Frequency Domain Hybrid Finite Element Methods for Electromagnetics.pdf
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1、P1: IML/FFXP2: IML/FFXQC: IML/FFXT1: IML MOBK040-FMMOBK040-Volakis.clsNovember 11, 200622:5 Frequency DomainHybrid Finite ElementMethodsfor Electromagnetics i P1: IML/FFXP2: IML/FFXQC: IML/FFXT1: IML MOBK040-FMMOBK040-Volakis.clsNovember 11, 200622:5 Copyright 2006 by Morgan ?) and H(Div;?) Spaces 7
2、 1.1.4Maxwells Equations . 10 1.2Parametric Geometry Fundamentals 12 1.2.1Parametric Geometry in 1D 13 1.2.2Parametric Geometry in 2D 15 1.2.3Parametric Geometry in 3D 18 1.3Curvilinear Finite Elements19 1.3.1Divergence Conforming Elements.20 1.3.2Curl Conforming Elements.21 1.4Overview.24 2.Two-Dim
3、ensional Hybrid FEBI . 25 2.1The Boundary Value Problem 26 2.1.1TE Polarization . 27 2.1.2TM Polarization.28 2.1.3Boundary Conditions 28 2.2Surface Equivalence and Boundary Integral Equations33 2.3Variational Formulation34 2.4Discretization.36 2.5Example Discretization 39 2.62D Scattering Applicatio
4、ns.42 3.Three-Dimensional Hybrid FEBI:FormulationandApplications51 3.1The Boundary Value Problem 52 3.2Boundary Integral Equations.53 3.3The FEBI Variational Statement 54 3.4Discretization.55 P1: IML/FFXP2: IML/FFXQC: IML/FFXT1: IML MOBK040-FMMOBK040-Volakis.clsNovember 11, 200622:5 viFREQUENCY DOMA
5、INHYBRID FINITE ELEMENT METHODS 3.5Applications 58 3.5.1Scattering.58 3.5.2Antenna Radiation.62 4.Hybrid Volume-Surface Integral Equation.69 4.1Generalized VSIE Formulation.70 4.2Boundary Conditions76 4.3Variational Form of the VSIE 77 4.4Discretization.78 4.4.1Junction Resolution 80 4.4.2MoM System
6、 Development 82 4.5Examples.84 4.5.1Junction Resolution Validation 84 4.5.2Scattering Examples . 85 4.5.3Antenna Examples.90 5.PeriodicStructures.93 5.1Periodic Boundary Conditions94 5.1.1Using the FEBI 96 5.1.2Using the VSIE . 98 6.Antenna Designand OptimizationUsingFEBIMethods.109 6.1Design Optimi
7、zation: Overview.111 6.1.1 Defi nition . 111 6.1.2 Classifi cation.111 6.2Design Examples 118 6.2.1Example 1: Dielectric Material Optimization of a Patch Antenna via Topology Optimization and SLP118 6.2.2Example 2: Optimization of an Irregular-shaped Dual-band Patch Antenna via SA and GA.122 6.2.3Mu
8、ltiobjective Antenna Design Using Volumetric Material Optimization and Genetic Algorithms124 6.3Comments 129 P1: IML/FFXP2: IML/FFXQC: IML/FFXT1: IML MOBK040-FMMOBK040-Volakis.clsNovember 11, 200622:5 vii Preface This book was started with the goal of providing a brief overview of the popular fi nit
9、e ele- ment method (FEM) and its hybrid versions for electromagnetics with applications to radar scattering, antennas and arrays, guided structures, microwave components, frequency selective surfaces, periodic media, and RF materials characterizations to mention a few. However, as the project evolve
10、d we realized that several developments had occurred since the publication of the book Finite Element Method for Electromagnetics: Antennas, Microwave Circuits, and Scat- tering Applications (1998) coauthored by Volakis, Chatterjee and Kempel. Thus, we enhanced this book to also include an update to
11、 applications and methods that occurred over the past few years. More specifi cally, it also includes applications of fi nite elementboundary integral (FEBI)methodstoinfi niteandfi niteperiodicmediaandintroducesthehybridvolumeintegral equations for high contrast dielectrics and metamaterials. The im
12、portance of design optimiza- tion and its integration within commercial numerical analysis packages is recognized by the inclusion of a chapter written by a former Ph.D. student Professor Gullu Kiziltas and current postdoctoral researcher Dr. Stavros Koulouridis. Given the routine use of numerical m
13、ethods for large-scale modeling, the book starts with theoretical concepts for generating robust matrix systems from partial differential equa- tions (PDEs) and integral equations (IEs). Hilbert and Sobolev spaces as well as H(Curl;?) and H(Div;?) spaces are presented in simple engineering terms and
14、 various basis functions, including parametric, curvilinear, curl and divergence conforming as well as higher order are concisely presented in the context of the Galerkin and PetrovGalerkin methods for casting PDEs and IEs into discrete systems. This is followed by Chapter 2, which gives a step-by-s
15、tep developmentoftheFEManditshybridFEBIversionfortwo-dimensionalscatteringapplica- tions with considerations for resistive and conductive (or magnetic) cards as well as impedance boundary conditions. Several examples are given with enough details for the reader to repeat them. Chapter 3 gives a thre
16、e-dimensional overview of the FEBI method with applications to scattering, conformal antennas and large fi nite arrays where the repeatability of the unit cell is exploited to reduce memory and computational resources. Chapters 4 and 5 are devoted to the hybrid volume integral equations, including t
17、he volume surface integral equations (VSIEs). These integral equations are particularly suited for high contrast dielectrics and can also be combined with PDE-based matrix systems to yield the most effi cient and robust hybrid method. Chapter 4 gives the mathematical details (including P1: IML/FFXP2
18、: IML/FFXQC: IML/FFXT1: IML MOBK040-FMMOBK040-Volakis.clsNovember 11, 200622:5 viiiFREQUENCYDOMAINHYBRID FINITE ELEMENT METHODS matrix element calculations) with simple applications for verifi cation and others for displaying theirgreatercapability.Chapter5isparticularlydevotedtoperiodicmedia,includ
19、ingfrequency selective surfaces (FSS) and frequency selective volumes (FSV) as well as metamaterial and electromagneticbandgapstructures.Examplesofperiodicmediathatyieldnegativeconstitutive parameters are discussed and their bandgap features examined. Finally, Chapter 6 starts by giving a brief surv
20、ey of gradient (namely, sequential quadratic or linear programming) and stochastic (namely, genetic algorithms) optimization methods used in RF design. The second half of Chapter 6 is devoted to shape, topology, and material design optimization examples for antennas using the hybrid FEBI methods as
21、the solver within the optimization algorithm. John L. Volakis Kubilay Sertel Brian C. Usner July 2, 2006 The Ohio State University Columbus, Ohio, USA P1: IML/FFXP2: IML MOBK040-01MOBK040-Volakis.clsNovember 8, 200618:27 1 C H A P T E R 1 Introduction A number of numerical solutions for electromagne
22、tics appeared in the 1960s employing mo- mentmethods1,2andfi niteelementtechniques35.However,theapplicationoftheseearly implementations was very limited. With the availability of mainframe computing machines in the 1970s and 1980s, focus was primarily on high-frequency techniques 6 and related appro
23、x- imations that could handle practical problems using available CPU resources. Signifi cant focus was seen in the 1980s on all methods, including the moment method 7 and fi nite difference methods 8,9. In regard to the fi nite element method, the focus was on developing approxi- mate absorber bound
24、ary conditions for truncating the fi nite element mesh as close as possible to the scatterer or radiator 10, 11. Concurrently, research on robust iterative solvers grew substantially in the 1980s and continued vigorously in the 1990s. Hybrid methods, involving a combination of integral, fi nite elem
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