTime-SteppingProceure
11.4.5.EddyCurrents-TheComplexFormulation
11.4.6.TheNewton-RaphsonMethod
11.4.7.TheDivergenceofJandOtherParticulars
11.5.ModelingofWaveguidesandCavityResonators
11.6.Examples
11.6.1.StaticCalculations(TEAMProblem13)
11.6.2.ALinearMotorwithPermanentMagnets
11.6.3.EddyCurrentCalculations(TEAMProblem21)
11.6.4.CalculationofResonantFrequencies
(TEAMProblem19)
ComputationalAspectsinFiniteElement
SoftwareImplementation
12.1.Introduction
12.2.GeometricRepetitionofDomains
12.2.1.Periodicity
12.2.2.Anti-Periodicity
12.3.StorageoftheCoefficientMatrix
12.3.1.SymmetryoftheCoefficientMatrix
12.3.2.TheBandedMatrixandItsStorage
12.3.3.CompactStorageoftheMatrix
12.4.InsertionofDirichletBoundaryConditions
12.5.QuadrilateralandHexahedralElements
12.6.MethodsofSolutionoftheLinearSystem
12.6.1.DirectMethods
12.6.2.IterativeMethods
12.7.MethodsofSolutionforEigenvaluesandEigenvectors
12.7.1.TheJacobiTransformation
12.7.2.TheGivensTransformation
12.7.3.TheQRandQZMethods
12.8.DiagramofaFiniteElementProgram
GeneralOrganizationofFieldComputation
Software
13.1.Introduction
13.2.ThePre-ProcessorModule
13.2.1.TheUser/SystemDialogue
13.2.2.DomainDiscretization
13.3.TheProcessorModule
13.4.ThePost-ProcessorModule
13.4.1.VisualizationofResults
13.4.2.CalculationofNumericalResults
13.5.TheComputationalOrganizationofaSoftwarePackage
13.5.1.TheEFCADSoftware
13.6.EvolvingSoftware
13.6.1.TheAdaptiveMeshMethod
13.6.2.ACoupledThermal/ElectricalSystem
13.6.3.ASoftwarePackageforElectricalMachines
13.6.4ASystemforSimultaneousSolutionofFieldEquations
andExtemalCircuits
13.6.5.ComputationalDifficultiesandExtensionstoField
ComputationPackages
13.7RecentTrends
Bibliography
SubjectIndex