Advances in the Formulations and Accuracy of the Method of Moments Applied to Electromagnetics

In this work we solve the scattering, a problem of electromagnetic analysis, by mixed homogeneous linear and isotropic three-dimensional materials with the Method of Moments in the harmonic... Continuer

The success of electromagnetic analysis and design during the past century would not have been possible without an accurate and complete theory, optimized numerical techniques and computers. In this work we solve the scattering by mixed homogeneous linear and isotropic three-dimensional materials with the Method of Moments in the harmonic case. New general methods, expressions and theorems have been derived to this end. They allowed to introduce a new numerical formulation able to fully solve metallic sheets. To perform the singular numerical integrations, high efficiency quadratures have been selected for their ease of implementation in a general purpose code. After careful assessment of their accuracy, the electric and magnetic field integral equations (EFIE/MFIE) have been compared. A great similarity was observed, except in the vicinity of sharp edges. A closer look revealed severe limitations inherent to the RWG basis functions. Future work will aim at unifying the EFIE and MFIE solutions everywhere.


Livre broché - En anglais 60,00 €
Info Les commandes en ligne se font via notre partenaire i6doc.

Spécifications


Éditeur
Presses universitaires de Louvain
Auteur
Thierry Gilles,
Collection
Thèses de l'École polytechnique de Louvain
Langue
anglais
Catégorie (éditeur)
Sciences appliquées > Electricité
Catégorie (éditeur)
Sciences appliquées
BISAC Subject Heading
TEC000000 TECHNOLOGY & ENGINEERING
Code publique Onix
06 Professional and scholarly
CLIL (Version 2013 )
3069 TECHNIQUES ET SCIENCES APPLIQUEES
Date de première publication du titre
01 novembre 2011
Subject Scheme Identifier Code
Thema subject category: T
Type d'ouvrage
Thèse
Avec
Bibliographie

Livre broché


Details de produit
1 A4
Date de publication
15 octobre 2011
ISBN-13
978-2-87463-288-4
Ampleur
Nombre de pages de contenu principal : 308
Dépôt Légal
D/2011/9964/25
Code interne
85236
Format
16 x 24 x 1,7 cm
Poids
497 grammes
Prix
60,00 €
ONIX XML
Version 2.1, Version 3

Google Livres Aperçu


Publier un commentaire sur cet ouvrage

Si vous avez une question, utilisez plutôt notre formulaire de contact

Sommaire


CONTENTS ...............................................................................................................I
LIST OF PUBLICATIONS ............................................................................................V
LIST OF FIGURES ...................................................................................................VII
LIST OF TABLES .....................................................................................................XI
LIST OF ABBREVIATIONS .......................................................................................XIII
PREFACE.................................................................................................................1
PART I ......................................................................................................................3
1 Electromagnetics ................................................................................5
1.1 Maxwell's equations ......................................................................5
1.2 Harmonic waves ............................................................................8
1.3 The Stratton-Chu equations .......................................................10
1.4 Fields on the surface S of a sheet ...............................................12
1.4.1 Fully embedded sheet ............................................................12
1.4.2 Sheet in contact with more than one volume........................17
1.5 Generalized formulation for mixed materials ............................19
1.6 Equivalent surface current densities .........................................22
1.7 Boundary conditions....................................................................22
1.8 Relations between normal and tangential components.............24
1.9 First and second form of the integro-differential equations......25
1.10 Near and far scattered fields ......................................................26
1.10.1 Exact near field expressions ..................................................26
1.10.2 Far field approximation .........................................................27
1.11 Normal and tangential components of the integro-differential
equations on the surface Si .........................................................28
1.12 Perfectly conducting sheets.........................................................29
1.13 Sum of Fields on both sides of a flat perfectly conducting sheet
of arbitrary shape ........................................................................30
1.14 Canonical expressions .................................................................31
1.15 Summary .....................................................................................33
2 Method of Moments ..........................................................................37
2.1 Preamble......................................................................................37
2.2 Basis functions ............................................................................38
2.2.1 Scalar or vector basis functions .............................................38
2.2.2 Discretized equations.............................................................39
2.2.3 Entire Domain basis functions ..............................................39
2.2.4 Subdomain basis functions ....................................................41
2.2.5 Conforming functions.............................................................43
2.2.6 Pulse basis function ...............................................................45
2.2.7 Linear basis function..............................................................45
2.2.8 Rao Wilton Glisson (RWG) basis functions...........................48
2.2.9 Rooftop functions....................................................................50
2.3 Testing .........................................................................................50
2.3.1 Normal and tangential testing ..............................................51
2.3.2 General considerations about testing....................................54
2.3.3 Galerkin testing .....................................................................57
2.3.4 Point Matching.......................................................................57
2.3.5 Razor blade testing.................................................................58
2.4 Summary .....................................................................................58
3 Method of Moments Formulation for Multiple Regions...........63
3.1 Preamble......................................................................................63
3.2 Singular edges and branches ......................................................65
3.3 RWG scheme on singular edges..................................................66
3.3.1 Physical Continuity and Sector Concept...............................66
3.3.2 Solder line...............................................................................67
3.3.3 Sector table.............................................................................67
3.4 Local ZI=V systems of equations ................................................69
3.5 Two properties of RWG sectors...................................................71
3.6 Global ZI=V system of equations ................................................73
3.7 PEC / PMC case...........................................................................75
3.8 Summary .....................................................................................76
4 Method of Moments for perfectly conducting sheets ..............81
4.1 Preamble......................................................................................81
4.2 Theory ..........................................................................................82
4.2.1 tEFIE-f and tMFIE-nxf for PEC sheets ................................82
4.2.2 tEFIE-f applied to PEC sheets ..............................................85
4.2.3 tMFIE-nxf applied to PEC sheets..........................................86
4.3 Singularities arising with PEC sheets .......................................87
4.3.1 Singularity of ZE obtained with the tEFIE-f .........................87
4.3.2 Singularity of ZM obtained with the tMFIE-nxf....................89
4.4 E-MFIE for PEC sheets...............................................................90
4.4.1 The E-MFIE formulation .......................................................90
4.4.2 Efficient implementation of the E-MFIE ..............................91
4.5 Summary .....................................................................................93
5 Accuracy of the Method of Moments ............................................95
5.1 Approximations introduced by the Method of Moments............95
5.2 Numerical issues and limitations ...............................................97
5.2.1 Problem size – CPU time limitation......................................97
5.2.2 Condition number ..................................................................98
5.2.3 Resonance .............................................................................101
5.2.4 Low frequency breakdown ...................................................102
5.3 Numerical integration...............................................................103
5.3.1 Quadratures over triangles..................................................103
5.3.2 Practical integration within the MoM.................................105
5.3.3 1/R and 1/R³ singularities ....................................................106
5.4 Extraction of the 1/R and 1/R³ singularities for the free-space
Green’s function.........................................................................108
5.4.1 Singularity associated with ZHJ ...........................................109
5.4.2 Singularities associated with ZEJ ........................................114
5.5 High efficiency quadratures and 1/R³ singularity....................117
5.5.1 Analytical analysis – regular triangles ...............................117
5.5.2 Numerical example ..............................................................120
5.5.3 Analytical analysis - very elongated triangles....................122
5.6 Summary ...................................................................................127
PART II.................................................................................................................135
6 Numerical examples .......................................................................137
6.1 Introduction...............................................................................138
6.1.1 Parameters common to all examples...................................138
6.1.2 Variable parameters ............................................................138
6.1.3 Presentation of the results...................................................139
6.1.4 The er = 1 reference solution ................................................140
6.2 Sphere ........................................................................................141
6.2.1 tEFIE-f..................................................................................143
6.2.2 tMFIE-nxf .............................................................................147
6.2.3 Homogeneous and inhomogeneous mesh............................149
6.2.4 Mesh density ........................................................................151
6.2.5 Dielectric sphere...................................................................153
6.3 Sphere in a half spherical shell ................................................156
6.3.1 PEC sphere inside a er = 1 shell...........................................156
6.3.2 PEC sphere inside a er = 9 shell...........................................160
6.4 Rounded cube.............................................................................162
6.4.1 Dielectric rounded cube........................................................163
6.4.2 PEC rounded cube................................................................166
6.5 Cube : regular meshes...............................................................168
6.5.1 Dielectric cube ......................................................................168
6.5.2 PEC cube ..............................................................................172
6.6 Cube : Log-distributed meshes .................................................175
6.6.1 Dielectric cube : er = 1...........................................................176
6.6.2 Dielectric cube : er = 2...........................................................180
6.6.3 PEC cube ..............................................................................182
6.7 Thin plates : regular meshes.....................................................186
6.7.1 Dielectric plate : er = 1..........................................................187
6.7.2 PEC plate..............................................................................193
6.8 Thin plate : log-distributed mesh .............................................198
6.8.1 Dielectric thin plate : er = 1..................................................199
6.8.2 Dielectric thin plate : er = 9..................................................203
6.8.3 PEC thin plate......................................................................206
6.9 Very thin and infinitely thin PEC plate : edge currents .........208
6.9.1 Introduction..........................................................................208
6.9.2 EFIE / MFIE and E-MFIE comparisons on Log-distributed
meshes..................................................................................217
6.10 PEC sheet on a thin dielectric plate .........................................227
6.10.1 PEC sheet on a er = 1 substrate...........................................228
6.10.2 PEC sheet on a er = 2 substrate...........................................234
6.11 Solder Line.................................................................................238
6.12 Examples where a 16 nodes quadrature is necessary .............241
6.12.1 Thin dielectric er = 1 plate ...................................................241
6.12.2 PEC and dielectric pyramids ...............................................244
6.13 Summary ...................................................................................247
CONCLUSION.......................................................................................................249
APPENDIX A........................................................................................................251
APPENDIX B........................................................................................................253
APPENDIX C........................................................................................................255
APPENDIX D........................................................................................................257
APPENDIX E........................................................................................................259
APPENDIX F ........................................................................................................271
APPENDIX G........................................................................................................273
APPENDIX H........................................................................................................283


Extrait