Finite element analysis of acoustic scattering:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1998
|
| Schriftenreihe: | Applied mathematical sciences
132 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 224 S. graph. Darst. |
| ISBN: | 0387983198 |
Internformat
MARC
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| 100 | 1 | |a Ihlenburg, Frank |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Finite element analysis of acoustic scattering |c Frank Ihlenburg |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1998 | |
| 300 | |a XIV, 224 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Applied mathematical sciences |v 132 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface vii
1 The Governing Equations of Time Harmonic Wave
Propagation 1
1.1 Acoustic Waves 1
1.1.1 Linearized Equations for Compressible Fluids .... 2
1.1.2 Wave Equation and Helmholtz Equation 3
1.1.3 The Sommerfeld Condition 6
1.2 Elastic Waves 8
1.2.1 Dynamic Equations of Elasticity 8
1.2.2 Vector Helmholtz Equations 9
1.3 Acoustic/Elastic Fluid Solid Interaction 11
1.3.1 Physical Assumptions 12
1.3.2 Governing Equations and Special Cases 13
1.4 Electromagnetic Waves 16
1.4.1 Electric Fields 16
1.4.2 Magnetic Fields 17
1.4.3 Maxwell s Equations 18
1.5 Summary 19
1.6 Bibliographical Remarks 20
2 Analytical and Variational Solutions of Helmholtz
Problems 21
2.1 Separation of Variables 22
xii Contents
2.1.1 Cartesian Coordinates 22
2.1.2 Spherical Coordinates 24
2.1.3 Cylindrical Coordinates 29
2.1.4 Atkinson Wilcox Expansion 31
2.1.5 Far Field Pattern 32
2.1.6 Computational Aspects 32
2.2 References from Functional Analysis 35
2.2.1 Norm and Scalar Product 35
2.2.2 Hilbert Spaces 36
2.2.3 Sesquilinear Forms and Linear Operators 38
2.2.4 Trace of a Function 39
2.3 Variational Formulation of Helmholtz Problems 40
2.3.1 Helmholtz Problems on Bounded Domains 40
2.3.2 Helmholtz Problems on Unbounded Domains .... 41
2.3.3 Weak Formulation for Solid Fluid Interaction .... 43
2.4 Well Posedness of Variational Problems 46
2.4.1 Positive Definite Forms 46
2.4.2 The inf sup Condition 48
2.4.3 Coercive Forms 51
2.4.4 Regularity and Stability 53
2.5 Variational Methods 53
2.5.1 Galerkin Method and Ritz Method 53
2.5.2 Convergence Results 55
2.5.3 Conclusions for Helmholtz Problems 57
2.6 Summary 58
2.7 Bibliographical Remarks 58
3 Discretization Methods for Exterior Helmholtz Problems 61
3.1 Decomposition of Exterior Domains 62
3.1.1 Introduction of an Artificial Boundary 62
3.1.2 Dirichlet to Neumann Operators 63
3.1.3 Well Posedness 64
3.2 The Dirichlet to Neumann Operator and Numerical
Applications 65
3.2.1 The Exact DtN Operator 65
3.2.2 Spectral Characterization of the DtN Operator ... 67
3.2.3 Truncation of the DtN Operator 69
3.2.4 Localizations of the Truncated DtN Operator .... 70
3.3 Absorbing Boundary Conditions 71
3.3.1 Recursion in the Atkinson Wilcox Expansion .... 72
3.3.2 Localization of a Pseudodifferential Operator .... 74
3.3.3 Comparison of ABC 76
3.3.4 The PML Method 78
3.4 The Finite Element Method in the Near Field 80
3.4.1 Finite Element Technology 81
Contents xiii
3.4.2 Identification of the FEM as a Galerkin Method . . 86
3.4.3 The h Version and the hp Version of the FEM ... 87
3.5 Infinite Elements and Coupled Finite Infinite Element
Discretization 87
3.5.1 Infinite Elements from Radial Expansion 87
3.5.2 Variational Formulations 89
3.5.3 Remarks on the Analysis of the Finite Infinite
Element Method 93
3.6 Summary 97
3.7 Bibliographical Remarks 98
4 Finite Element Error Analysis and Control for Helmholtz
Problems 101
4.1 Convergence of Galerkin FEM 102
4.1.1 Error Function and Residual 103
4.1.2 Positive Definite Problems 103
4.1.3 Indefinite Problems 105
4.2 Model Problems for the Helmholtz Equation 106
4.2.1 Model Problem I: Uniaxial Propagation of a Plane
Wave 107
4.2.2 Model Problem II: Propagation of Plane Waves with
Variable Direction 108
4.2.3 Model Problem III: Uniaxial Fluid Solid Interaction 109
4.3 Stability Estimates for Helmholtz Problems 110
4.3.1 The inf sup Condition 110
4.3.2 Stability Estimates for Data of Higher Regularity . . 113
4.4 Quasioptimal Convergence of FE Solutions to the Helmholtz
Equation 116
4.4.1 Approximation Rule and Interpolation Error .... 116
4.4.2 An Asymptotic Error Estimate 119
4.4.3 Conclusions 121
4.5 Preasymptotic Error Estimates for the h Version of the FEM 122
4.5.1 Dispersion Analysis of the FE Solution 122
4.5.2 The Discrete inf sup Condition 124
4.5.3 A Sharp Preasymptotic Error Estimate 125
4.5.4 Results of Computational Experiments 128
4.6 Pollution of FE Solutions with Large Wave Number .... 132
4.6.1 Numerical Pollution 133
4.6.2 The Typical Convergence Pattern of FE Solutions to
the Helmholtz Equation 134
4.6.3 Influence of the Boundary Conditions 136
4.6.4 Error estimation in the L2 norm 137
4.6.5 Results from 2 D Computations 138
4.7 Analysis of the hp FEM 140
4.7.1 ftp Approximation 140
xiv Contents
4.7.2 Dual Stability 145
4.7.3 FEM Solution Procedure. Static Condensation . . . 147
4.7.4 Dispersion Analysis and Phase Lag 149
4.7.5 Discrete Stability 151
4.7.6 Error Estimates 153
4.7.7 Numerical Results 155
4.8 Generalized FEM for Helmholtz Problems 158
4.8.1 Generalized FEM in One Dimension 158
4.8.2 Generalized FEM in Two Dimensions 162
4.9 The Influence of Damped Resonance in Fluid Solid Interaction 170
4.9.1 Analysis and Parameter Discussion 170
4.9.2 Numerical Evaluation 171
4.10 A Posteriori Error Analysis 174
4.10.1 Notation 174
4.10.2 Bounds for the Effectivity Index 175
4.10.3 Numerical Results 179
4.11 Summary and Conclusions for Computational Application . 185
4.12 Bibliographical Remarks 187
5 Computational Simulation of Elastic Scattering 189
5.1 Elastic Scattering from a Sphere 189
5.1.1 Implementation of a Coupled Finite Infinite Element
Method for Axisymmetric Problems 189
5.1.2 Model Problem 191
5.1.3 Computational Results 194
5.1.4 Conclusions 201
5.2 Elastic Scattering from a Cylinder with Spherical Endcaps . 202
5.2.1 Model Parameters 202
5.2.2 Convergence Tests 203
5.2.3 Comparison with Experiments 206
5.3 Summary 210
References 211
Index 221
|
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| indexdate | 2024-07-09T18:23:16Z |
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| isbn | 0387983198 |
| language | English |
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| series | Applied mathematical sciences |
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| spelling | Ihlenburg, Frank Verfasser aut Finite element analysis of acoustic scattering Frank Ihlenburg New York [u.a.] Springer 1998 XIV, 224 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 132 Fluid (DE-588)4017690-3 gnd rswk-swf Helmholtz-Schwingungsgleichung (DE-588)4159528-2 gnd rswk-swf Schallwelle (DE-588)4191490-9 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Streuung (DE-588)4058056-8 gnd rswk-swf Wellenausbreitung (DE-588)4121912-0 gnd rswk-swf Schallwelle (DE-588)4191490-9 s Wellenausbreitung (DE-588)4121912-0 s Streuung (DE-588)4058056-8 s Fluid (DE-588)4017690-3 s Helmholtz-Schwingungsgleichung (DE-588)4159528-2 s Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Applied mathematical sciences 132 (DE-604)BV000005274 132 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008258743&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ihlenburg, Frank Finite element analysis of acoustic scattering Applied mathematical sciences Fluid (DE-588)4017690-3 gnd Helmholtz-Schwingungsgleichung (DE-588)4159528-2 gnd Schallwelle (DE-588)4191490-9 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Streuung (DE-588)4058056-8 gnd Wellenausbreitung (DE-588)4121912-0 gnd |
| subject_GND | (DE-588)4017690-3 (DE-588)4159528-2 (DE-588)4191490-9 (DE-588)4017233-8 (DE-588)4058056-8 (DE-588)4121912-0 |
| title | Finite element analysis of acoustic scattering |
| title_auth | Finite element analysis of acoustic scattering |
| title_exact_search | Finite element analysis of acoustic scattering |
| title_full | Finite element analysis of acoustic scattering Frank Ihlenburg |
| title_fullStr | Finite element analysis of acoustic scattering Frank Ihlenburg |
| title_full_unstemmed | Finite element analysis of acoustic scattering Frank Ihlenburg |
| title_short | Finite element analysis of acoustic scattering |
| title_sort | finite element analysis of acoustic scattering |
| topic | Fluid (DE-588)4017690-3 gnd Helmholtz-Schwingungsgleichung (DE-588)4159528-2 gnd Schallwelle (DE-588)4191490-9 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd Streuung (DE-588)4058056-8 gnd Wellenausbreitung (DE-588)4121912-0 gnd |
| topic_facet | Fluid Helmholtz-Schwingungsgleichung Schallwelle Finite-Elemente-Methode Streuung Wellenausbreitung |
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