Acoustic and electromagnetic equations: integral representations for harmonic problems
Acoustic and electromagnetic waves underlie a range of modern technology from sonar, radio, and television to microwave heating and electromagnetic compatibility analysis. This book, written by an international researcher, presents some of the research in a complete way. It is useful for graduate st...
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2001
|
| Series: | Applied mathematical sciences
144 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | Acoustic and electromagnetic waves underlie a range of modern technology from sonar, radio, and television to microwave heating and electromagnetic compatibility analysis. This book, written by an international researcher, presents some of the research in a complete way. It is useful for graduate students in mathematics, physics, and engineering. |
| Physical Description: | IX, 316 S. |
| ISBN: | 0387951555 |
Staff View
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| 245 | 1 | 0 | |a Acoustic and electromagnetic equations |b integral representations for harmonic problems |c Jean-Claude Nédélec |
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Record in the Search Index
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| adam_text | Contents
Preface v
1 Some Wave Equations 1
1.1 Introduction 1
1.2 Physical Background 3
1.2.1 The acoustic equation 3
1.2.2 The Maxwell equations 4
1.2.3 Elastic waves 6
2 The Helmholtz Equation 9
2.1 Introduction 9
2.2 Harmonic Solutions 10
2.3 Fundamental Solutions 12
2.4 The Case of the Sphere in R3 13
2.4.1 Spherical harmonics 15
2.4.2 Legendre polynomials 17
2.4.3 Associated Legendre functions 22
2.4.4 Vectorial spherical harmonics 35
2.5 The Laplace Equation in R3 40
2.5.1 The sphere 40
2.5.2 Surfaces and Sobolev spaces 47
2.5.3 Interior problems: Variational formulations .... 55
2.5.4 Exterior problems 59
2.5.5 Regularity properties of solutions in Hn 65
viii Contents
2.5.6 Elementary differential geometry 67
2.5.7 Regularity properties 79
2.6 The Helmholtz Equation in M3 84
2.6.1 The spherical Bessel functions 85
2.6.2 Dirichlet and Neumann problems for a sphere . . 90
2.6.3 The capacity operator T 97
2.6.4 The case of a plane wave 97
2.6.5 The exterior problem for
the Helmholtz equation 102
3 Integral Representations and Integral Equations 110
3.1 Integral Representations 110
3.2 Integral Equations for Helmholtz Problems 117
3.2.1 Equations for the single layer potential 117
3.2.2 Equations for the double layer potential 119
3.2.3 The spherical case 120
3.2.4 The far field 122
3.2.5 The physical optics approximation
for the sphere 130
3.3 Integral Equations for the Laplace Problem 135
3.4 Variational Formulations for the Helmholtz Problems . . 141
3.4.1 The operator 5 141
3.4.2 Fredholm operators 142
3.4.3 The operator TV 143
3.4.4 Formulation with the far field 146
4 Singular Integral Operators 150
4.1 The Hilbert Transform 150
4.2 Singular Integral Operators in R 157
4.2.1 Odd kernels 158
4.2.2 The M. Riesz transforms 160
4.2.3 Adjoint operators 166
4.3 Application to Integral Equations 167
4.3.1 Introduction 167
4.3.2 Homogeneous kernels 168
4.3.3 Pseudo homogeneous kernels 173
4.4 Application to Integral Equations 175
5 Maxwell Equations and Electromagnetic Waves 177
5.1 Introduction 177
5.2 Fundamental Solution and Radiation Conditions 179
5.3 Multipole Solutions 185
5.3.1 Multipoles 185
5.3.2 The capacity operator 200
Contents ix
5.4 Exterior Problems 204
5.4.1 Trace and lifting associated
with the space ff(curl) 205
5.4.2 Variational formulations for the
perfect conductor problem 214
5.4.3 Coupled variational formulations
for impedance conditions 226
5.5 Integral Representations 234
5.6 Integral Equations 243
5.6.1 The perfect conductor 243
5.6.2 The zero frequency limit 250
5.6.3 The dielectric case 253
5.6.4 The infinite conductivity limit:
The perfect conductor 266
5.7 The Far Field 288
5.7.1 Far field and scattering amplitude 288
5.7.2 Integral equations and far field 298
References 301
Index 313
|
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| id | DE-604.BV013701352 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:50:30Z |
| institution | BVB |
| isbn | 0387951555 |
| language | English |
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| physical | IX, 316 S. |
| publishDate | 2001 |
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| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Nédélec, Jean-Claude Verfasser aut Acoustic and electromagnetic equations integral representations for harmonic problems Jean-Claude Nédélec New York [u.a.] Springer 2001 IX, 316 S. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 144 Acoustic and electromagnetic waves underlie a range of modern technology from sonar, radio, and television to microwave heating and electromagnetic compatibility analysis. This book, written by an international researcher, presents some of the research in a complete way. It is useful for graduate students in mathematics, physics, and engineering. Wellengleichung - Integraldarstellung Maxwell equations Numerical solutions Wave equations Numerical solutions Wellengleichung (DE-588)4065315-8 gnd rswk-swf Integraldarstellung (DE-588)4127585-8 gnd rswk-swf Wellengleichung (DE-588)4065315-8 s Integraldarstellung (DE-588)4127585-8 s DE-604 Applied mathematical sciences 144 (DE-604)BV000005274 144 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009364032&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nédélec, Jean-Claude Acoustic and electromagnetic equations integral representations for harmonic problems Applied mathematical sciences Wellengleichung - Integraldarstellung Maxwell equations Numerical solutions Wave equations Numerical solutions Wellengleichung (DE-588)4065315-8 gnd Integraldarstellung (DE-588)4127585-8 gnd |
| subject_GND | (DE-588)4065315-8 (DE-588)4127585-8 |
| title | Acoustic and electromagnetic equations integral representations for harmonic problems |
| title_auth | Acoustic and electromagnetic equations integral representations for harmonic problems |
| title_exact_search | Acoustic and electromagnetic equations integral representations for harmonic problems |
| title_full | Acoustic and electromagnetic equations integral representations for harmonic problems Jean-Claude Nédélec |
| title_fullStr | Acoustic and electromagnetic equations integral representations for harmonic problems Jean-Claude Nédélec |
| title_full_unstemmed | Acoustic and electromagnetic equations integral representations for harmonic problems Jean-Claude Nédélec |
| title_short | Acoustic and electromagnetic equations |
| title_sort | acoustic and electromagnetic equations integral representations for harmonic problems |
| title_sub | integral representations for harmonic problems |
| topic | Wellengleichung - Integraldarstellung Maxwell equations Numerical solutions Wave equations Numerical solutions Wellengleichung (DE-588)4065315-8 gnd Integraldarstellung (DE-588)4127585-8 gnd |
| topic_facet | Wellengleichung - Integraldarstellung Maxwell equations Numerical solutions Wave equations Numerical solutions Wellengleichung Integraldarstellung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009364032&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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