This interdisciplinary book deals with the solution of large linear systems as they typically arise in computational electrodynamics. It presents a collection of topics which are important for the solution of real life electromagnetic problems with numerical methods - covering all aspects ranging from numerical mathematics up to measurement techniques. Special highlights include a first detailed treatment of the Finite Integration Technique (FIT) in a book - in theory and applications, a documentation of most recent algorithms in use in the field of Krylov subspace methods in a unified style, a discussion on the interplay between simulation and measurement with many practical examples.

Acknowledgements XI Overview XIII Introduction 1 1. Classical Electrodynamics 11 1.1 Maxwell's Equations11 1.2 Energy Flow and Processes of Thermal Conduction 13 1.2.1 Energy and Power of Electromagnetic Fields 13 1.2.2 Thermal Effects 14 1.3 Classification of Electromagnetic Fields 15 1.3.1 Stationary Fields 15 1.3.2 Quasistatic Fields 17 1.3.3 General Time-Dependent Fields and Electromagnetic Waves 21 1.3.4 Overview and Solution Methods 22 1.4 Analytical Solution Methods 23 1.4.1 Potential Theory 23 1.4.2 Decoupling by Differentiation 25 1.4.3 Method of Separation 26 1.5 Boundary Value Problems 29 1.5.1 Boundary Value Problems of the Potential Theory 29 1.5.2 Further Boundary Conditions 30 1.5.3 Complete Systems of Orthogonal Functions 31 1.6 Bibliographical Comments 33 2. Numerical Field Theory 35 2.1 Mode Matching Technique 36 2.1.1 Mathematical Treatment of the Field Problem 37 2.1.2 Scattering Matrix Formulation 38 2.1.3 Standing Waves and Travelling Waves 42 2.1.4 Convergence and Error Investigations 44 2.2 Finite Element Method 48 2.2.1 General Outline of the Finite Element Approach 49 2.2.2 Weighted Residual Method; Galerkin Approach 50 2.2.3 Duality Methods 52 2.2.4 Finite Element Discretizations of Maxwell's Equations 54 2.2.5 Synthesis Between FEM with Whitney Forms and Finite Integration Technique 56 2.3 Finite Integration Technique 56 2.3.1 FIT Discretization of Maxwell's Equations 56 2.3.2 Stationary Fields 70 2.3.3 Quasistatic Fields 72 2.3.4 General Time-Dependent Fields and Electromagnetic Waves 74 2.4 Resulting Linear Systems 76 2.4.1 Special Properties of Complex Matrices 76 2.4.2 Mode Matching Technique 77 2.4.3 Finite Integration Technique 78 2.5 Bibliographical Comments 80 3. Numerical Treatment of Linear Systems 83 3.1 Direct Solution Methods 87 3.1.1 LU-decomposition; Gaussian Elimination 87 3.2 Classical Iteration Methods 91 3.2.1 Practical Use of Iterative Methods Stopping Criteria 92 3.2.2 Gauss-Seidel and SOR 92 3.2.3 SGS and SSOR Algorithms 94 3.2.4 The Kaczmarz Algorithm 95 3.3 Chebyshev Iteration 96 3.4 Krylov Subspace Methods 99 3.4.1 The CG Algorithm 100 3.4.2 Algorithms of Lanczos Type 105 3.4.3 Look-Ahead Lanczos Algorithm 108 3.4.4 CG Variants for Non-Hermitian or Indefinite Systems 109 3.5 Minimal Residual Algorithms and Hybrid Algorithms 114 3.5.1 GMRES Algorithm (Generalized Minimal Residual) 115 3.5.2 Hybrid Methods 116 3.5.3 GCG-LS(s) Algorithm (Generalized Conjugate Gradient, Least Square) 120 3.5.4 Overview of BiCG-like Solvers 121 3.6 Multigrid Techniques 121 3.6.1 Smoothing and Local Fourier Analysis 123 3.6.2 The Two-Grid Method 124 3.6.3 The Multigrid Technique 127 3.6.4 Embedding of the Multigrid Method into a Problem Solving Environment 128 3.7 Special MG-Algorithm for Non-Hermitian Indefinite System 131 3.7.1 Pecularities of the Special Problem and Corresponding Measures 132 3.7.2 The Multigrid Algorithm; Properties of the Linear System and its Solution 137 3.7.3 Grid Transfers for Vector Fields 141 3.7.4 The Relaxation 145 3.7.5 The Choice of the Cycles in the FMG Approach 148 3.7.6 The Solution Method on the Coarsest Grid 148 3.7.7 Concluding Remarks on the Multigrid Algorithm and Possible Outlook 149 3.8 Preconditioning 150 3.8.1 Incomplete LU Decompositions 151 3.8.2 Iteration Methods 154 3.8.3 Polynomial Preconditioning 154 3.8.4 MultigridMethods 155 3.9 Real-Valued Iteration Methods for Complex Systems 156 3.9.1 Axelsson's Reduction of a Complex Linear System to Real Form 156 3.9.2 Efficient Preconditioning of the C-to-R Method 158 3.9.3 C-to-R Method and Electro-Quasistatics 160 3.10 Convergence Studies for Selected Solution Methods 161 3.10.1 Real Symmetric Positive Definite Matrices 162 3.10.2 Complex Symmetric Positive Stable Matrices 176 3.10.3 Complex Indefinite Matrices 182 3.11 Bibliographical Comments 199 4. Applications from Electrical Engineering 205 4.1 Electrostatics 205 4.1.1 Plug 205 4.2 Magnetostatics 211 4.2.1 C-Magnet 212 4.2.2 Current Sensor 213 4.2.3 Velocity Sensor 214 4.2.4 Nonlinear C-magnet 216 4.3 Stationary Currents; Coupled Problems 217 4.3.1 Hall Element 219 4.3.2 Semiconductor 220 4.3.3 Circuit Breaker 221 4.4 Stationary Heat Conduction; Coupled Problems 223 4.4.1 Temperature Distribution on a Board 223 4.5 Electro-Quasistatics 224 4.5.1 High Voltage Insulators with Contaminations 224 4.5.2 Surface Contaminations 226 4.5.3 Fields on High Voltage Insulators 227 4.5.4 Outlook 229 4.6 Magneto-Quasistatics 233 4.6.1 TEAM Benchmark Problem 234 4.7 Time-Harmonic Problems 234 4.7.1 3 dB Waveguide Coupler 237 4.7.2 Microchip 237 4.8 General Time-Dependent Problems 239 4.9 Bibliographical Comments 239 5. Applications from Accelerator Physics 243 5.1 Acceleration of Elementary Particles 243 5.2 Linear Colliders 245 5.2.1 Actual Linear Collider Studies 247 5.2.2 Acceleration in Linear Colliders 250 5.2.3 The S-Band Linear Collider Study 265 5.3 Beam Dynamics in a Linear Collider 268 5.3.1 Emittance 268 5.3.2 Wake Fields and Wake Potential 270 5.3.3 Single Bunch and Multibunch Instabilities 279 5.4 Numerical Analysis of Higher Order Modes 280 5.4.1 Computation of the First Dipole Band of the S-Band Structure with 30 Homogeneous Sections 281 5.4.2 Developments That Followed the ORTHO Studies 288 5.4.3 Geometry and Convergence Studies of Trapped Modes 288 5.4.4 Comparison with the Coupled Oscillator Model COM 290 5.4.5 Comparison with Measurements for the LINAC II Structure at DESY 294 5.5 36-Cell Experiment on Higher Order Modes 295 5.5.1 Design 297 5.5.2 Numerical Results for the First Dipole Band 299 5.5.3 Measurement Methods 302 5.5.4 Bead Pull Measurements 304 5.5.5 Comparison of Measurement and Simulation 305 5.5.6 Measurement with Local Damping 310 5.5.7 Comments and Outlook 314 5.5.8 Suppression of Parasitic Modes 315 5.5.9Design of the Damped SBLC Structure 318 5.5.10 Concluding Remarks about the Linear Collider Studies 319 5.6 Coupled Temperature Problems 320 5.6.1 Inductive Soldering of a Traveling Wave Tube 320 5.6.2 Temperature Distribution in Accelerating Structures 322 5.6.3 RF-Window 323 5.6.4 Waveguide with a Load 324 5.7 Bibliographical Comments324 References 337 Symbols 353 Index 363

등록된 사용후기

사용후기 쓰기 새 창 더보기

사용후기가 없습니다.

등록된 상품문의

상품문의 쓰기새 창 더보기

상품문의가 없습니다.

배송정보

교환/반품 정보