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9783540676294

Numerical Methods in Computational Electrodynamics

by ; ; ; ; ;
  • ISBN13:

    9783540676294

  • ISBN10:

    3540676295

  • Format: Paperback
  • Copyright: 2001-01-01
  • Publisher: Springer Verlag
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Supplemental Materials

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Summary

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.

Table of Contents

Acknowledgements xi
Overview xiii
Introduction 1(10)
Classical Electrodynamics
11(24)
Maxwell's Equations
11(2)
Energy Flow and Processes of Thermal Conduction
13(2)
Energy and Power of Electromagnetic Fields
13(1)
Thermal Effects
14(1)
Classification of Electromagnetic Fields
15(8)
Stationary Fields
15(2)
Quasistatic Fields
17(4)
General Time-Dependent Fields and Electromagnetic Waves
21(1)
Overview and Solution Methods
22(1)
Analytical Solution Methods
23(6)
Potential Theory
23(2)
Decoupling by Differentiation
25(1)
Method of Separation
26(3)
Boundary Value Problems
29(4)
Boundary Value Problems of the Potential Theory
29(1)
Further Boundary Conditions
30(1)
Complete Systems of Orthogonal Functions
31(2)
Bibliographical Comments
33(2)
Numerical Field Theory
35(48)
Mode Matching Technique
36(12)
Mathematical Treatment of the Field Problem
37(1)
Scattering Matrix Formulation
38(4)
Standing Waves and Traveling Waves
42(2)
Convergence and Error Investigations
44(4)
Finite Element Method
48(8)
General Outline of the Finite Element Approach
49(1)
Weighted Residual Method; Galerkin Approach
50(2)
Duality Methods
52(2)
Finite Element Discretizations of Maxwell's Equations
54(2)
Synthesis Between FEM with Whitney Forms and Finite Integration Technique
56(1)
Finite Integration Technique
56(20)
FIT Discretization of Maxwell's Equations
56(14)
Stationary Fields
70(2)
Quasistatic Fields
72(2)
General Time-Dependent Fields and Electromagnetic Waves
74(2)
Resulting Linear Systems
76(4)
Special Properties of Complex Matrices
76(1)
Mode Matching Technique
77(1)
Finite Integration Technique
78(2)
Bibliographical Comments
80(3)
Numerical Treatment of Linear Systems
83(122)
Direct Solution Methods
87(4)
LU-decomposition; Gaussian Elimination
87(4)
Classical Iteration Methods
91(5)
Practical Use of Iterative Methods: Stopping Criteria
92(1)
Gauss-Seidel and SOR
92(2)
SGS and SSOR Algorithms
94(1)
The Kaczmarz Algorithm
95(1)
Chebyshev Iteration
96(3)
Krylov Subspace Methods
99(15)
The CG Algorithm
100(5)
Algorithms of Lanczos Type
105(3)
Look-Ahead Lanczos Algorithm
108(1)
CG Variants for Non-Hermitian or Indefinite Systems
109(5)
Minimal Residual Algorithms and Hybrid Algorithms
114(7)
GMRES Algorithm (Generalized Minimal Residual)
115(1)
Hybrid Methods
116(4)
GCG-LS(s) Algorithm (Generalized Conjugate Gradient, Least Square)
120(1)
Overview of BiCG-like Solvers
121(1)
Multigrid Techniques
121(10)
Smoothing and Local Fourier Analysis
123(1)
The Two-Grid Method
124(3)
The Multigrid Technique
127(1)
Embedding of the Multigrid Method into a Problem Solving Environment
128(3)
Special MG-Algorithm for Non-Hermitian Indefinite System
131(19)
Pecularities of the Special Problem and Corresponding Measures
132(5)
The Multigrid Algorithm; Properties of the Linear System and its Solution
137(4)
Grid Transfers for Vector Fields
141(4)
The Relaxation
145(3)
The Choice of the Cycles in the FMG Approach
148(1)
The Solution Method on the Coarsest Grid
148(1)
Concluding Remarks on the Multigrid Algorithm and Possible Outlook
149(1)
Preconditioning
150(6)
Incomplete LU Decompositions
151(3)
Iteration Methods
154(1)
Polynomial Preconditioning
154(1)
Multigrid Methods
155(1)
Real-Valued Iteration Methods for Complex Systems
156(5)
Axelsson's Reduction of a Complex Linear System to Real Form
156(2)
Efficient Preconditioning of the C-to-R Method
158(2)
C-to-R Method and Electro-Quasistatics
160(1)
Convergence Studies for Selected Solution Methods
161(38)
Real Symmetric Positive Definite Matrices
162(14)
Complex Symmetric Positive Stable Matrices
176(6)
Complex Indefinite Matrices
182(17)
Bibliographical Comments
199(6)
Applications from Electrical Engineering
205(38)
Electrostatics
205(6)
Plug
205(6)
Magnetostatics
211(6)
C-Magnet
212(1)
Current Sensor
213(1)
Velocity Sensor
214(2)
Nonlinear C-magnet
216(1)
Stationary Currents; Coupled Problems
217(6)
Hall Element
219(1)
Semiconductor
220(1)
Circuit Breaker
221(2)
Stationary Heat Conduction; Coupled Problems
223(1)
Temperature Distribution on a Board
223(1)
Electro-Quasistatics
224(9)
High Voltage Insulators with Contaminations
224(2)
Surface Contaminations
226(1)
Fields on High Voltage Insulators
227(2)
Outlook
229(4)
Magneto-Quasistatics
233(1)
TEAM Benchmark Problem
234(1)
Time-Harmonic Problems
234(5)
3 dB Waveguide Coupler
237(1)
Microchip
237(2)
General Time-Dependent Problems
239(1)
Bibliographical Comments
239(4)
Applications from Accelerator Physics
243(92)
Acceleration of Elementary Particles
243(2)
Linear Colliders
245(23)
Actual Linear Collider Studies
247(3)
Acceleration in Linear Colliders
250(15)
The S-Band Linear Collider Study
265(3)
Beam Dynamics in a Linear Collider
268(12)
Emittance
268(2)
Wake Fields and Wake Potential
270(9)
Single Bunch and Multibunch Instabilities
279(1)
Numerical Analysis of Higher Order Modes
280(15)
Computation of the First Dipole Band of the S-Band Structure with 30 Homogeneous Sections
281(7)
Developments That Followed the ORTHO Studies
288(1)
Geometry and Convergence Studies of Trapped Modes
288(2)
Comparison with the Coupled Oscillator Model COM
290(4)
Comparison with Measurements for the LINAC II Structure at DESY
294(1)
36-Cell Experiment on Higher Order Modes
295(25)
Design
297(2)
Numerical Results for the First Dipole Band
299(3)
Measurement Methods
302(2)
Bead Pull Measurements
304(1)
Comparison of Measurement and Simulation
305(5)
Measurement with Local Damping
310(4)
Comments and Outlook
314(1)
Suppression of Parasitic Modes
315(3)
Design of the Damped SBLC Structure
318(1)
Concluding Remarks about the Linear Collider Studies
319(1)
Coupled Temperature Problems
320(4)
Inductive Soldering of a Traveling Wave Tube
320(2)
Temperature Distribution in Accelerating Structures
322(1)
RF-Window
323(1)
Waveguide with a Load
324(1)
Bibliographical Comments
324(11)
Summary 335(2)
References 337(16)
Symbols 353(10)
Index 363

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