Inverse problems and optimal design in electricity and magnetism
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| Format: | Buch |
| Sprache: | English |
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Oxford
Clarendon Pr.
1996
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| Schriftenreihe: | Monographs in electrical and electronic engineering
35 |
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| 245 | 1 | 0 | |a Inverse problems and optimal design in electricity and magnetism |c P. Neittaanmäki, M. Rudnicki and A. Savini |
| 264 | 1 | |a Oxford |b Clarendon Pr. |c 1996 | |
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Datensatz im Suchindex
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| adam_text | Inverse Problems
and Optimal Design in
Electricity and Magnetism
P Neittaanmäki
Department of Mathematics,
University of Jyväskylä
M Rudnicki
Institute of Electrical Engineering,
Warsaw
and
A Savini
Department of Electrical Engineering,
University of Pavia
CLARENDON PRESS • OXFORD
Contents
I Mathematical methodology
1 Mathematical preliminaries 3
1 1 Basic notation 3
1 2 Vectors, matrices, norms 4
121 Matrices 4
122 Independence, orthogonality, subspaces 6
123 Special matrices 7
124 Block matrices 8
125 Vector norms 9
126 Matrix norms 11
1 3 Functions 12
1 4 Domains 13
1 5 Function spaces 14
1 6 Classical integral formulae 21
1 7 References 23
2 Boundary-value problems 24
2 1 Variational methods for elliptic problems 24
211 Classical formulation 24
212 Variational formulation 25
2 2 Integral-equation formulation for partial differential 33
equations
2 3 References 36
3 Numerical methods for boundary-value problems 38
3 1 Introduction 38
3 2 Finite-element method for elliptic problems 42
321 Triangulation of the domain 42
322 Finite-element equations 45
3 3 Boundary-element method 51
3 4 References 54
4 Regularization 56
4 1 Ill-posed problems 56
4 2 Regularization schemes 57
4 3 Discrepancy principle 59
4 4 Linear integral equations of the first kind 61
4 5 Tikhonov regularization 62
4 6 Truncated singular-value decomposition 66
4 7 Regularization parameter 67
Contents
4 8 Solving Fredholm integral equations of the first 69
kind using regularization
4 9 References 72
5 Numerical methods for systems of equations 76
5 1 Solving linear systems 76
511 Elementary iterative methods 77
512 The conjugate gradient method 78
513 The preconditioned biconjugate gradient method 79
5 2 Solving nonlinear systems 80
521 Slope methods 80
522 Newton-Raphson method 82
523 Powell’s hybrid method 83
524 Brown-Brent methods 84
5 3 References 87
6 Unconstrained optimization 89
6 1 Optimality conditions 94
6 2 Search methods 100
6 3 Steepest-descent method 102
6 4 Conjugate gradient method 103
6 5 Newton method with a linear search 105
6 6 Quasi-Newton or variable-metric method 107
6 7 Polytope method 111
6 8 Stochastic optimization 115
681 Random-search methods 115
682 Genetic algorithms 116
683 Simulated annealing 116
684 Simulated annealing optimization code 119
6 9 Neural computing 123
691 Introduction 123
692 Preliminaries 123
693 Multilayer feedforward networks 124
694 Optimization by neural networks 128
6 10 References 131
7 Constrained optimization 137
7 1 Linear programming 137
7 2 Optimality (Karush-Kuhn-Tucker) conditions 139
721 Smooth case 139
722 Nonsmooth case 141
7 3 Sequential linear programming 142
7 4 Sequential quadratic programming 147
7 5 Nonsmooth and multicriteria optimization 151
751 Smooth multicriteria optimization 152
752 Unconstrained convex optimization 152
753 Unconstrained nonconvex optimization 153
754 Constrained optimization 154
Contents xi
755 Multicriteria optimization 154
756 Proximal bundle nonsmooth optimization code 155
7 6 Concluding remarks 158
7 7 References 159
8 Linear least-squares 161
8 1 Overdetermined systems of equations 161
8 2 Normal equations and ill-conditioning 163
8 3 Singular-value decomposition 164
8 4 Constrained linear least-squares 167
8 5 References 170
9 Nonlinear least-squares 172
9 1 Gauss-Newton method 173
9 2 Levenberg-Marquardt method 175
9 3 Powell’s hybrid method 178
9 4 Derivative-free methods 179
9 5 Large-residual problems 180
9 6 Trust-region method 181
9 7 Constrained nonlinear least-squares 183
9 8 References 185
II Fundamentals of electromagnetism
10 Introduction 191
11 Maxwell’s equations 192
11 1 Basic equations 192
11 2 Interface conditions 195
11 3 References 197
12 Potential equations in electricity and magnetism 198
12 1 Laplace’s equation 198
12 2 Poisson’s equation 200
12 3 Nonlinear magnetostatic fields in R2 201
12 4 Quasistatic linear electromagnetic fields 202
12 5 Electromagnetic fields in linear isotropic media 205
12 6 Further elements of electromagnetic theory 207
12 6 1 Energy, power and forces 207
12 6 2 Coulomb’s law and the Biot-Savart law 208
12 7 References 209
13 Numerical methods in electromagnetism 210
13 1 Introduction 210
13 2 Approximation of the static case 210
13 2 1 Least-squares variational methods in 210
electromagnetism
13 2 2 Least-squares finite-element methods 212
for electric fields
13 2 3 The nonlinear case 213
xii Contents
13 3 Approximation of quasistatic electric and 216
magnetic fields
13 4 Approximation of the wave equation for electric 221
scalar potentials
13 5 Concluding remarks 223
13 6 References 224
III Inverse problems and optimal design
in electromagnetic applications
14 Inverse problems and optimal design 231
14 1 Introduction 231
14 2 Inverse electromagnetic problems: methodology 232
14 3 Optimal design techniques for solving inverse 233
electromagnetic problems
14 3 1 Deterministic optimization methods (DOMs) 235
14 3 2 Stochastic optimization methods (SOMs) 235
14 4 References 236
15 Synthesis of sources 237
15 1 Synthesis of the magnetic field in a solenoid 237
15 2 Synthesis of the magnetic field on a solenoid axis 239
15 3 Synthesis of an electric field due to a point charge 243
15 4 Synthesis of an electric field due to a surface charge 245
15 4 1 Parallel-plate capacitors 245
15 4 2 Thin conducting plate 247
15 5 Synthesis of a magnetic field in a wire system 249
15 6 Synthesis of electromagnets 256
15 7 References 258
16 Synthesis of boundary conditions 259
16 1 Synthesis of the electric field in a finite domain 259
16 2 Synthesis of an electric field due to a boundary 262
potential
16 3 Synthesis of the magnetic field due to a boundary 266
current
16 4 References 268
17 Synthesis of material properties 269
17 1 Synthesis of permittivity 270
17 2 References 275
18 Optimal shape synthesis 276
18 1 Optimal shape design of a solenoid 276
18 2 Optimal shape design of the shim coil of a solenoid 279
18 3 Optimal shape design of an electromagnet 282
18 4 Optimal shape design of an air-filled capacitor 285
18 5 Optimal shape design of a pole profile in a linear 288
H-shaped magnet
18 6 Optimal shape design of a pole profile in a nonlinear 291
H-shaped magnet
18 7 References 297
19 Remarks on inverse and design problems 298
19 1 Survey of solved problems 298
19 2 References 304
20 Artificial neural networks (ANNs) for inverse electromagnetic 309
modelling
20 1 Remarks on artificial neural networks 309
20 2 References 312
IV Implementation of the FEM,
design-sensitivity and shape design procedures
21 Introduction 315
22 Implementation of the finite-element method 316
22 1 Linear elliptic boundary-value problems 316
22 1 1 Discretization of the problem 316
22 1 2 Isoparametric elements 317
22 1 3 Data structures 320
22 1 4 General program structure 322
22 2 A nonlinear FEM solver using a quasi-Newton method 322
22 3 References 324
23 Finite-element design-sensitivity analysis 325
23 1 Setting of the optimal shape design problem 325
23 2 Design-sensitivity analysis for linear problems 327
23 3 Sensitivity for the nonlinear potential equation 330
23 4 Implementation of optimal shape design procedures 333
23 5 Automatic differentiation of computer programs 335
23 6 References 338
24 Subroutine libraries 339
24 1 General-purpose software libraries 339
24 2 Partial differential equations and electromagnetic 341
software
24 3 Software libraries for nonsmooth and multicriterion 348
optimization
24 4 Artificial intelligence tools and software for optimal 349
shape design
24 5 References 349
Author index 355
Subject index 359
Contents xiii
|
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| isbn | 019859383X |
| language | English |
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| series | Monographs in electrical and electronic engineering |
| series2 | Monographs in electrical and electronic engineering |
| spellingShingle | Neittaanmäki, Pekka 1951- Rudnicki, M. Savini, A. Inverse problems and optimal design in electricity and magnetism Monographs in electrical and electronic engineering Electromagnétisme et Mathématiques ram Optimisation mathématique ram Mathematik Mathematisches Modell Electrical engineering Mathematics Electromagnetism Mathematical models Mathematical optimization Elektromagnetismus (DE-588)4014306-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4014306-5 (DE-588)4128130-5 |
| title | Inverse problems and optimal design in electricity and magnetism |
| title_auth | Inverse problems and optimal design in electricity and magnetism |
| title_exact_search | Inverse problems and optimal design in electricity and magnetism |
| title_full | Inverse problems and optimal design in electricity and magnetism P. Neittaanmäki, M. Rudnicki and A. Savini |
| title_fullStr | Inverse problems and optimal design in electricity and magnetism P. Neittaanmäki, M. Rudnicki and A. Savini |
| title_full_unstemmed | Inverse problems and optimal design in electricity and magnetism P. Neittaanmäki, M. Rudnicki and A. Savini |
| title_short | Inverse problems and optimal design in electricity and magnetism |
| title_sort | inverse problems and optimal design in electricity and magnetism |
| topic | Electromagnétisme et Mathématiques ram Optimisation mathématique ram Mathematik Mathematisches Modell Electrical engineering Mathematics Electromagnetism Mathematical models Mathematical optimization Elektromagnetismus (DE-588)4014306-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Electromagnétisme et Mathématiques Optimisation mathématique Mathematik Mathematisches Modell Electrical engineering Mathematics Electromagnetism Mathematical models Mathematical optimization Elektromagnetismus Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007075353&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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