Finite Element Method for Eigenvalue Problems in Electromagnetics

many complex problems in electromagnetics. The goal of the current … plied to electromagnetic problems, it was primarily long-….

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Finite Element Method for Eigenvalue Problems in Electromagnetics
Table of Contents

  • Symbols . . . vii
  • Abstract . . . 1
  • 1. Introduction . . . 1
  • 2. Two-DimensionalProblems . . . 2
  • 2.1. Homogeneous Waveguides|ScalarFormulation . . . 2
  • 2.1.1. Formulation. . . 2
  • 2.1.2. Discretization . . . 2
  • 2.1.3. Field ComputationFrom Scalar Potential . . . 4
  • 2.1.4. Numerical Examples . . . 4
  • 2.1.5. Summary . . . 8
  • 2.2. InhomogeneousWaveguides|VectorFormulation . . . 8
  • 2.2.1. Solution of Homogeneous Waveguide Problem With Two-Component
  • Transverse VectorFields . . . 10
  • 2.2.1.1. Formulation. . . 10
  • 2.2.1.2. Discretization . . . 10
  • 2.2.1.3. Finite element formulation . . . 11
  • 2.2.1.4. Finite element matrices. . . 12
  • 2.2.1.5. Numerical examples . . . 12
  • 2.2.2. Inhomogeneous Waveguide Problems Using Three-Component Vector Fields . . . 12
  • 2.2.2.1. Formulation. . . 13
  • 2.2.2.2. Discretization . . . 13
  • 2.2.2.3. Finite element formulation . . . 13
  • 2.2.2.4. Finite element matrices. . . 14
  • 2.2.2.5. Numerical examples . . . 14
  • 2.2.3. Wave-Number Determination for Given Propagation Constant . . . 15
  • 2.2.3.1. Formulation. . . 15
  • 2.2.3.2. Discretization . . . 16
  • 2.2.3.3. Finite element formulation . . . 16
  • 2.2.3.4. Finite element matrices. . . 17
  • 2.2.3.5. Numerical example. . . 17
  • 2.2.4. Dispersion Characteristics of Waveguides . . . 17
  • 2.2.4.1. Formulation. . . 17
  • 2.2.4.2. Discretization . . . 17
  • 2.2.4.3. Finite element formulation . . . 18
  • 2.2.4.4. Finite element matrices. . . 18
  • 2.2.4.5. Numerical examples . . . 19
  • 2.2.5. Summary . . . 19
  • 3. Three-Dimensional Problems . . . 19
  • 3.1. Eigenvalues of Three-Dimensional Cavity|Vector Formulation . . . 19
  • 3.1.1. Formulation. . . 20
  • 3.1.2. Discretization . . . 21
  • 3.1.3. Finite Element Formulation . . . 22
  • 3.1.4. Finite ElementMatrices . . . 22
  • 3.1.5. NumericalExamples . . . 23
  • 3.1.6. Summary . . . 24
  • 4. ConcludingRemarks . . . 24
  • Appendix . . . 26
  • References . . . 27
  • Tables
  • Table1.Cuto WaveNumbersforRectangularWaveguide . . . 5
  • Table 2. Cuto Wave Numbers for Circular Waveguide . . . 5
  • Table 3. Cuto Wave Numbers for Coaxial Line With r2=r1 = 4 . . . 8
  • Table 4. Cuto Wave Numbers for Rectangular Waveguide . . . 12
  • Table 5. Cuto Wave Numbers for Circular Waveguide . . . 13
  • Table 6. Cuto Wave Numbers for Rectangular Waveguide . . . 14
  • Table 7. Cuto Wave Numbers for Circular Waveguide . . . 14
  • Table 8. Wave Numbers for LSM Modes of Square Waveguide With =10 . . . 17
  • Table 9. Dispersion Characteristics of Partially Filled Rectangular WaveguideofFigure12 . . . 19
  • Table 10. Dispersion Characteristics of Partially Filled Rectangular WaveguideofFigure13 . . . 20
  • Table 11. Formation of Edges of Tetrahedral Element . . . 21
  • Table 12. Eigenvalues of Air-Filled Rectangular Cavity . . . 23
  • Table 13. Eigenvalues of Half-Filled Rectangular Cavity . . . 24
  • Table 14. Eigenvalues of Air-Filled Circular Cylindrical Cavity . . . 24
  • Table 15. Eigenvalues of Spherical Cavity With Radius of 1 cm . . . 24
  • Figures
  • Figure 1.Geometryofproblem. . . 2
  • Figure 2.Singletriangularelement. . . 2
  • Figure 3.FlowchartforFEMsolution. . . 4
  • Figure 4.Geometry ofrectangular waveguide. . . 5
  • Figure 5. Electric eld distribution of some modes for rectangular waveguide. . . 6
  • Figure 6.Crosssection ofcircular waveguide. . . 6
  • Figure 7. Electric eld distribution of some modes for circular waveguide. . . 7
  • Figure 8.Crosssectionofcoaxialline. . . 8
  • Figure 9. Electric eld distribution of some modes for coaxial line. . . 9
  • Figure 10. Con guration of tangential edge elements. . . 11
  • Figure 11.Partially lledsquarewaveguide. . . 17
  • Figure 12. Partially lled rectangular waveguide with br=ar = 0:45, d=br = 0:5,and \
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