Preface |
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xiii | |
Acknowledgment |
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xv | |
A Note to Students |
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xvii | |
Author |
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xix | |
1 Fundamental Concepts |
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1 | (28) |
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1 | (2) |
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3 | (12) |
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1.2.1 Electrostatic Fields |
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3 | (1) |
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1.2.2 Magnetostatic Fields |
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4 | (1) |
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1.2.3 Time-Varying Fields |
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5 | (2) |
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1.2.4 Boundary Conditions |
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7 | (1) |
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8 | (1) |
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1.2.6 Time-Varying Potentials |
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9 | (2) |
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1.2.7 Time-Harmonic Fields |
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11 | (4) |
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1.3 Classification of EM Problems |
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15 | (6) |
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1.3.1 Classification of Solution Regions |
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15 | (1) |
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1.3.2 Classification of Differential Equations |
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15 | (4) |
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1.3.3 Classification of Boundary Conditions |
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19 | (2) |
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1.4 Some Important Theorems |
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21 | (6) |
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1.4.1 Superposition Principle |
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21 | (1) |
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21 | (6) |
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27 | (2) |
2 Analytical Methods |
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29 | (94) |
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29 | (1) |
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2.2 Separation of Variables |
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29 | (3) |
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2.3 Separation of Variables in Rectangular Coordinates |
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32 | (10) |
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32 | (4) |
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36 | (6) |
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2.4 Separation of Variables in Cylindrical Coordinates |
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42 | (14) |
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45 | (11) |
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2.5 Separation of Variables in Spherical Coordinates |
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56 | (15) |
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57 | (4) |
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61 | (10) |
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2.6 Some Useful Orthogonal Functions |
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71 | (9) |
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80 | (10) |
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2.7.1 Poisson's Equation in a Cube |
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80 | (2) |
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2.7.2 Poisson's Equation in a Cylinder |
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82 | (3) |
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2.7.3 Strip Transmission Line |
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85 | (5) |
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2.8 Practical Applications |
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90 | (8) |
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2.8.1 Scattering by Dielectric Sphere |
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90 | (5) |
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2.8.2 Scattering Cross Sections |
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95 | (3) |
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2.9 Attenuation due to Raindrops |
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98 | (7) |
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105 | (15) |
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120 | (3) |
3 Finite Difference Methods |
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123 | (106) |
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123 | (1) |
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3.2 Finite Difference Schemes |
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124 | (3) |
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3.3 Finite Differencing of Parabolic PDEs |
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127 | (5) |
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3.4 Finite Differencing of Hyperbolic PDEs |
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132 | (4) |
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3.5 Finite Differencing of Elliptic PDEs |
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136 | (4) |
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137 | (1) |
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137 | (3) |
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3.6 Accuracy and Stability of FD Solutions |
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140 | (7) |
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3.7 Practical Applications I: Guided Structures |
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147 | (9) |
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147 | (6) |
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153 | (3) |
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3.8 Practical Applications II: Wave Scattering (FDTD) |
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156 | (17) |
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3.8.1 Yee's Finite Difference Algorithm |
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159 | (2) |
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3.8.2 Accuracy and Stability |
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161 | (1) |
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3.8.3 Lattice Truncation Conditions |
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162 | (2) |
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164 | (1) |
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3.8.5 Programming Aspects |
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165 | (8) |
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3.9 Absorbing Boundary Conditions for FDTD |
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173 | (8) |
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3.10 Advanced Applications of FDTD |
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181 | (2) |
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3.10.1 Periodic Structures |
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181 | (1) |
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182 | (1) |
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182 | (1) |
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182 | (1) |
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182 | (1) |
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183 | (1) |
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3.11 Finite Differencing for Nonrectangular Systems |
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183 | (6) |
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3.11.1 Cylindrical Coordinates |
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183 | (4) |
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3.11.2 Spherical Coordinates |
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187 | (2) |
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3.12 Numerical Integration |
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189 | (13) |
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190 | (2) |
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192 | (1) |
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193 | |
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3.12.4 Newton-Cotes Rules |
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1' | (195) |
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196 | (1) |
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3.12.6 Multiple Integration |
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197 | (5) |
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202 | (19) |
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221 | (8) |
4 Variational Methods |
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229 | (50) |
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229 | (1) |
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4.2 Operators in Linear Spaces |
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229 | (3) |
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4.3 Calculus of Variations |
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232 | (4) |
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4.4 Construction of Functionals from PDEs |
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236 | (3) |
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239 | (7) |
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4.6 Weighted Residual Method |
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246 | (1) |
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247 | (8) |
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248 | (1) |
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249 | (1) |
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4.7.3 Least Squares Method |
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249 | (6) |
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255 | (6) |
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4.9 Practical Applications |
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261 | (7) |
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268 | (8) |
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276 | (3) |
5 Moment Methods |
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279 | (92) |
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279 | (1) |
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5.2 Differential Equations |
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280 | (2) |
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282 | (5) |
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5.3.1 Classification of IEs |
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283 | (1) |
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5.3.2 Connection between Differential and IEs |
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284 | (3) |
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287 | (18) |
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288 | (5) |
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5.4.2 For Domain with Conducting Boundaries |
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293 | (17) |
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293 | (2) |
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5.4.2.2 Eigenfunction Expansion |
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295 | (10) |
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5.5 Applications I: Quasi-Static Problems |
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305 | (5) |
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5.6 Applications II: Scattering Problems |
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310 | (10) |
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5.6.1 Scattering by Conducting Cylinder |
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311 | (3) |
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5.6.2 Scattering by an Arbitrary Array of Parallel Wires |
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314 | (6) |
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5.7 Applications III: Radiation Problems |
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320 | (14) |
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322 | (1) |
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323 | (1) |
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5.7.3 Expansion and Weighting Functions |
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323 | (11) |
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5.8 Applications IV: EM Absorption in the Human Body |
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334 | (17) |
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335 | (3) |
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5.8.2 Transformation to Matrix Equation (Discretization) |
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338 | (1) |
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5.8.3 Evaluation of Matrix Elements |
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339 | (1) |
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5.8.4 Solution of the Matrix Equation |
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340 | (11) |
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351 | (15) |
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366 | (5) |
6 Finite Element Method |
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371 | (80) |
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371 | (1) |
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6.2 Solution of Laplace's Equation |
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372 | (13) |
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6.2.1 Finite Element Discretization |
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372 | (1) |
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6.2.2 Element Governing Equations |
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373 | (4) |
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6.2.3 Assembling of All Elements |
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377 | (2) |
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6.2.4 Solving the Resulting Equations |
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379 | (6) |
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6.3 Solution of Poisson's Equation |
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385 | (7) |
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6.3.1 Deriving Element-Governing Equations |
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387 | (3) |
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6.3.2 Solving the Resulting Equations |
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390 | (2) |
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6.4 Solution of the Wave Equation |
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392 | (3) |
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6.5 Automatic Mesh Generation I: Rectangular Domains |
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395 | (4) |
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6.6 Automatic Mesh Generation II: Arbitrary Domains |
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399 | (3) |
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6.6.1 Definition of Blocks |
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400 | (1) |
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6.6.2 Subdivision of Each Block |
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401 | (1) |
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6.6.3 Connection of Individual Blocks |
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402 | (1) |
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402 | (6) |
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6.8 Higher-Order Elements |
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408 | (12) |
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408 | (1) |
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409 | (2) |
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411 | (2) |
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6.8.4 Fundamental Matrices |
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413 | (7) |
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6.9 Three-Dimensional Elements |
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420 | (5) |
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6.10 FEMs for Exterior Problems |
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425 | (3) |
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6.10.1 Infinite Element Method |
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425 | (1) |
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6.10.2 Boundary Element Method |
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426 | (1) |
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6.10.3 Absorbing Boundary Condition |
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427 | (1) |
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6.11 Finite-Element Time-Domain Method |
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428 | (2) |
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6.12 Applications: Microstrip Lines |
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430 | (2) |
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432 | (12) |
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444 | (7) |
7 Transmission-Line-Matrix Method |
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451 | (62) |
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451 | (2) |
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7.2 Transmission-Line Equations |
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453 | (3) |
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7.3 Solution of Diffusion Equation |
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456 | (4) |
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7.4 Solution of Wave Equations |
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460 | (15) |
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7.4.1 Equivalence between Network and Field Parameters |
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461 | (3) |
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7.4.2 Dispersion Relation of Propagation Velocity |
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464 | (2) |
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466 | (2) |
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7.4.4 Boundary Representation |
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468 | (1) |
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7.4.5 Computation of Fields and Frequency Response |
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469 | (1) |
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7.4.6 Output Response and Accuracy of Results |
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470 | (5) |
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7.5 Inhomogeneous and Lossy Media in TLM |
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475 | (8) |
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7.5.1 General 2-D Shunt Node |
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475 | (2) |
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477 | (1) |
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7.5.3 Representation of Lossy Boundaries |
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478 | (5) |
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483 | (14) |
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483 | (2) |
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485 | (4) |
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7.6.3 Boundary Conditions |
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489 | (8) |
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7.7 Error Sources and Correction |
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497 | (2) |
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498 | (1) |
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498 | (1) |
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498 | (1) |
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499 | (1) |
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7.8 Absorbing Boundary Conditions |
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499 | (2) |
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501 | (7) |
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508 | (5) |
8 Monte Carlo Methods |
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513 | (64) |
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513 | (1) |
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8.2 Generation of Random Numbers and Variables |
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514 | (3) |
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517 | (4) |
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8.4 Numerical Integration |
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521 | (5) |
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8.4.1 Crude Monte Carlo Integration |
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521 | (2) |
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8.4.2 Monte Carlo Integration with Antithetic Variates |
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523 | (1) |
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524 | (2) |
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8.5 Solution of Potential Problems |
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526 | (19) |
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526 | (4) |
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8.5.2 Floating Random Walk |
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530 | (3) |
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533 | (12) |
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8.6 Markov Chain Regional MCM |
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545 | (7) |
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8.7 MCMC for Poisson's Equation |
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552 | (4) |
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8.8 Time-Dependent Problems |
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556 | (6) |
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562 | (10) |
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572 | (5) |
9 Method of Lines |
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577 | (36) |
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577 | (1) |
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9.2 Solution of Laplace's Equation |
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578 | (10) |
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9.2.1 Rectangular Coordinates |
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578 | (6) |
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9.2.2 Cylindrical Coordinates |
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584 | (4) |
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9.3 Solution of Wave Equation |
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588 | (16) |
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9.3.1 Planar Microstrip Structures |
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590 | (7) |
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9.3.2 Cylindrical Microstrip Structures |
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597 | (7) |
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604 | (2) |
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606 | (3) |
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609 | (4) |
Selected Bibliography |
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613 | (4) |
Appendix A: Vector Relations |
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617 | (4) |
Appendix B: Programming in MATLAB |
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621 | (14) |
Appendix C: Solution of Simultaneous Equations |
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635 | (20) |
Appendix D: Computational Electromagnetic Codes |
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655 | (2) |
Appendix E: Answers to Odd-Numbered Problems |
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657 | (20) |
Index |
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677 | |