Verfügbarkeit: Time-domain scattering

Time-domain scattering:

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Bibliographische Detailangaben
1. Verfasser:	Martin, Paul A. ca. 20./21. Jh (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Cambridge ; New York, NY ; Port Melbourne ; New Delhi ; Singapore Cambridge University Press 2021
Schriftenreihe:	Encyclopedia of mathematics and its applications 180
Schlagworte:	Zeitreihenanalyse Streutheorie Wellengleichung Scattering (Mathematics) Wave equation Time-domain analysis
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	xi, 250 Seiten Diagramme
ISBN:	9781108835596

Internformat

MARC


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Datensatz im Suchindex

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adam_text	ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS Time-Domain Scattering P A MARTIN Colorado School of Mines Contents Preface page xiii 1 Acoustics and the Wave Equation 1 1 1 Governing Equations 1 111 Linearisation: Ambient Flows 2 112 Linearisation: Acoustics 3 113 Zero Ambient Velocity: Bergmann’s Equation 4 114 Zero Ambient Velocity and Constant Ambient Density 4 115 Zero Ambient Velocity and Homogeneous Fluid 5 116 Non-Zero Ambient Velocity and Homogeneous Fluid 5 117 Non-Uniform Ambient Flows and Dynamic Materials 6 118 Nonlinear Acoustics 10 1 2 Acoustic Scattering 10 1 3 Waves on a String il 131 An Initial-Value Problem 13 132A Bead on an Infinite String: Solution for All t 13 133A Bead on an Infinite String: Initial- Value Problem 15 134A Simple Initial-Boundary Value Problem 16 135A Bead on an Infinite String: Use of Laplace Transforms 17 136 Discussion and Summary 18 137 Damping, Dissipation, Absorption and Losses 18 138 The Forced Wave Equation 20 1 4 Laplace Transforms: Formal Properties 21 1 5 Causality 22 1 6 Electromagnetics, Elastodynamics and Hydrodynamics 24 161 Electromagnetics 24 162 Elastodynamics 25 163 Hydrodynamics 26 1 7 Overview of the Book 27 viii Contents Wavefunctions 2 Simple Solutions 3 1 Plane Waves Chara Initial, 2,12 Spherical Polar Coordinates 2 13 Spherically Symmetric Wavefunctions The Time-Domain Far-Field Pattern Use of Spherical Harmonics 23 1 Separated Solutions 232 Similarity Solutions 733 Smirnov’s Representation 134 A Bateman-Like Wavefunction 935 Multipole Representation 23 6 Lamb, Grote and Keller 23 7 Changing the Independent Variables Harry Bateman and the Wave Equation 24 1 Integral Representations 2,42 Transformations Similar to Kelvin Inversion 2 43 Some Two-Dimensional Wavefunctions 744 Further Transformations Spheroidal Wavefunctions 251 Spheroidal Wave Equation 252 Angular Spheroidal Wavefunctions 253 Radial Spheroidal Wavefunctions 254 Summary Moving Sources cteristics and Discontinuities Characteristics The Eikonal Equations Discontinuous Solutions Weak Solutions and Discontinuities 341 Green s Formula 342 Weak Solutions of the Wave Equation 343 Discontinuous Weak Solutions Jump Relations in Continuum Mechanics “Boundary Value Problems Formulation of IBVPs Acoustic Energy #21 Energy Conservation 422 Energy Inequality 4 23 Energy Decay Incident Sound Pulses Compatibility Conditions n 4 5 Contents Bateman’s IBVP for a Sphere Further Problems and Boundary Conditions 461 Locally Reacting Surfaces 462 Transmission Problems 463 Membrane Problems 464 Elastic Shells 465 Hydrodynamic Problems The Forced Wave Equation 471 Forward Problem 472 The Limiting Amplitude Principle 4 713 Aerodynamic Sound 474 Inverse Source Problems Existence and Uniqueness Results 481 Function Spaces and Notation 4 82 Problem Dig 4 83 Problem Nip 484 Summary Use of Laplace Transforms Formal Treatment Laplace Transform of Discontinuous Functions Laplace Transform of Wavefunctions Laplace Transform of Boundary Conditions Synthesis Fourier Transforms 561 Basic Definitions and Strategy 562A Time-Domain Radiation Condition 563 Further Remarks Laguerre Transforms Problems with Spherical Symmetry 6 1 Use of Simple Sources 611 Dirichlet Boundary Condition 612 Pressure Boundary Condition 613 Neumann Boundary Condition 614 Discussion and Special Cases 6 2 Use of Laplace Transforms 621 Dirichlet Boundary Condition 622 Pressure Boundary Condition 623 Neumann Boundary Condition Scattering by a Sphere 7 1 Preliminaries 7 2 Use of Laplace Transforms 7 21 Dirichlet Boundary Condition Contents Boundary Condition essure 2 7 Boundary Condition 72,3 Neumann 72,4 Literature Residual Potential Methods, Nonreflecting Boundary Kernels and Dirichlet-to-Neumann Mappings 7 Application of the Similarity Representation 7 41 Dirichlet Boundary Condition 74 2 Pressure Boundary Condition 7 43 Neumann Boundary Condition Moving Spheres 1 Scattering by a Spheroid Scattering Frequencies and the Singularity Expansion Method 8 1 Fourier Transforms 82 Scattering Frequencies 83 Boundary Integral Equations 8 4 Generalised Eigenfunctions; Quasinormal Modes 8 5 Moving the Inversion Contour 8 6 The Singularity Expansion Method (SEM) 8 7 The Eigenmode Expansion Method (EEM) 871 Self-Adjoint Operators and Normal Operators 8 72 The Time-Harmonic Single-Layer Operator 8 73 Singular Value Decomposition (SVD) 8 74 The Eigenmode Expansion Method (EEM) Integral Representations 9 1 Kirchhoff’s Formula: Classical Derivations 911 Kirchhoff’s Formula for Bounded Domains 912 Kirchhoff’s Formula for Exterior Domains 913 Special Cases of Kirchhoff’s Formula 9 14 A Formula for the Pressure 915 Use of Laplace Transforms 916 Weakening the Smoothness Assumptions 917 Literature 3 Kaas Formula a Space-Time Derivation 931 nn ormula: Use of Generalised Functions ae ixed Surface § 94 an ring Surface S(t) entials oo Single-Layer Potential 03 Double-Layer Potential Notation and Definitions 944 Kirchhoff’s Formula lig lig lig 12) 13] 10 Contents Integral Equations Integral Equations: Indirect Method 10 2 Integral Equations: Direct Method 10 3 Integral Equations: Numerical Methods 10 3 1 Basic Time-Stepping Method 10 3 2 Instabilities and Remedies 10 4 Convolution Quadrature Methods 10 41A Volterra Integral Equation 10 4 2 Application to Time-Domain Boundary Integral Equations 10 4 3 Application to Scattering by a Sphere 10 4 4 An Alternative View of CQMs 10 5 Electromagnetics 10 6 Elastodynamics 10 7 Hydrodynamics 10 7 1 Clément’s Equation 10 8 Method of Fundamental Solutions (MFS, ESM) 10 9 Use of Fourier Transforms 10 10 Cracks, Screens and Other Thin Scatterers 10 10 1 Derivation of Integral Equations Using Fourier Transforms 10 10 2 Derivation of Integral Equations Using Layer Potentials 10 10 3 Comments and Literature References Citation index Index
adam_txt	ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS Time-Domain Scattering P A MARTIN Colorado School of Mines Contents Preface page xiii ' 1 Acoustics and the Wave Equation 1 1 1 Governing Equations 1 111 Linearisation: Ambient Flows 2 112 Linearisation: Acoustics 3 113 Zero Ambient Velocity: Bergmann’s Equation 4 114 Zero Ambient Velocity and Constant Ambient Density 4 115 Zero Ambient Velocity and Homogeneous Fluid 5 116 Non-Zero Ambient Velocity and Homogeneous Fluid 5 117 Non-Uniform Ambient Flows and Dynamic Materials 6 118 Nonlinear Acoustics 10 1 2 Acoustic Scattering 10 1 3 Waves on a String il 131 An Initial-Value Problem 13 132A Bead on an Infinite String: Solution for All t 13 133A Bead on an Infinite String: Initial- Value Problem 15 134A Simple Initial-Boundary Value Problem 16 135A Bead on an Infinite String: Use of Laplace Transforms 17 136 Discussion and Summary 18 137 Damping, Dissipation, Absorption and Losses 18 138 The Forced Wave Equation 20 1 4 Laplace Transforms: Formal Properties 21 1 5 Causality 22 1 6 Electromagnetics, Elastodynamics and Hydrodynamics 24 161 Electromagnetics 24 162 Elastodynamics 25 163 Hydrodynamics 26 1 7 Overview of the Book 27 viii Contents Wavefunctions 2 Simple Solutions 3 1 Plane Waves Chara Initial, 2,12 Spherical Polar Coordinates 2 13 Spherically Symmetric Wavefunctions The Time-Domain Far-Field Pattern Use of Spherical Harmonics 23 1 Separated Solutions 232 Similarity Solutions 733 Smirnov’s Representation 134 A Bateman-Like Wavefunction 935 Multipole Representation 23 6 Lamb, Grote and Keller 23 7 Changing the Independent Variables Harry Bateman and the Wave Equation 24 1 Integral Representations 2,42 Transformations Similar to Kelvin Inversion 2 43 Some Two-Dimensional Wavefunctions 744 Further Transformations Spheroidal Wavefunctions 251 Spheroidal Wave Equation 252 Angular Spheroidal Wavefunctions 253 Radial Spheroidal Wavefunctions 254 Summary Moving Sources cteristics and Discontinuities Characteristics The Eikonal Equations Discontinuous Solutions Weak Solutions and Discontinuities 341 Green's Formula 342 Weak Solutions of the Wave Equation 343 Discontinuous Weak Solutions Jump Relations in Continuum Mechanics “Boundary Value Problems Formulation of IBVPs Acoustic Energy #21 Energy Conservation 422 Energy Inequality 4 23 Energy Decay Incident Sound Pulses Compatibility Conditions n 4 5 Contents Bateman’s IBVP for a Sphere Further Problems and Boundary Conditions 461 Locally Reacting Surfaces 462 Transmission Problems 463 Membrane Problems 464 Elastic Shells 465 Hydrodynamic Problems The Forced Wave Equation 471 Forward Problem 472 The Limiting Amplitude Principle 4 713 Aerodynamic Sound 474 Inverse Source Problems Existence and Uniqueness Results 481 Function Spaces and Notation 4 82 Problem Dig 4 83 Problem Nip 484 Summary Use of Laplace Transforms Formal Treatment Laplace Transform of Discontinuous Functions Laplace Transform of Wavefunctions Laplace Transform of Boundary Conditions Synthesis Fourier Transforms 561 Basic Definitions and Strategy 562A Time-Domain Radiation Condition 563 Further Remarks Laguerre Transforms Problems with Spherical Symmetry 6 1 Use of Simple Sources 611 Dirichlet Boundary Condition 612 Pressure Boundary Condition 613 Neumann Boundary Condition 614 Discussion and Special Cases 6 2 Use of Laplace Transforms 621 Dirichlet Boundary Condition 622 Pressure Boundary Condition 623 Neumann Boundary Condition Scattering by a Sphere 7 1 Preliminaries 7 2 Use of Laplace Transforms 7 21 Dirichlet Boundary Condition Contents Boundary Condition essure 2 7 Boundary Condition 72,3 Neumann 72,4 Literature Residual Potential Methods, Nonreflecting Boundary Kernels and Dirichlet-to-Neumann Mappings 7 Application of the Similarity Representation 7 41 Dirichlet Boundary Condition 74 2 Pressure Boundary Condition 7 43 Neumann Boundary Condition Moving Spheres 1 Scattering by a Spheroid Scattering Frequencies and the Singularity Expansion Method 8 1 Fourier Transforms 82 Scattering Frequencies 83 Boundary Integral Equations 8 4 Generalised Eigenfunctions; Quasinormal Modes 8 5 Moving the Inversion Contour 8 6 The Singularity Expansion Method (SEM) 8 7 The Eigenmode Expansion Method (EEM) 871 Self-Adjoint Operators and Normal Operators 8 72 The Time-Harmonic Single-Layer Operator 8 73 Singular Value Decomposition (SVD) 8 74 The Eigenmode Expansion Method (EEM) Integral Representations 9 1 Kirchhoff’s Formula: Classical Derivations 911 Kirchhoff’s Formula for Bounded Domains 912 Kirchhoff’s Formula for Exterior Domains 913 Special Cases of Kirchhoff’s Formula 9 14 A Formula for the Pressure 915 Use of Laplace Transforms 916 Weakening the Smoothness Assumptions 917 Literature 3 Kaas Formula a Space-Time Derivation 931 nn ormula: Use of Generalised Functions ae ixed Surface § 94 an ring Surface S(t) entials oo Single-Layer Potential 03 Double-Layer Potential Notation and Definitions 944 Kirchhoff’s Formula lig lig lig 12) 13] 10 Contents Integral Equations Integral Equations: Indirect Method 10 2 Integral Equations: Direct Method 10 3 Integral Equations: Numerical Methods 10 3 1 Basic Time-Stepping Method 10 3 2 Instabilities and Remedies 10 4 Convolution Quadrature Methods 10 41A Volterra Integral Equation 10 4 2 Application to Time-Domain Boundary Integral Equations 10 4 3 Application to Scattering by a Sphere 10 4 4 An Alternative View of CQMs 10 5 Electromagnetics 10 6 Elastodynamics 10 7 Hydrodynamics 10 7 1 Clément’s Equation 10 8 Method of Fundamental Solutions (MFS, ESM) 10 9 Use of Fourier Transforms 10 10 Cracks, Screens and Other Thin Scatterers 10 10 1 Derivation of Integral Equations Using Fourier Transforms 10 10 2 Derivation of Integral Equations Using Layer Potentials 10 10 3 Comments and Literature References Citation index Index
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spelling	Martin, Paul A. ca. 20./21. Jh. (DE-588)1206131497 aut Time-domain scattering P.A. Martin ; Colorado School of Mines Cambridge ; New York, NY ; Port Melbourne ; New Delhi ; Singapore Cambridge University Press 2021 © 2021 xi, 250 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 180 Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Streutheorie (DE-588)4183697-2 gnd rswk-swf Wellengleichung (DE-588)4065315-8 gnd rswk-swf Scattering (Mathematics) Wave equation Time-domain analysis Wellengleichung (DE-588)4065315-8 s Streutheorie (DE-588)4183697-2 s Zeitreihenanalyse (DE-588)4067486-1 s DE-604 Erscheint auch als Online-Ausgabe 978-1-108-89106-6 Encyclopedia of mathematics and its applications 180 (DE-604)BV000903719 180 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032860126&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Martin, Paul A. ca. 20./21. Jh Time-domain scattering Encyclopedia of mathematics and its applications Zeitreihenanalyse (DE-588)4067486-1 gnd Streutheorie (DE-588)4183697-2 gnd Wellengleichung (DE-588)4065315-8 gnd
subject_GND	(DE-588)4067486-1 (DE-588)4183697-2 (DE-588)4065315-8
title	Time-domain scattering
title_auth	Time-domain scattering
title_exact_search	Time-domain scattering
title_exact_search_txtP	Time-domain scattering
title_full	Time-domain scattering P.A. Martin ; Colorado School of Mines
title_fullStr	Time-domain scattering P.A. Martin ; Colorado School of Mines
title_full_unstemmed	Time-domain scattering P.A. Martin ; Colorado School of Mines
title_short	Time-domain scattering
title_sort	time domain scattering
topic	Zeitreihenanalyse (DE-588)4067486-1 gnd Streutheorie (DE-588)4183697-2 gnd Wellengleichung (DE-588)4065315-8 gnd
topic_facet	Zeitreihenanalyse Streutheorie Wellengleichung
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