时域积分方程时间步进算法及其快速算法学士学位论文撰写范例英文.docx

1、时域积分方程时间步进算法及其快速算法学士学位论文撰写范例英文摘 要本文基于电磁理论中的Caldern关系与Caldern恒等式所揭示的不同积分算子之间的关系，系统地研究了Caldern预条件技术及其在计算电磁学积分方程方法中的应用。研究内容全面覆盖了求解理想导电体目标和均匀或分层均匀介质目标电磁散射与辐射问题的积分方程中的Caldern预条件技术。在导体积分方程方面，研究了电场积分方程在中频，低频，以及高频区的Caldern预处理方法。在介质积分方程方面，则研究了PMCHWT积分方程的Caldern预处理方法，和N-Mller积分方程的Caldern技术。本文对金属问题中的第二类Fredhol

2、m积分方程和介质问题中的第二类Fredholm积分方的精度改善进行了深入详尽的研究。关键词：电磁散射，面积分方程方法，Caldern预条件方法，数值计算精度，第二类Fredholm积分方程ABSTRACTRevealed by the Caldern relation and the Caldern identities in electromagnetic theory, the properties and relation of different integral operators in the computational electromagnetics (CEM) are uti

3、lized to construct the Caldern preconditioning techniques, which are applied in the integral-equation-based methods in this thesis. A thorough and systematic research has been accomplished to cover the Caldern preconditioning techniques for the perfect electric conductor (PEC) and the dielectric cas

4、es. For the PEC case, the Caldern preconditioning for the electric-field integral equation (EFIE) at mid, low, and high frequencies are constructed and studied. For the dielectric cases, the Caldern preconditioning for the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) integral equation are investi

5、gated, and the Caldern technique for the N-Mller integral equation is developed. Moreover, the accuracy improving technique for the second-kind Fredholm integral equation for both PEC and dielectric cases is also studied in this thesis.Keywords: Electromagnetic scattering and radiation, surface-inte

6、gral-equation-based Methods, Caldern preconditioning methods, numerical accuracy, Fred-holm integral equations of the second kindContentsChapter 1 Introduction 11.1 Research Background and Significance 11.2 State of Arts 11.3 Contents and Innovations of the Thesis 21.4 Outline of the Thesis 2Chapter

7、 2 Theoretical Basics 32.1 Integral Equations in Electromagnetics 32.2 270 MHz Plan Wave Excitation 32.3 The Solution of Integral Equations in Electromagnetics 42.3.1 General Principle of the Method of Moments 42.3.2 Geometrical Modeling and Discretization of Object 42.3.2.1 Planar Triangular Model

8、42.3.2.2 Curvilinear Triangular Model 42.3.3 The Choice of Basis Functions 52.3.3.1 Planar RWG Basis Functions 62.3.3.2 Curvilinear RWG Basis Functions 62.3.4 The Solution of Matrix Equations 62.3.4.1 Direct Algorithms 62.3.4.2 Iterative Algorithms 62.4 Conclusion 6Chapter 3 Caldern Preconditioner a

9、t Mid Frequencies 73.1 Introduction 73.2 Caldern Relation and Caldern Identities 73.3 Caldern Preconditioner at Mid Frequencies 73.4 Numerical Examples 73.5 Conclusion 7Chapter 4 Caldern Preconditioning Technique for N-Mller 84.1 Introduction 84.2 N-Mller Integral Equations 84.3 The Derivation of N-

10、Mller Equations 84.4 The Discretization of N-Mller Equations 84.5 Numerical Examples 84.6 Conclusion 8Chapter 5 Conclusions 95.1 Concluding Remarks 95.2 Future Work 9Acknowledgements 10References 11Origin of Foreign Language Materials 12Translation of Foreign Language Materials 13Chapter 1 Introduct

11、ion1.1 Research Background and SignificanceIntegral-equation-based numerical methods combined with fast algorithms are capable of solving electromagnetic problems of complex structures and material properties with a good accuracy and a high efficiency. They are widely used in a variety of engineerin

12、g applications, such as the efficient analysis of three dimensional radar scattering problems, the simulation of the input impedance and the radiation properties of antenna systems, the calculation of the input response and the transmission efficiency of microwave circuits, the evaluation of the ele

13、ctromagnetic interference (EMI) between complex electromagnetic systems, and the computer aided electromagnetic compatibility (EMC) designs. The versatility, capability, accuracy and efficiency of the integral-equation-based methods have made them an important and cost effective approach in the anal

14、ysis and design of electromagnetic problems and applications. 1.2 State of ArtsFrom the 1960s, the numerical methods of electromagnetic analysis have been fast developed because of their versatility and flexibility. Many well-known numerical methods have been introduced during that time, including t

15、he finite element method (FEM) 1 and the finite difference time domain method (FDTD) 2,3, which are based on the solution to the Maxwells equations in differential form, and the method of moments (MoM) 2, 4-6, which is based on the solution to the Maxwells equations in integral form. Especially from

16、 1990s, with the fast developments of high performance computing systems, the theories and methods of computational electromagnetics have been advanced dramatically. The increases of the clock speed and the memory size of computer systems and the developments of highly efficient electromagnetic comp

17、uting algorithms make the numerical methods capable of solving electromagnetic engineering problems.1.3 Contents and Innovations of the ThesisBased on the Caldern relation and the Caldern identities, this thesis has developed several Caldern preconditioning techniques and investigated their applicat

18、ions in the integral-equation-based computational electromagnetic methods. The research content has covered the Caldern preconditioning techniques for the perfect electric conductor (PEC) and dielectric cases. For the PEC case, the Caldern preconditions at mid, low, and high frequencies are investig

19、ated. For the dielectric case, the Caldern preconditioning techniques for the PMCHWT and N-Mller integral equations are developed. The numerical accuracy of the second-kind Fredholm integral equations are investigated and improved in this thesis.1.4 Outline of the ThesisThis thesis is organized as f

20、ollows.Chapter 2 Theoretical BasicsIn this chapter, the general methods of constructing the commonly used integral equations in electromagnetics are introduced based on the surface equivalence principle and the volume equivalence principle.2.1 Integral Equations in ElectromagneticsIn the integral-eq

21、uation-based computational electromagnetic methods, the unknown functions in the electromagnetic problems such as the scattering or radiation fields are modeled in terms of the equivalent surface or volume electric/magnetic sources by applying the surface or volume equivalence principles, respective

22、ly. 2.2 270 MHz Plan Wave ExcitationIn order to investigate the its performance in handling electrically very large problems with over one million unknowns, the same numerical example is repeated again by increasing the frequency to 270 MHz, and keeping the incident angle and polarization of the pla

23、ne wave unchanged. To have a better insight, the memory consumption and CPU time requirements of the EFIE, the CP-CFIE(0.8), and the CP-AEFIE algorithms are given in Table 2-1.Table 2-1 Comparison of Computational Data of Different AlgorithmsTotal Memory (Mb)CPU TimeSetup (h)Solution TimeIter. (m)To

24、l. (h)EFIE3215.841.143.1863CP-CFIE(0.8)6386.127.847.0427.69CP-AEFIE5750.436.717.4719.05All the calculations are carried out on a HP Z400 workstation with a Fedora 10 operating system.2.3 The Solution of Integral Equations in Electromagnetics2.3.1 General Principle of the Method of MomentsThe integra

25、l equations constructed in the preceding section can be solved with adequate numerical methods. One of the most commonly used methods in solving integral equations is the method of moments (MoM) introduced by R. F. Harrington in 19685. The general principle and key points of MoM will be reviewed in

26、this section.2.3.2 Geometrical Modeling and Discretization of ObjectFrom the description in the preceding section, it is clear that in order to solve for the unknown equivalent electromagnetic currents defined on the surface or in the volume of an obstruction, the definition domain of the unknown cu

27、rrents, which is the geometry, needs to be described mathematically. This is the so-called geometrical modeling. In computational electromagnetics, geometrical modeling is the basic of electromagnetic modeling and numerical calculation, and its quality will affect the accuracy of the numerical solut

28、ion directly. 2.3.2.1 Planar Triangular ModelThe simplest and most commonly used element in the geometrical modeling is the planar triangle, which is defined by its three vertices (nodes). 2.3.2.2 Curvilinear Triangular ModelThe curved surface of an object can be better modeled with curvilinear tria

29、ngular elements which are the second-order curved surfaces. A curvilinear triangle can be defined by six nodes, three of which are the vertices of the triangle, the other three are the midpoints of three curved edges. Shown in Figure 2-1 is the sketch of a curvilinear triangular element. The curved

30、surface of an object can be better modeled with curvilinear triangular elements which are the second-order curved surfaces. A curvilinear triangle can be defined by six nodes, three of which are the vertices of the triangle, the other three are the midpoints of three curved edges. Shown in Figure 2-

31、1 is the sketch of a curvilinear triangular element. Figure 2-1 The sketch of a curvilinear triangular element. (a) The curvilinear triangle in the coordinate system; (b) The curvilinear triangle in the coordinate systemUsing the following coordinate transformation, the curvilinear triangle in the r

32、ectangular coordinate system, as shown in Figure 2-1(a), can be mapped onto the triangle defined in a parametric coordinate system, as shown in Figure 2-1(b) (2-1)where denotes the rectangular coordinates of the six controlling nodes in Figure 2-1a,， are the parametric coordinates varying from 0 to 1, and they satisfy the relation (2-2)From (2-2), it is clear that only two var