TABLE OF CONTENTS
INTRODUCTION 1
CHAPTER 1
Description of Scattering Problems 3
1.1 MAXWELL’S EQUATIONS 3
1.2 DESCRIPTION OF SCATTERING PROBLEM 6
1.3 INTEGRAL EQUATIONS 10
1.3.1 Electric Field Integral Equation (EFIE) Formulation 11 1.3.2 PMCHW for homogeneous lossy dielectric objects 14
1.3.3 Multilayered Green’s function 19
1.4 RADAR CROSS SECTION 21
CHAPTER 2
The Method of Moments 25
2.1 INTRODUCTION 25
2.2 THE METHOD OF MOMENTS 28
2.3 BASIS AND TESTING FUNCTIONS 30
2.3.1 Basis Functions 31
2.3.2 Testing Functions 33
2.4 RWG BASIS FUNCTION 34
2.5 SOLUTION OF INTEGRAL EQUATIONS WITH MoM 37
2.5.1 Testing of the EFIE for Perfect Conductor 37
2.5.2 Testing of the PMCHW 40
2.5.3 Testing of the multilayered case 43
2.6 CONCLUSION 44
CHAPTER 3
Characteristic Basis Function Method 46
3.1 INTRODUCTION 47
3.2 CHARACTERISTIC BASIS FUNCTION METHOD 49
3.3 IMPROVEMENT OF THE CBFM 55
3.3.1 Singular Value Decomposition 55
3.3.2 Plane Wave Spectrum and CBFM 56
3.4 CONCLUSION 62 CHAPTER 4 Numerical Results 64 4.1 INTRODUCTION 64 4.2 DIELECTRIC OBJECTS 66 4.2.1 Code validation 66 4.2.2 Sphere 68 4.2.3 Cube 75 4.2.4 Comments 79
4.3.1 Code results validation 80 4.3.2 Helicopter 83 4.3.3 Ship 92 4.4 CONCLUSION 97 CONCLUSION 98 APPENDIX A Integration 100 A.1 INTRODUCTION 100
A.2 INTEGRATION PROCEDURES 101
A.2.1 Numerical integration 101
A.2.2 Analytical integration 102
A.2.3 Analytical integration of 1 / R 103
A.3 APPLICATION TO EM EQUATIONS 105
A.3.1 Integrals of singularity 1 / R 106
A.3.2 Integrals of singularity 1 / R 2 107
A.4 Code’s implementation 109
A.5 Conclusion 110
BIBLIOGRAPHY 111
