Numerical analysis of electromagnetic fields:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1993
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| Series: | Electric energy systems and engineering series
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XXI, 406 S. graph. Darst. |
| ISBN: | 3540547223 0387547223 |
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MARC
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| 100 | 1 | |a Zhou, Pei-bai |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Numerical analysis of electromagnetic fields |c Pei-bai Zhou |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1993 | |
| 300 | |a XXI, 406 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Electric energy systems and engineering series | |
| 500 | |a Literaturangaben | ||
| 650 | 7 | |a Analise numerica |2 larpcal | |
| 650 | 7 | |a Campos eletromagneticos |2 larpcal | |
| 650 | 7 | |a Elementos e diferencas finitos |2 larpcal | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Boundary element methods | |
| 650 | 4 | |a Electromagnetic fields |x Mathematics | |
| 650 | 4 | |a Field theory (Physics) |x Mathematics | |
| 650 | 4 | |a Finite element method | |
| 650 | 4 | |a Numerical analysis | |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Elektromagnetisches Feld |0 (DE-588)4014305-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Elektromagnetisches Feld |0 (DE-588)4014305-3 |D s |
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Record in the Search Index
| _version_ | 1804122773040136192 |
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| adam_text | PEI-BAI ZHOU NUMERICAL ANALYSIS OF ELECTROMAGNETIC FIELDS WITH 157
FIGURES SPRINGER-VERLAG BERLIN HEIDELBERG NEW YORK LONDON PARIS TOKYO
HONG KONG BARCELONA BUDAPEST CONTENTS PART 1 UNIVERSAL CONCEPTS FOR
NUMERICAL ANALYSIS OF ELECTROMAGNETIC FIELD PROBLEMS CHAPTER 1
FUNDAMENTAL CONCEPTS OF ELECTROMAGNETIC FIELD THEORY .... 3 1.1
MAXWELL S EQUATIONS AND BOUNDARY VALUE PROBLEMS 3 1.1.1 POTENTIAL
EQUATIONS IN DIFFERENT FREQUENCY RANGES 4 1.1.2 BOUNDARY CONDITIONS OF
THE INTERFACE 8 1.1.3 BOUNDARY VALUE PROBLEMS 10 1.2 GREEN S THEOREM,
GREEN S FUNCTIONS AND FUNDAMENTAL SOLUTIONS 11 1.2.1 GREEN S THEOREM 12
1.2.2 VECTOR ANALOGUE OF GREEN S THEOREM 14 1.2.3 GREEN S FUNCTION 15
1.2.3.1 DIRAC-DELTA FUNCTION 15 1.2.3.2 GREEN S FUNCTION 16 1.2.4
FUNDAMENTAL SOLUTIONS 18 1.3 EQUIVALENT SOURCES 19 1.3.1 SINGLE LAYER
CHARGE DISTRIBUTION 20 1.3.2 DOUBLE LAYER SOURCE DISTRIBUTIONS 22 1.3.3
EQUIVALENT POLARIZATION CHARGE AND MAGNETIZATION CURRENT .. 26 1.4
INTEGRAL EQUATIONS OF ELECTROMAGNETIC FIELDS 28 1.4.1 INTEGRAL FORM OF
POISSON S EQUATION 28 1.4.2 INTEGRAL EQUATION FOR THE EXTERIOR REGION 29
1.5 SUMMARY 30 REFERENCES 31 APPENDIX 1.1 THE INTEGRAL EQUATION OF 3-D
MAGNETIC FIELDS 31 CHAPTER 2 GENERAL OUTLINE OF NUMERICAL METHODS 35 2.1
INTRODUCTION 35 2.2 OPERATOR EQUATIONS 37 2.2.1 HILBERT SPACE 38 XIV
CONTENTS 2.2.2 DEFINITION AND PROPERTIES OF OPERATORS 40 2.2.3 THE
RELATIONSHIP BETWEEN THE PROPERTIES OF THE OPERATORS AND THE SOLUTION OF
OPERATOR EQUATIONS 42 2.2.4 OPERATOR EQUATIONS OF ELECTROMAGNETIC FIELDS
43 2.3 PRINCIPLES OF ERROR MINIMIZATION 46 2.3.1 PRINCIPLE OF WEIGHTED
RESIDUALS 47 2.3.2 ORTHOGONAL PROJECTION PRINCIPLE 48 2.3.2.1 PROJECTION
OPERATOR 49 2.3.2.2 ORTHOGONAL PROJECTION 49 2.3.2.3 ORTHOGONAL
PROJECTION METHODS 51 2.3.2.4 NON-ORTHOGONAL PROJECTION METHODS 51 2.3.3
VARIATIONAL PRINCIPLE 51 2.4 CATEGORIES OF VARIOUS NUMERICAL METHODS 52
2.4.1 METHODS OF WEIGHTED RESIDUALS 53 2.4.1.1 METHOD OF MOMENTS 53
2.4.1.2 GALERKIN S FINITE ELEMENT METHOD 54 2.4.1.3 COLLOCATION METHODS
55 2.4.1.4 BOUNDARY ELEMENT METHODS 55 2.4.2 VARIATIONAL APPROACH 56 2.5
SUMMARY 58 REFERENCES 59 PART 2 DOMAIN METHODS CBAPTER 3 FINITE
DIFFERENCE METHOD (FDM) 63 3.1 INTRODUCTION 63 3.2 DIFFERENCE
FORMULATION OF POISSON S EQUATION 64 3.2.1 DISCRETIZATION MODE FOR 2-D
PROBLEMS 64 3.2.2 DIFFERENCE EQUATIONS IN 2-D CARTESIAN COORDINATES 64
3.2.3 DISCRETIZATION EQUATION IN POLAR COORDINATES 69 3.2.4
DISCRETIZATION FORMULA OF AXISYMMETRIC FIELDS 72 3.2.5 DISCRETIZATION
FORMULA OF THE NON-LINEAR MAGNETIC FIELDS ... 73 3.2.6 DIFFERENCE
EQUATIONS FOR TIME-DEPENDENT PROBLEMS 73 3.3 SOLUTION METHODS FOR
DIFFERENCE EQUATIONS 76 3.3.1 PROPERTIES OF SIMULTANEOUS EQUATIONS 76
3.3.2 SUCCESSIVE OVER-RELAXATION (SOR) METHOD 77 3.3.3 CONVERGENCE
CRITERION 80 3.4. DIFFERENCE FORMULATIONS OF ARBITRARY BOUNDARIES AND
INTERFACIAL BOUNDARIES BETWEEN DIFFERENT MATERIALS 80 3.4.1 DIFFERENCE
FORMULATIONS ON THE LINES OF SYMMETRY 81 3.4.2 DIFFERENCE EQUATION OF A
CURVED BOUNDARY 81 3.4.3 DIFFERENCE FORMULATIONS FOR THE INTERFACE OF
DIFFERENT MATERIALS 82 CONTENTS XV 3.5 EXAMPLES 84 3.6 FURTHER
DISCUSSIONS ABOUT THE FINITE DIFFERENCE METHOD .... 87 3.6.1 PHYSICAL
EXPLANATION OF THE FINITE DIFFERENCE METHOD 87 3.6.2 THE ERROR ANALYSIS
OF THE FINITE DIFFERENCE METHOD 88 3.6.3 DIFFERENCE EQUATION AND THE
PRINCIPLE OF WEIGHTED RESIDUALS . 90 3.6.4 DIFFERENCE EQUATION AND THE
VARIATIONAL PRINCIPLE 91 3.7 SUMMARY 92 REFERENCES 93 CHAPTER 4
FUNDAMENTALS OF FINITE ELEMENT METHOD (FFM) 95 4.1 INTRODUCTION 95 4.2
GENERAL PROCEDURES OF THE FINITE DEMENT METHOD 96 4.2.1 DOMAIN
DISCRETIZATION AND SHAPE FUNCTIONS 97 4.2.2 METHOD USING GALERKIN
RESIDUALS 100 4.2.2.1 ELEMENT MATRIX EQUATIONS 101 4.2.2.2 SYSTEM MATRIX
EQUATION 106 4.2.2.3 STORAGE OF THE SYSTEM MATRIX 109 4.2.2.4 TREATMENT
OF THE DIRICHLET BOUNDARY CONDITION 111 4.3 SOLUTION METHODS OF FINITE
ELEMENT EQUATIONS 113 4.3.1 DIRECT METHODS 113 4.3.1.1 GAUSSIAN
ELIMINATION METHOD 113 4.3.1.2 CHOLESKY S DECOMPOSITION (TRIANGULAER
DECOMPOSITION) 115 4.3.2 ITERATIVE METHODS 117 4.3.2.1 METHOD OF
OVER-RELAXATION ITERATION 118 4.3.2.2 CONJUGATE-GRADIENT METHOD (CGM)
119 4.4 MESH GENERATION 120 4.4.1 MESH GENERATION OF A TRIANGULAER
ELEMENT 121 4.4.2 AUTOMATIC MESH GENERATION 123 4.5 EXAMPLES 124 4.6
SUMMARY 127 REFERENCES 128 CHAPTER 5 VARIATIONAL FINITE ELEMENT METHOD
130 5.1 INTRODUCTION 130 5.2 BASIC CONCEPTS OF THE FUNCTIONAL AND ITS
VARIATIONS 131 5.2.1 DEFINITION OF THE FUNCTIONAL AND ITS VARIATIONS 132
5.2.1.1 THE FUNCTIONAL 132 5.2.1.2 THE DIFFERENTIATION AND VARIATION OF
A FUNCTION 134 5.2.1.3 VARIATION OF THE FUNCTIONAL 135 XVI CONTENTS
5.2.2 CALCULUS OF VARIATIONS AND EULER S EQUATION 136 5.2.2.1 EULER S
EQUATION 137 5.2.2.2 EULER S EQUATION FOR MULTIVARIABLE FUNCTIONS 138
5.2.2.3 THE SHORTEST LENGTH OF A CURVE 140 5.2.3 RELATIONSHIP BETWEEN
THE OPERATOR EQUATION AND THE FUNCTIONAL . 141 5.3 VARIATIONAL
EXPRESSIONS FOR ELECTROMAGNETIC FIELD PROBLEMS . . 142 5.3.1 VARIATIONAL
EXPRESSION FOR POISSON S EQUATION 143 5.3.1.1 MATHEMATICAL MANIPULATION
143 5.3.1.2 PHYSICAL MANIPULATION 146 5.3.2 VARIATIONAL EXPRESSIONS FOR
POISSON S EQUATIONS IN PIECE-WISE HOMOGENEOUS MATERIALS 147 5.3.3
VARIATIONAL EXPRESSION FOR THE SCALAR HELMHOLTZ EQUATION . . . 148 5.3.4
VARIATIONAL EXPRESSION FOR THE MAGNETIC FIELD IN A NON-LINEAR MEDIUM 150
5.4 VARIATIONAL FINITE ELEMENT METHOD 153 5.4.1 RITZ METHOD 153 5.4.2
FINITE ELEMENT METHOD (FEM) 155 5.4.2.1 DOMAIN DISCRETIZATION 155
5.4.2.2 FINITE ELEMENT EQUATION OF A LAPLACIAN PROBLEM 156 5.4.2.3
FINITE ELEMENT EQUATION FOR 2-D MAGNETIC FIELDS 161 5.4.2.4 FINITE
ELEMENT EQUATION FOR NON-LINEAR MAGNETIC FIELDS .... 163 5.4.2.5 FINITE
ELEMENT EQUATION FOR HELMHOLTZ S EQUATION (2-D-CASE) 164 5.5 SPECIAL
PROBLEMS USING THE FINITE ELEMENT METHOD 166 5.5.1 APPROACHING FLOATING
ELECTRODES BY THE VARIATIONAL FINITE ELEMENT METHOD 166 5.5.2 OPEN
BOUNDARY PROBLEMS 167 5.5.2.1 INTRODUCTION 167 5.5.2.2 BALLOONING METHOD
168 5.6 SUMMARY 170 REFERENCES 171 CHAPTER 6 ELEMENTS AND SHAPE
FUNCTIONS 172 6.1 INTRODUCTION 172 6.2 TYPES AND REQUIREMENTS OF THE
APPROXIMATING FUNCTIONS ... 173 6.2.1 LAGRANGE AND HERMITE SHAPE
FUNCTIONS 173 6.2.2 REQUIREMENTS OF THE APPROXIMATING FUNCTIONS 174 6.3
GLOBAL, NATURAL, AND LOCAL COORDINATES 176 6.3.1 NATURAL COORDINATES 176
6.3.2 LOCAL COORDINATES 182 6.4 LAGRANGE SHAPE FUNCTION 183 6.4.1
TRIANGULAER ELEMENTS 184 6.4.2 QUADRILATERAL ELEMENTS 186 6.4.3
TETRAHEDRAL AND HEXAHEDRAL ELEMENTS 188 CONTENTS XVII 6.5 PARAMETRIC
ELEMENTS 189 6.6 ELEMENT MATRIX EQUATION 191 6.6.1 COORDINATE
TRANSFORMATIONS, JACOBIAN MATRIX 192 6.6.2 EVALUATION OF THE LAGRANGIAN
ELEMENT MATRIX 193 6.6.3 UNIVERSAL MATRIX 195 6.7 HERMITE SHAPE FUNCTION
199 6.7.1 ONE DIMENSIONAL HERMITE SHAPE FUNCTION 199 6.7.2 TRIANGULAER
HERMITE SHAPE FUNCTIONS 200 6.7.3 EVALUATION OF A HERMITE ELEMENT MATRIX
202 6.8 APPLICATION DISCUSSIONS 204 6.9 SUMMARY 206 REFERENCES 206
APPENDIX 6.1 LANGRANGIAN SHAPE FUNCTIONS FOR 2-D CASES 207 APPENDIX 6.2
COMMONLY USED SHAPE FUNCTIONS FOR 3-D CASES 208 APPENDIX 6.3 THE
UNIVERSAL MATRIX OF AXISYMMETRIC FIELDS 209 PART 3 BOUNDARY METHODS
CHAPTER 7 CHARGE SIMULATION METHOD (CSM) 215 7.1 INTRODUCTION 215 7.2
MATRIX EQUATIONS OF SIMULATED CHARGES 216 7.2.1 MATRIX EQUATION IN
HOMOGENEOUS DIELECTRICS 216 7.2.1.1 GOVERNING EQUATION SUBJECT TO
DIRICHLET BOUNDARY CONDITIONS 216 7.2.1.2 GOVERNING EQUATION SUBJECT TO
NEUMANN BOUNDARY CONDITIONS . 218 7.2.1.3 MIXED BOUNDARY CONDITIONS AND
FREE POTENTIAL CONDUCTORS .. 218 7.2.1.4 MATRIX FORM OF POISSON S
EQUATION 219 7.2.2 MATRIX EQUATION IN PIECE-WISE HOMOGENEOUS DIELECTRICS
.... 220 7.3 COMMONLY USED SIMULATED CHARGES 221 7.3.1 POINT CHARGE 222
7.3.2 LINE CHARGE 223 7.3.3 RING CHARGE 223 7.3.4 CHARGED ELLIPTIC
CYLINDER , 225 7.4 APPLICATIONS OF THE CHARGE SIMULATION METHOD 226 7.5
COORDINATE TRANSFORMATIONS 232 7.5.1 TRANSFORMATION MATRIX 233 7.5.2
INVERSE TRANSFORMATION OF THE FIELD STRENGTH 234 7.6 OPTIMIZED CHARGE
SIMULATION METHOD (OCSM) 235 7.6.1 OBJECTIVE FUNCTION 235 7.6.2
TRANSFORMATION OF CONSTRAINED CONDITIONS 237 7.6.3 EXAMPLES 237 7.7
ERROR ANALYSIS IN THE CHARGE SIMULATION METHOD 241 7.7.1 PROPERTIES OF
THE ERRORS 241 XVIII CONTENTS 7.7.2 ERROR DISTRIBUTION PATTERN ALONG THE
ELECTRODE CONTOUR .... 242 7.7.3 FACTORS INFLUENCING THE ERRORS 243 7.8
SUMMARY 246 REFERENCES 247 APPENDIX 7.1 FORMULATIONS FOR A POINT CHARGE
248 APPENDIX 7.2 FORMULATIONS FOR A LINE CHARGE 248 APPENDIX 7.3
FORMULATIONS FOR A RING CHARGE 249 APPENDIX 7.4 FORMULATIONS FOR A
CHARGED ELLIPTIC CYLINDER 249 APPENDIX 7.5 APPROXIMATE FORMULATIONS FOR
CALCULATING K(K) AND E(K) 250 CHAPTER 8 SURFACE CHARGE SIMULATION METHOD
(SSM) 251 8.1 INTRODUCTION 251 8.1.1 EXAMPLE 252 8.2 SURFACE INTEGRAL
EQUATIONS 254 8.2.1 SINGLE LAYER OR DOUBLE LAYER INTEGRAL EQUATIONS 254
8.2.2 INTEGRAL EQUATIONS OF THE INTERFACIAL SURFACE 255 8.3 TYPES OF
SURFACE BOUNDARY ELEMENTS AND SURFACE CHARGE DENSITIES 257 8.3.1
REPRESENTATIONS OF BOUNDARY AND CHARGE DENSITY 257 8.3.2 POTENTIAL AND
FIELD STRENGTH COEFFICIENTS FOR 2-D AND AXISYMMETRICAL PROBLEMS 258
8.3.2.1 PLANAR ELEMENT WITH CONSTANT OR LINEAR CHARGE DENSITY 259
8.3.2.2 ARCED ELEMENT WITH CONSTANT OR LINEAR CHARGE DENSITY 262 8.3.2.3
RING ELEMENT WITH LINEAR CHARGE DENSITY 264 8.3.3 ELEMENTS FOR 3-D
PROBLEMS 267 8.3.3.1 PLANAR TRIANGULAER ELEMENT 267 8.3.3.2 CYLINDRICAL
TETRAGONAL BILINEAR ELEMENT 267 8.3.3.3 ISOPARAMETRIC HIGH ORDER ELEMENT
268 8.3.3.4 SPLINE FUNCTION ELEMENT 269 8.4 MAGNETIC SURFACE CHARGE
SIMULATION METHOD 270 8.5 EVALUATION OF SINGULAR INTEGRALS 272 8.5.1 THE
SEMI-ANALYTICAL TECHNIQUE 273 8.5.2 METHOD USING COORDINATE
TRANSFORMATIONS 274 8.5.3 NUMERICAL TECHNIQUES 275 8.5.4 COMBINE THE
ANALYTICAL INTEGRAL AND GAUSSIAN QUADRATURE . . 275 8.6 APPLICATIONS 275
8.7 SUMMARY 280 REFERENCES 280 APPENDIX 8.1 POTENTIAL AND FIELD STRENGTH
COEFFICIENTS OF 2-D PLANAR ELEMENTS WITH CONSTANT AND LINEAR CHARGE
DENSITY .... 281 APPENDIX 8.2 POTENTIAL AND FIELD STRENGTH COEFFICIENTS
OF 2-D ARCED ELEMENTS WITH CONSTANT AND LINEAR CHARGE DENSITY .... 283
APPENDIX 8.3 COEFFICIENTS OF RING ELEMENTS WITH LINEAR CHARGE DENSITY
285 CONTENTS XIX CHAPTER 9 BOUNDARY ELEMENT METHOD (BEM) 287 9.1
INTRODUCTION 287 9.2 BOUNDARY ELEMENT EQUATIONS 288 9.2.1 METHOD OF
WEIGHTED RESIDUALS 288 9.2.2 GREEN S THEOREM 291 9.2.3 VARIATIONAL
PRINCIPLE 291 9.2.4 BOUNDARY INTEGRAL EQUATION 292 9.2.5 INDIRECT
BOUNDARY INTEGRAL EQUATION 295 9.3 MATRIX FORMULATIONS OF THE BOUNDARY
INTEGRAL EQUATION .... 295 9.3.1 DISCRETIZATION AND SHAPE FUNCTIONS 296
9.3.2 MATRIX EQUATION OF A 2-DIMENSIONAL CONSTANT ELEMENT 298 9.3.2.1
EVALUATION OF H {J AND G {J 300 9.3.2.2 EVALUATION OF H UE AND G* 301
9.3.3 MATRIX EQUATION OF 2-D LINEAR ELEMENTS 302 9.3.4 MATRIX FORM OF
POISSON S EQUATION 304 9.3.5 MATRIX EQUATION OF A PIECEWISE HOMOGENEOUS
DOMAIN 305 9.3.6 MATRIX EQUATION OF AXISYMMETRIC PROBLEMS 306 9.3.7
DISCRETIZATION OF 3-DIMENSIONAL PROBLEMS 307 9.3.8 USE OF SYMMETRY 309
9.4 EDDY CURRENT PROBLEMS 310 9.4.1 EDDY CURRENT EQUATIONS 310 9.4.1.1
A-CP FORMULATIONS 311 9.4.1.2 T-Q FORMULATIONS 311 9.4.2 ONE-DIMENSIONAL
SOLUTION OF AN EDDY CURRENT PROBLEM .... 312 9.4.3 BEM FOR SOLVING EDDY
CURRENT PROBLEMS 313 9.4.4 SURFACE IMPEDANCE BOUNDARY CONDITIONS 316 9.5
NON-LINEAR AND TIME-DEPENDENT PROBLEMS 317 9.5.1 BEM FOR NON-LINEAR
PROBLEMS 317 9.5.2 TIME-DEPENDENT PROBLEMS 320 9.6 SUMMARY 321
REFERENCES 322 APPENDIX 9.1 BESSEL FUNCTION 323 CHAPTER 10 MOMENT
METHODS 327 10.1 INTRODUCTION 327 10.2 BASIS FUNCTIONS AND WEIGHTING
FUNCTIONS 330 10.2.1 GALERKIN S METHODS 332 10.2.2 POINT MATCHING METHOD
332 10.2.3 SUB-REGIONS AND SUB-SECTIONAL BASIS 334 10.3 INTERPRETATION
USING VARIATIONS 335 XX CONTENTS 10.4 MOMENT METHODS FOR SOLVING STATIC
FIELD PROBLEMS 336 10.4.1 CHARGE DISTRIBUTION OF AN ISOLATED PLATE 336
10.4.2 CHARGE DISTRIBUTION OF A CHARGED CYLINDER 338 10.5 MOMENT METHODS
FOR SOLVING EDDY CURRENT PROBLEMS 341 10.5.1 INTEGRAL EQUATION OF A 2-D
EDDY CURRENT PROBLEM 341 10.5.2 SUB-SECTIONAL BASIS METHOD 342 10.6
MOMENT METHODS TO SOLVE THE CURRENT DISTRIBUTION OF A LINE ANTENNA 343
10.6.1 INTEGRAL EQUATION OF A LINE ANTENNA 343 10.6.2 SOLUTION OF
HALLEN S EQUATION 345 10.7 SUMMARY 347 REFERENCES 348 PART 4
OPTIMIZATION METHODS OF ELECTROMAGNETIC FIELD PROBLEMS CHAPTER 11
METHODS OF APPLIED OPTIMIZATION 351 11.1 INTRODUCTION 351 11.2
FUNDAMENTAL CONCEPTS 351 11.2.1 NECESSARY AND SUFFICIENT CONDITIONS FOR
THE LOCAL MINIMUM . . 352 11.2.2 GEOMETRICAL INTERPRETATION OF THE
MINIMIZER 354 11.2.3 QUADRATIC FUNCTIONS 355 11.2.4 BASIC METHOD FOR
SOLVING UNCONSTRAINED NON-LINEAR OPTIMIZATION PROBLEMS 356 11.2.5
STABILITY AND CONVERGENCE 357 11.3 LINEAR SEARCH AND SINGLE VARIABLE
OPTIMIZATION 358 11.3.1 GOLDEN SECTION METHOD 358 11.3.2 METHODS OF
POLYNOMIAL INTERPOLATION 360 11.4 ANALYTIC METHODS OF UNCONSTRAINED
OPTIMIZATION PROBLEMS . . 362 11.4.1 THE METHOD OF STEEPEST DESCENT 363
11.4.2 CONJUGATE GRADIENT METHOD 364 11.4.2.1 CONJUGATE DIRECTION 364
11.4.2.2 QUADRATIC CONVERGENCE 364 11.4.2.3 SELECTION OF CONJUGATE
DIRECTIONS 365 11.4.3 QUASI-NEWTON S METHODS 367 11.4.3.1
DAVIDON-FLETCHER-POWELL (DFP) METHOD 368 11.4.3.2 BFGS FORMULATION 370
11.4.3.3 B MATRIX FORMULAE 371 11.4.3.4 CHOLESKY FACTORIZATION OF THE
HESSIAN MATRIX 371 11.4.4 METHOD OF NON-LINEAR LEAST SQUARES 372
11.4.4.1 GAUSS-NEWTON METHOD 372 11.4.4.2 LEVENBERG-MARQUARDT METHOD 373
11.5 FUNCTION COMPARISON METHODS 374 CONTENTS XXI 11.5.1 POLYTYPE METHOD
374 11.5.2 POWELL S METHOD OF QUADRATIC CONVERGENCE 375 11.6 CONSTRAINED
OPTIMIZATION METHODS 376 11.6.1 BASIC CONCEPTS OF CONSTRAINED
OPTIMIZATION 377 11.6.2 KUHN-TUCKER CONDITIONS 378 11.6.2.1 LAGRANGE
MULTIPLIER METHOD 378 11.6.2.2 NECESSARY CONDITION OF THE FIRST ORDER
379 11.6.2.3 NECESSARY AND SUFFICIENT CONDITIONS OF THE SECOND ORDER . .
. 380 11.6.3 PENALTY AND BARRIER FUNCTION METHODS 381 11.6.4 SEQUENTIAL
UNCONSTRAINED MINIMIZATION TECHNIQUE 384 11.7 SUMMARY 385 REFERENCES 386
CHAPTER 12 OPTIMIZING ELECTROMAGNETIC DEVICES 387 12.1 INTRODUCTION 387
12.2 GENERAL CONCEPTS OF OPTIMUM DESIGN 388 12.2.1 OBJECTIVE FUNCTION
388 12.2.2 MATHEMATICAL EXPRESSIONS OF THE BOUNDARY VALUE PROBLEM .. 389
12.2.3 OPTIMIZATION METHODS 390 12.2.4 CATEGORIES OF OPTIMIZATION 391
12.3 CONTOUR OPTIMIZATION 391 12.3.1 METHOD OF CURVATURE ADJUSTMENT 391
12.3.2 METHOD OF CHARGE REDISTRIBUTION 393 12.3.3 CONTOUR OPTIMIZATION
BY USING NON-LINEAR PROGRAMMING . . . 395 12.4 PROBLEMS OF DOMAIN
OPTIMIZATION 396 12.4.1 FIELD SYNTHESIS BY USING FREDHOLM S INTEGRAL
EQUATION 396 12.4.2 DOMAIN OPTIMIZATION BY USING NON-LINEAR PROGRAMMING
. . . 398 12.5 SUMMARY 400 REFERENCES 400 SUBJECT INDEX 403
|
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| discipline | Physik Elektrotechnik Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
| format | Book |
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| id | DE-604.BV008404105 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:19:12Z |
| institution | BVB |
| isbn | 3540547223 0387547223 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005537185 |
| oclc_num | 26973751 |
| open_access_boolean | |
| owner | DE-Aug4 DE-29T DE-91 DE-BY-TUM DE-703 DE-858 DE-83 DE-188 |
| owner_facet | DE-Aug4 DE-29T DE-91 DE-BY-TUM DE-703 DE-858 DE-83 DE-188 |
| physical | XXI, 406 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer |
| record_format | marc |
| series2 | Electric energy systems and engineering series |
| spelling | Zhou, Pei-bai Verfasser aut Numerical analysis of electromagnetic fields Pei-bai Zhou Berlin u.a. Springer 1993 XXI, 406 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Electric energy systems and engineering series Literaturangaben Analise numerica larpcal Campos eletromagneticos larpcal Elementos e diferencas finitos larpcal Mathematik Boundary element methods Electromagnetic fields Mathematics Field theory (Physics) Mathematics Finite element method Numerical analysis Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Elektromagnetisches Feld (DE-588)4014305-3 gnd rswk-swf Elektromagnetisches Feld (DE-588)4014305-3 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005537185&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zhou, Pei-bai Numerical analysis of electromagnetic fields Analise numerica larpcal Campos eletromagneticos larpcal Elementos e diferencas finitos larpcal Mathematik Boundary element methods Electromagnetic fields Mathematics Field theory (Physics) Mathematics Finite element method Numerical analysis Numerisches Verfahren (DE-588)4128130-5 gnd Elektromagnetisches Feld (DE-588)4014305-3 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4014305-3 |
| title | Numerical analysis of electromagnetic fields |
| title_auth | Numerical analysis of electromagnetic fields |
| title_exact_search | Numerical analysis of electromagnetic fields |
| title_full | Numerical analysis of electromagnetic fields Pei-bai Zhou |
| title_fullStr | Numerical analysis of electromagnetic fields Pei-bai Zhou |
| title_full_unstemmed | Numerical analysis of electromagnetic fields Pei-bai Zhou |
| title_short | Numerical analysis of electromagnetic fields |
| title_sort | numerical analysis of electromagnetic fields |
| topic | Analise numerica larpcal Campos eletromagneticos larpcal Elementos e diferencas finitos larpcal Mathematik Boundary element methods Electromagnetic fields Mathematics Field theory (Physics) Mathematics Finite element method Numerical analysis Numerisches Verfahren (DE-588)4128130-5 gnd Elektromagnetisches Feld (DE-588)4014305-3 gnd |
| topic_facet | Analise numerica Campos eletromagneticos Elementos e diferencas finitos Mathematik Boundary element methods Electromagnetic fields Mathematics Field theory (Physics) Mathematics Finite element method Numerical analysis Numerisches Verfahren Elektromagnetisches Feld |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005537185&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT zhoupeibai numericalanalysisofelectromagneticfields |