Time domain boundary integral equations analysis [Elektronische Ressource] / von Amir Geranmayeh

Sujets

• Informatik
• Mathematics
• Physik

Informations

• Publié par: technischen_universitat_darmstadt
• Publié le: 01 janvier 2011
• Nombre de lectures: 41
• Langue: Deutsch
• Poids de l'ouvrage: 11 Mo

Extrait

Time Domain Boundary Integral Equations Analysis
Vom Fachbereich Elektrotechnik und Informationstechnik
der Technischen Universita¨t Darmstadt
zur Erlangung des akademischen Grades
eines Doctor Ingenieurs (Dr.-Ing.)
genehmigte
Dissertation
von
M.Sc. Amir Geranmayeh
geboren am 14. September 1980 in Tehran
Darmstadt 2011
Referent: Prof. Dr.-Ing. Thomas Weiland
Korreferent: Prof. Dr.-Ing. Thomas Eibert
Tag der Einreichung: 20.10.2010
Tag der mu¨ndlichen Pru¨fung: 20.12.2010
D 17
Darmstadt 2011i
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Kontakt: [e-mail]
Maryam Geranmaye
in BerlinContents
Abstract ix
Kurzfassung xi
1 Introduction 1
1.1 Background and Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Advances Proposed by This Work . . . . . . . . . . . . . . . . . . . . . . . 2
2 Boundary Integral Equations 5
2.1 Electric Field Integral Equation (EFIE) . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Alternative Forms of TD-EFIE . . . . . . . . . . . . . . . . . . . . 8
2.2 Magnetic Field Integral Equation (MFIE) . . . . . . . . . . . . . . . . . . 9
2.2.1 Simplifications of the MFIE . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Combined Field Integral Equation (CFIE) . . . . . . . . . . . . . . . . . . 10
2.3.1 Dielectric Scatterer . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.2 Narrow-Band Formulations. . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Spatial Discretization Using Vector Basis Functions (BF) . . . . . . . . . . 13
2.4.1 Divergence-Conforming Rao-Wilton-Glisson (RWG) BF . . . . . . . 13
2.4.2 Roof-Top (RT) BF . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.3 Linearly-Varying Hybrid BF . . . . . . . . . . . . . . . . . . . . . . 15
2.4.4 Mesh Plantation along Generatrices . . . . . . . . . . . . . . . . . . 17
2.5 Galerkin’s Testing Procedure in Boundary Element Method . . . . . . . . 18
2.5.1 Adaptive Space Quadrature Schemes . . . . . . . . . . . . . . . . . 20
3 Temporal Discretization 23
3.1 Marching-on-in-Time (MOT) Schemes . . . . . . . . . . . . . . . . . . . . 23
3.2 Time Integration Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.1 Theta Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.2 Time Interpolation Methods . . . . . . . . . . . . . . . . . . . . . . 28
3.2.3 Delay Differential Equation (DDE) Context . . . . . . . . . . . . . 29
3.3 Subdomain Lagrange Basis Functions . . . . . . . . . . . . . . . . . . . . . 30
3.3.1 B-Spline Bases with Entire-Domain Interpolation . . . . . . . . . . 34
3.4 Entire-Domain Basis Functions . . . . . . . . . . . . . . . . . . . . . . . . 35
3.4.1 Laguerre Expansion Method . . . . . . . . . . . . . . . . . . . . . . 36
3.4.2 Marching-on-in-Degree (MOD) Recipes . . . . . . . . . . . . . . . . 39
3.4.3 Advanced Marching-on-in-Degree (AMOD) Methods . . . . . . . . 41
3.4.4 Summation Reduction Technique . . . . . . . . . . . . . . . . . . . 42
3.4.5 Alternative AMOD with Reduced Sums . . . . . . . . . . . . . . . 44
iiiiv CONTENTS
3.4.6 Marching-on-in-Hermite Polynomials . . . . . . . . . . . . . . . . . 47
3.5 Finite Difference Delay Modeling (FDDM) . . . . . . . . . . . . . . . . . . 49
3.5.1 Convolution Quadrature Methods (CQM) . . . . . . . . . . . . . . 54
3.6 Symplectic Time Integration for Energy Conservation . . . . . . . . . . . . 56
3.6.1 Symmetric Adaptive Refining Quadrature Routines . . . . . . . . . 56
3.7 Algebraic Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4 Accelerated Solvers 61
4.1 Comparison of MOT and MOD Methods . . . . . . . . . . . . . . . . . . . 61
4.2 Space Convolution Products . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3 Periodicity and Multilevel Toeplitz Matrices . . . . . . . . . . . . . . . . . 67
4.4 Toeplitz Property on Time (Order) Indices . . . . . . . . . . . . . . . . . . 70
4.4.1 Computational Complexity Analysis . . . . . . . . . . . . . . . . . 74
4.5 Wavelet-Based Matrix Compression . . . . . . . . . . . . . . . . . . . . . . 76
4.5.1 Wavelet Packet Transform . . . . . . . . . . . . . . . . . . . . . . . 77
4.6 Adaptive Integral Methods and Precorrected-FFT . . . . . . . . . . . . . . 78
5 Near−Field Computations 81
5.1 Closed-Form Fields of Linear Potentials . . . . . . . . . . . . . . . . . . . . 81
5.2 Closed-Form Fields of Time-Varying RWG Sources . . . . . . . . . . . . . 84
5.2.1 Precise Evaluation of the MOT Four-Fold Integrals . . . . . . . . . 87
5.3 Polar Integration for Space-Time Quadratures . . . . . . . . . . . . . . . . 88
5.3.1 A Nystro¨m Method without Local Corrections . . . . . . . . . . . . 93
5.3.2 Analytical Evaluation of Arc Length and Bisecting Vector . . . . . 94
5.4 Exact Evaluation of Retarded Potential Integrals . . . . . . . . . . . . . . 96
5.5 Far-Field Approximations and RCS Calculations . . . . . . . . . . . . . . . 97
6 Numerical Results and Discussion 99
6.1 Convergence Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.2 Consistent Integrator−Interpolator Pairs . . . . . . . . . . . . . . . . . . . 101
6.3 Subdomain Temporal Basis Functions . . . . . . . . . . . . . . . . . . . . . 104
6.4 Orthogonal Time Basis Functions . . . . . . . . . . . . . . . . . . . . . . . 107
6.5 Hybrid Meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.6 FDDM and CQM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.7 Space-FFT Acceleration on Uniform Meshes . . . . . . . . . . . . . . . . . 119
6.7.1 Finite Periodic Structures . . . . . . . . . . . . . . . . . . . . . . . 121
6.8 Reduced Sum Convolution Products . . . . . . . . . . . . . . . . . . . . . 121
6.9 Time-FFT Speed Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.10 Polynomial Eigenvalues of TDIE Solvers . . . . . . . . . . . . . . . . . . . 124
6.11 Wake Field Simulation in Particle Accelerators . . . . . . . . . . . . . . . . 139
6.11.1 Wake Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
6.11.2 Cylindrical, Pillbox, and Tesla Cell Cavities . . . . . . . . . . . . . 145
6.12 Realistic Complex Structures . . . . . . . . . . . . . . . . . . . . . . . . . 146
7 Summary and Outlook 159CONTENTS v
8 Appendix 163
8.1 Hilbert Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
8.2 Duffy Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
8.3 Inner Products of Vector Bases . . . . . . . . . . . . . . . . . . . . . . . . 165
8.4 Laguerre Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
8.4.1 Time Weighted Expansion . . . . . . . . . . . . . . . . . . . . . . . 167
8.5 Hermite Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
8.5.1 Choice of Expansion Order . . . . . . . . . . . . . . . . . . . . . . . 168
8.6 z-Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.7 Same Side Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
Nomenclature 171
Bibliography 186
Biography avi CONTENTSAcknowledgment
First and foremost, I wish to express my sincere gratitude and deepest appreciation to my
PhD advisor, Prof. Thomas Weiland, whose abundant support has greatly helped me in
the last five years. My probable future academic achievements surely would be beholden
to his outstanding credibility. This work is heavily indebted to his broad vision in the field
and the gracious credence he earnestly honored me.
I would like to cordially thank Prof. Thomas Eibert, Prof. Klaus Hofmann, Prof.
Abdelhak M. Zoubir, and Prof. Gerd Balzer for the attention they devoted to review and
evaluate my work as the examination committee.
Especial thanks should also go to Prof. Hideki Kawaguchi for providing suggestions
courteously every year I met him.
I am deeply grateful to diligent mentor Dr. Wolfgang Ackermann whose ever-constant
guidancelearned me what theprofoundstudy throughendless patience is allabout andhis
scientific enthusiasm for performing pure flawless research tasks will remain as an utmost
source of inspiration throughout my future career.
All my accomplishments would not have been possible without decades of steady en-
couragement and loving self-sacrifice of my adorable parents, Dr. Bahman and Tooba de
Granmayeh.
And last but certainly not the least, I feel truly privileged to work with all affectionate
friends and fellow colleagues who created such cheerful atmosphere in the TEMF institute;
I indeed owe many TEMF graduate affiliates and the administrative assistants.
The financial support provided by the Deutschen Forschungsgemeinschaft (DFG) is
highly acknowledged.
viiviii CONTENTSAbstract
The present research study mainly involves a survey of diverse time-domain boundary
element methods that can be used t