Computational acoustics : theory and implementation / David R. Bergman.

Covers the theory and practice of innovative new approaches to modelling acoustic propagation There are as many types of acoustic phenomena as there are media, from longitudinal pressure waves in a fluid to S and P waves in seismology. This text focuses on the application of computational methods to...

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Bibliographic Details
Online Access:	Full text (Emerson users only)
Main Author:	Bergman, David R. (Author)
Format:	Electronic eBook
Language:	English
Published:	Hoboken, NJ : John Wiley & Sons, Inc., 2018.
Subjects:	Sound-waves > Measurement. Sound-waves > Computer simulation. Sound-waves > Mathematical models.
Genre/Form:	Electronic books

Table of Contents:

Intro
Title Page
Copyright Page
Contents
Series Preface
Chapter 1 Introduction
Chapter 2 Computation and Related Topics
2.1 Floating-Point Numbers
2.1.1 Representations of Numbers
2.1.2 Floating-Point Numbers
2.2 Computational Cost
2.3 Fidelity
2.4 Code Development
2.5 List of Open-Source Tools
2.6 Exercises
References
Chapter 3 Derivation of the Wave Equation
3.1 Introduction
3.2 General Properties of Waves
3.3 One-Dimensional Waves on a String
3.4 Waves in Elastic Solids
3.5 Waves in Ideal Fluids
3.5.1 Setting Up the Derivation
3.5.2 A Simple Example
3.5.3 Linearized Equations
3.5.4 A Second-Order Equation from Differentiation
3.5.5 A Second-Order Equation from a Velocity Potential
3.5.6 Second-Order Equation without Perturbations
3.5.7 Special Form of the Operator
3.5.8 Discussion Regarding Fluid Acoustics
3.6 Thin Rods and Plates
3.7 Phonons
3.8 Tensors Lite
3.9 Exercises
References
Chapter 4 Methods for Solving the Wave Equation
4.1 Introduction
4.2 Method of Characteristics
4.3 Separation of Variables
4.4 Homogeneous Solution in Separable Coordinates
4.4.1 Cartesian Coordinates
4.4.2 Cylindrical Coordinates
4.4.3 Spherical Coordinates
4.5 Boundary Conditions
4.6 Representing Functions with the Homogeneous Solutions
4.7 Greeńs Function
4.7.1 Greeńs Function in Free Space
4.7.2 Mode Expansion of Greeńs Functions
4.8 Method of Images
4.9 Comparison of Modes to Images
4.10 Exercises
References
Chapter 5 Wave Propagation
5.1 Introduction
5.2 Fourier Decomposition and Synthesis
5.3 Dispersion
5.4 Transmission and Reflection
5.5 Attenuation
5.6 Exercises
References
Chapter 6 Normal Modes
6.1 Introduction
6.2 Mode Theory
6.3 Profile Models.
6.4 Analytic Examples
6.4.1 Example 1: Harmonic Oscillator
6.4.2 Example 2: Linear
6.5 Perturbation Theory
6.6 Multidimensional Problems and Degeneracy
6.7 Numerical Approach to Modes
6.7.1 Derivation of the Relaxation Equation
6.7.2 Boundary Conditions in the Relaxation Method
6.7.3 Initializing the Relaxation
6.7.4 Stopping the Relaxation
6.8 Coupled Modes and the Pekeris Waveguide
6.8.1 Pekeris Waveguide
6.8.2 Coupled Modes
6.9 Exercises
References
Chapter 7 Ray Theory
7.1 Introduction
7.2 High Frequency Expansion of the Wave Equation
7.2.1 Eikonal Equation and Ray Paths
7.2.2 Paraxial Rays
7.3 Amplitude
7.4 Ray Path Integrals
7.5 Building a Field from Rays
7.6 Numerical Approach to Ray Tracing
7.7 Complete Paraxial Ray Trace
7.8 Implementation Notes
7.9 Gaussian Beam Tracing
7.10 Exercises
References
Chapter 8 Finite Difference and Finite Difference Time Domain
8.1 Introduction
8.2 Finite Difference
8.3 Time Domain
8.4 FDTD Representation of the Linear Wave Equation
8.5 Exercises
References
Chapter 9 Parabolic Equation
9.1 Introduction
9.2 The Paraxial Approximation
9.3 Operator Factoring
9.4 Pauli Spin Matrices
9.5 Reduction of Order
9.5.1 The Padé Approximation
9.5.2 Phase Space Representation
9.5.3 Diagonalizing the Hamiltonian
9.6 Numerical Approach
9.7 Exercises
References
Chapter 10 Finite Element Method
10.1 Introduction
10.2 The Finite Element Technique
10.3 Discretization of the Domain
10.3.1 One-Dimensional Domains
10.3.2 Two-Dimensional Domains
10.3.3 Three-Dimensional Domains
10.3.4 Using Gmsh
10.4 Defining Basis Elements
10.4.1 One-Dimensional Basis Elements
10.4.2 Two-Dimensional Basis Elements
10.4.3 Three-Dimensional Basis Elements.
10.5 Expressing the Helmholtz Equation in the FEM Basis
10.6 Numerical Integration over Triangular and Tetrahedral Domains
10.6.1 Gaussian Quadrature
10.6.2 Integration over Triangular Domains
10.6.3 Integration over Tetrahedral Domains
10.7 Implementation Notes
10.8 Exercises
References
Chapter 11 Boundary Element Method
11.1 Introduction
11.2 The Boundary Integral Equations
11.3 Discretization of the BIE
11.4 Basis Elements and Test Functions
11.5 Coupling Integrals
11.5.1 Derivation of Coupling Terms
11.5.2 Singularity Extraction
11.5.3 Evaluation of the Singular Part
11.5.3.1 Closed-Form Expression for the Singular Part of K
11.5.3.2 Method for Partial Analytic Evaluation
11.5.3.3 The Hypersingular Integral
11.6 Scattering from Closed Surfaces
11.7 Implementation Notes
11.8 Comments on Additional Techniques
11.8.1 Higher-Order Methods
11.8.2 Body of Revolution
11.9 Exercises
References
Index
EULA.

Computational acoustics : theory and implementation / David R. Bergman.

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