Computational conformal mapping:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Boston ; Basel ; Berlin
Birkhäuser
1998
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 431 - 448 |
| Physical Description: | XIV, 462 S. graph. Darst. |
| ISBN: | 3764339969 0817639969 |
Staff View
MARC
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| 245 | 1 | 0 | |a Computational conformal mapping |c Prem K. Kythe |
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| 650 | 7 | |a équation Fredholm |2 inriac | |
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| 650 | 4 | |a Conformal mapping |x Data processing | |
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Record in the Search Index
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| adam_text | Contents
Preface, ix
Chapter 0. Introduction, 1
0.1. Historical Background, 1
0.2. Modern Developments, 8
Chapter 1. Basic Concepts, 15
1.1. Notation and Definitions, 15
1.2. Some Basic Theorems, 23
1.3. Harmonic Functions, 27
1.4. Conformal Mapping, 30
1.5. Problems, 38
Chapter 2. Conformal Mappings, 41
2.1. Polynomials, 41
2.2. Bilinear Transformations, 45
2.3. Schwarz Christoffel Transformations, 51
2.4. Catalog of Conformal Maps, 64
2.5. Problems, 65
Chapter 3. Schwarz Christoffel Integrals, 68
3.1. Parameter Problem, 68
3.2. Newton s Method, 72
3.3. Numerical Computations, 76
3.4. Kirchhoff Flow Problem, 83
3.5. Problems, 89
V
vi CONTENTS
Chapter 4. Polynomial Approximations, 92
4.1. Minimum Area Problem, 92
4.1.1. Bergman Kernel, 94
4.2. Numerical Methods for Problem I, 95
4.2.1. Ritz Method, 95
4.2.2. Bergman Kernel Method, 101
4.3. Minimum Boundary Problem, 103
4.4. Ritz Method for Problem II, 105
4.5. Orthogonal Polynomials, 109
4.5.1. Polynomials Orthogonal to the Boundary, 109
4.5.2. Polynomials Orthogonal to a Region, 116
4.6. Problems, 118
Chapter 5. Nearly Circular Regions, 120
5.1. Small Parameter Expansions, 120
5.2. Method of Infinite Systems, 125
5.3. Three Special Cases, 132
5.4. Exterior Regions, 140
5.5. Problems, 145
Chapter 6. Green s Functions, 147
6.1. Mean Value Theorem, 147
6.2. Dirichlet Problem, 148
6.3. Numerical Computation, 152
6.4. Schwarz Formula, 158
6.5. Neumann Problem, 159
6.6. Series Representations, 162
6.7. Problems, 165
Chapter 7. Integral Equation Methods, 168
7.1. Neumann Kernel, 168
7.2. Interior Regions, 171
7.2.1. Lichtenstein s Integral Equation, 171
7.2.2. Gershgorin s Integral Equation, 172
7.2.3. Carrier s Integral Equation, 173
7.3. Exterior Regions, 174
7.3.1. Banin s Integral Equation, 176
7.3.2. Warschawski Stiefel s Integral Equation, 177
7.3.3. Interior and Exterior Maps, 177
7.4. Iterative Method, 178
7.5. Degenerate Kernel, 192
7.6. Szego Kernel, 198
7.7. Problems, 204
CONTENTS vii
Chapter 8. Theodorsen s Integral Equation, 207
8.1. Classical Iterative Method, 207
8.2. Convergence, 209
8.3. Proofs, 211
8.4. Integral Representation, 222
8.5. Starlike Regions, 224
8.6. Exterior Regions, 226
8.7. Trigonometric Interpolation, 228
8.8. Wegmann s Method, 229
8.9. Newton s Method, 234
8.10. Problems, 236
Chapter 9. Symm s Integral Equation, 237
9.1. Symm s Integral Equation, 237
9.1.1. Interior Regions, 237
9.1.2. Exterior Regions, 239
9.2. Orthonormal Polynomial Method, 240
9.3. Modified ONP Method, 247
9.4. Lagrange Interpolation, 251
9.5. Spline Approximations, 258
9.6. Problems, 265
Chapter 10. Airfoils, 269
10.1. Joukowski Function, 269
10.2. Generalized Joukowski Mappings, 274
10.2.1. Glauert s Modification, 275
10.2.2. Symmetric Joukowski Airfoil, 276
10.3. Nearly Circular Approximations, 277
10.4. James s Method, 279
10.4.1. Single Element Airfoils, 280
10.4.2. von Karman Trefftz transformations, 283
10.4.3. Two Element Airfoils, 288
10.4.4. Multi Element Airfoils, 291
10.5. Problems, 292
Chapter 11. Doubly Connected Regions, 295
11.1. Conformal Modulus, 295
11.1.1. Conformal Invariants, 296
11.1.2. Area Theorem, 298
11.2. Source Density, 305
11.3. Dipole Distribution, 308
11.4. Problems, 317
viii CONTENTS
Chapter 12. Singularities, 320
12.1. Arbenz s Integral Equation, 320
12.2. Boundary Corner, 325
12.3. Singularity Behavior, 328
12.4. Pole Type Singularities, 330
12.5. Exterior Regions, 339
12.6. Doubly Connected Regions, 345
12.7. Problems, 351
Chapter 13. Multiply Connected Regions, 358
13.1. Existence and Uniqueness, 359
13.2. Dirichlet Problem, 364
13.3. Mikhlin s Integral Equation, 367
13.4. Mayo s Method, 370
13.5. Fast Poisson Solver, 373
13.6. Problems, 377
Chapter 14. Grid Generation, 379
14.1. Computational Region, 379
14.2. Inlet Configurations, 384
14.3. Cascade Configurations, 390
14.4. Problems, 399
Appendix A. Cauchy P. V. Integrals, 401
A.I. Numerical Evaluation, 401
Appendix B. Green s Identities, 407
Appendix C. Riemann Hilbert Problem, 410
C.I. Homogeneous Hilbert Problem, 410
C.2. Nonhomogeneous Hilbert Problem, 415
C.3. Riemann Hilbert Problem, 417
Appendix D. Successive Approximations, 425
D.I. Tables, 425
Appendix E. Catalog of Conformal Mappings, 428
Bibliography, 431
Notation, 449
Index, 453
|
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| id | DE-604.BV012370562 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:26:24Z |
| institution | BVB |
| isbn | 3764339969 0817639969 |
| language | German |
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| physical | XIV, 462 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | Kythe, Prem K. 1930- Verfasser (DE-588)12072362X aut Computational conformal mapping Prem K. Kythe Boston ; Basel ; Berlin Birkhäuser 1998 XIV, 462 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 431 - 448 Applications conformes - Informatique ram application conforme inriac approximation polynomiale inriac calcul intégral inriac fonction Green inriac intégrale Schwarz-Christoffel inriac équation Fredholm inriac Datenverarbeitung Conformal mapping Data processing Konforme Abbildung (DE-588)4164968-0 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Konforme Abbildung (DE-588)4164968-0 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008389543&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kythe, Prem K. 1930- Computational conformal mapping Applications conformes - Informatique ram application conforme inriac approximation polynomiale inriac calcul intégral inriac fonction Green inriac intégrale Schwarz-Christoffel inriac équation Fredholm inriac Datenverarbeitung Conformal mapping Data processing Konforme Abbildung (DE-588)4164968-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4164968-0 (DE-588)4128130-5 |
| title | Computational conformal mapping |
| title_auth | Computational conformal mapping |
| title_exact_search | Computational conformal mapping |
| title_full | Computational conformal mapping Prem K. Kythe |
| title_fullStr | Computational conformal mapping Prem K. Kythe |
| title_full_unstemmed | Computational conformal mapping Prem K. Kythe |
| title_short | Computational conformal mapping |
| title_sort | computational conformal mapping |
| topic | Applications conformes - Informatique ram application conforme inriac approximation polynomiale inriac calcul intégral inriac fonction Green inriac intégrale Schwarz-Christoffel inriac équation Fredholm inriac Datenverarbeitung Conformal mapping Data processing Konforme Abbildung (DE-588)4164968-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Applications conformes - Informatique application conforme approximation polynomiale calcul intégral fonction Green intégrale Schwarz-Christoffel équation Fredholm Datenverarbeitung Conformal mapping Data processing Konforme Abbildung Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008389543&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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