由於存在被曲面金屬結構截短的細小網格，CFDTD法主要的缺點在於必須全面性降低時間步階用來確保數值穩定。在本論文中，等效介質常數的概念用來取代積分形式的法拉第定律並分析覆蓋塗層的曲面結構，因此，根據相同的CFL穩定準則之推導過程，我們能夠從理論上推導每一個不規則網格的穩定條件，所以可以適應性選擇每一個細小網格的時間步階尺寸，本論文提出適應性調整時間步階的機制並驗證數值方法的穩定性。透過計算不同散射體的雷達散射截面，我們方法和其他已建立的方法比較方法的準確性和計算效率。

The chief shortcoming of the conventional conformal finite-difference time-domain (CFDTD) method is a global time step reduction to ensure stability, due to the small irregular cells truncated by the curved conducting geometry. In this dissertation, we employ the concept of the equivalent material constants into the integral form of Faraday’s law to analyze the curved configuration with the coating. Hence, we can theoretically derive the stability criterion of each irregular cell based on the same procedure for the Courant-Friedrichs-Lewy (CFL) stability criterion. Therefore, the local time step size of each small irregular cell can be chosen adaptively. An adaptively adjusted time-stepping procedure is presented and is theoretically proven to ensure numerical stability. The radar cross section (RCS) results of various curved conducting objects with the coating are computed. Comparisons of accuracy and efficiency of our method with other established methods are performed.

Contents

Acknowledgment i
Abstract iii
Contents v
List of Figures vii
List of Tables ix


1. Introduction 1
1.1 Development of the Finite-Difference Time-Domain method 1
1.2 Development of the Conformal Finite-Difference Time-Domain method 2
1.3 A Novel FDTD Time-Stepping Scheme for Analyzing the Curved Objects 6
1.4 Overview of Dissertation 7
2. Finite-Difference Time-Domain Method 9
2.1 FDTD Algorithm 9
2.2 Stability Condition 13
2.3 Anisotropic Perfectly Matched Layer 14
3. A Novel FDTD Time-Stepping Scheme for Modeling the Thinly Coated Curved Conducting Objects 17
3.1 A Novel FDTD Formulations for Modeling the Curved Conducting Object 19
3.2 Effective Parameters for the Thinly Coated Curved Conductor 22
3.2.1 The Concept of Effective Parameters with the Coating 22
3.2.2 Possible Intersections of an FDTD cell Truncated by the Curved Objects 25
3.3 An Adaptively Adjusted Time-Stepping Procedure 27
4. Radar Cross Section Calculations in FDTD Simulations Using Kirchhoff Surface Integral Representation 34
4.1 Introduction 34
4.2 Radar Cross Section Calculations in FDTD Simulation 35
4.3 Far-Field Calculation Using Kirchhoff Surface Integral Representation 37
4.3.1 Kirchhoff Surface Integral Representation 37
4.3.2 Discretization of KSIR 38
4.3.3 Modification of KSIR’s Integral Area 40
5. FDTD Analyses of Curved Conducting objects by Our Proposed Method 42
5.1 A Spherical Cavity Model 42
5.1.1 Analytical Solution of the Spherical Cavity 42
5.1.2 Numerical Analysis of a Spherical Cavity 44
5.2 A Conducting Sphere Model with the Coating 49
5.2.1 Mie Series Solution 49
5.2.2 Numerical Analysis of a Conducting Sphere with the Coating 51
5.3 A Simplified Missile Model 57
6. Conclusions 61
Bibliography 63
Appendix 68
Vita 73
Publication List 73

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