Finite Element and Finite Difference Methods in Electromagnetic Scattering (eBook)

Front Cover 1
Finite Element and Finite Difference Methods in Electromagnetic Scattering 4
Copyright Page 5
Table of Contents 12
ADVISORY BOARD 6
PREFACE 8
CONTRIBUTORS 10
Chapter 1. PRINCIPLES OF FINITE METHODS IN ELECTROMAGNETIC SCATTERING 16
1.1 Introduction 16
1.2 Finite Methods 18
1.3 Mesh Termination 44
1.4 Conclusion 77
References 80
Chapter 2. A FINITE ELEMENT METHOD FOR COMPOSITE SCATTERERS 84
2.1 Introduction 84
2.2 Formulation 88
2.3 Finite Element Method 94
2.4 Numerical and Experimental Results 110
2.5 Conclusions 120
2.6 Future Developments 120
References 125
Chapter 3. COUPLED FINITE ELEMENT AND BOUNDARY ELEMENT METHODS IN ELECTROMAGNETIC SCATTERING 128
3.1 Introduction 128
3.2 General Formulation 130
3.3 Implementation and Numerical Results 141
3.4 Conclusion 145
References 146
Chapter 4. ABSORBING BOUNDARY CONDITIONS FOR THE DIRECT SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS ARISING IN ELECTROMAGNETIC SCATTERING PROBLEMS 148
4.1 Introduction 148
4.2 Derivation of the BGT Operators 151
4.3 Alternate Boundary Condition for 2-D Scattering 155
4.4 Performance of Boundary Operators 158
4.5 Absorbing Boundary Condition for the FEM 165
4.6 Improvement in the ABC-Based Solution 173
4.7 ABC for 3-D Scalar and Vector Fields 177
References 187
Chapter 5. APPLICATION OF THE CONTROL REGION APPROXIMATION TO TWO-DIMENSIONAL ELECTROMAGNETIC SCATTERING 190
5.1 Introduction 190
5.2 Problem Formulation 192
5.3 Asymptotic Boundary Conditions 195
5.4 Discretization 201
5.5 Solution of Discrete Equations 207
5.6 Cross Section Calculation 208
5.7 Numerical Results 213
5.8 Conclusion 221
References 223
Chapter 6. COUPLED POTENTIALS FOR ELECTROMAGNETIC FIELDS IN INHOMOGENEOUS MEDIA 226
6.1 Introduction 226
6.2 Coupled Potential Formulation 228
6.3 Numerical Algorithm 240
6.4 Computer Validations 249
6.5 Discussion 259
References 260
Chapter 7. THE METHOD OF CONFORMING BOUNDARY ELEMENTS FOR TRANSIENT ELECTROMAGNETICS 264
7.1 Introduction 264
7.2 Initial Boundary Value Problem 266
7.3 Method of Conforming Boundary Elements 267
7.4 Radiation Boundary Condition 275
7.5 Field Singularities at Wedges and Corners 280
7.6 Numerical Results 287
7.7 Discussion 295
References 296
Chapter 8. THE FINITE-DIFFERENCE TIME-DOMAIN METHOD FOR NUMERICAL MODELING OF ELECTROMAGNETIC WAVE INTERACTIONS WITH ARBITRARY STRUCTURES 302
8.1 Introduction 303
8.2 General Characteristics of FD-TD 305
8.3 Basic FD-TD Algorithm Details 308
8.4 Contour Path Interpretation 319
8.5 Radiation Boundary Conditions 327
8.6 FD-TD Modeling Validations in 2-D 344
8.7 FD-TD Modeling Validation in 3-D 355
8.8 Penetration and Coupling in 2-D and 3-D 360
8.9 Modeling Very Complex 3-D Structures 371
8.10 Microstrip and Microwave Circuits 376
8.11 Inverse Scattering Reconstructions 378
8.12 Very Large-Scale Software 381
8.13 Conclusion 383
References 384
INDEX 390