The Multilevel Fast Multipole Algorithm (MLFMA) for Solving Large-Scale Computational Electromagnetics Problems - Ozgur Ergul

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Auteur(s) : Ozgur Ergul

Editeur : John Wiley & Sons

Langue : Anglais

Parution : 01/06/2014

Format : Moyen, de 350g à 1kg

Nombre de pages : 480

Expédition : 957

Dimensions : 24.6 x 17.3 x 3.0

ISBN : 9781119977414

Résumé :

Dr Ozgur Ergul,?Middle East Technical University, Turkey
Ozgur Ergul received B.Sc., M.S., and PhD degrees from Bilkent University, Turkey, in 2001, 2003 and 2009, respectively, all in electrical and electronic engineering.

Dr Levent Gurel, Bilkent University, Turkey
Levent Gurel received the B.Sc. degree from the Middle East Technical University, Turkey, in 1986, and the M.S. and PhD degrees from the University of Illinois at Urbana-Champaign in 1988 and 1991, respectively, all in electrical engineering.

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Sommaire:

Preface xi

List of Abbreviations xiii

1 Basics 1

1.1 Introduction 1

1.2 Simulation Environments Based on MLFMA 2

1.3 From Maxwell's Equations to Integro-Differential Operators 3

1.4 Surface Integral Equations 7

1.5 Boundary Conditions 9

1.6 Surface Formulations 10

1.7 Method of Moments and Discretization 12

1.7.1 Linear Functions 15

1.8 Integrals on Triangular Domains 21

1.8.1 Analytical Integrals 22

1.8.2 Gaussian Quadratures 26

1.8.3 Adaptive Integration 26

1.9 Electromagnetic Excitation 29

1.9.1 Plane-Wave Excitation 29

1.9.2 Hertzian Dipole 31

1.9.3 Complex-Source-Point Excitation 31

1.9.4 Delta-Gap Excitation 32

1.9.5 Current-Source Excitation 34

1.10 Multilevel Fast Multipole Algorithm 35

1.11 Low-Frequency Breakdown of MLFMA 39

1.12 Iterative Algorithms 41

1.12.1 Symmetric Lanczos Process 42

1.12.2 Nonsymmetric Lanczos Process 44

1.12.3 Arnoldi Process 45

1.12.4 Golub-Kahan Process 45

1.13 Preconditioning 46

1.14 Parallelization of MLFMA 50

2 Solutions of Electromagnetics Problems with Surface Integral Equations 53

2.1 Homogeneous Dielectric Objects 53

2.1.1 Surface Integral Equations 54

2.1.2 Surface Formulations 55

2.1.3 Discretizations of Surface Formulations 58

2.1.4 Direct Calculations of Interactions 60

2.1.5 General Properties of Surface Formulations 67

2.1.6 Decoupling for Perfectly Conducting Surfaces 73

2.1.7 Accuracy with Respect to Contrast 74

2.2 Low-Contrast Breakdown and Its Solution 77

2.2.1 A Combined Tangential Formulation 77

2.2.2 Nonradiating Currents 80

2.2.3 Conventional Formulations in the Limit Case 81

2.2.4 Low-Contrast Breakdown 82

2.2.5 Stabilization by Extraction 82

2.2.6 Double-Stabilized Combined Tangential Formulation 87

2.2.7 Numerical Results for Low Contrasts 88

2.2.8 Breakdown for Extremely Low Contrasts 91

2.2.9 Field-Based-Stabilized Formulations 93

2.2.10 Numerical Results for Extremely Low Contrasts 95

2.3 Perfectly Conducting Objects 105

2.3.1 Comments on the Integral Equations 106

2.3.2 Internal-Resonance Problem 108

2.3.3 Formulations of Open Surfaces 108

2.3.4 Low-Frequency Breakdown 111

2.3.5 Accuracy with the RWG Functions 115

2.3.6 Compatibility of the Integral Equations 122

2.3.7 Convergence to Minimum Achievable Error 124

2.3.8 Alternative Implementations of MFIE 130

2.3.9 Curl-Conforming Basis Functions for MFIE 131

2.3.10 LN-LT Type Basis Functions for MFIE and CFIE 137

2.3.11 Excessive Discretization Error of the Identity Operator 160

2.4 Composite Objects with Multiple Dielectric and Metallic Regions 165

2.4.1 Special Case: Homogeneous Dielectric Object 168

2.4.2 Special Case: Coated Dielectric Object 169

2.4.3 Special Case: Coated Metallic Object 172

2.5 Concluding Remarks 175

3 Iterative Solutions of Electromagnetics Problems with MLFMA 177

3.1 Factorization and Diagonalization of the Green's Function 177

3.1.1 Addition Theorem 177

3.1.2 Factorization of the Translation Functions 180

3.1.3 Expansions 183

3.1.4 Diagonalization 184

3.2 Multilevel Fast Multipole Algorithm 186

3.2.1 Recursive Clustering 186

3.2.2 Far-Field Interactions 187

3.2.3 Radiation and Receiving Patterns 188

3.2.4 Near-Field Interactions 190

3.2.5 Sampling 190

3.2.6 Computational Requirements 192

3.2.7 Anterpolation 194

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