Includes bibliographical references and index.

Online resource; title from digital title page (viewed on January 17, 2018).

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 the fields of linear acoustics. Techniques for solving the linear wave equation in homogeneous medium are explored in depth, as are techniques for modelling wave propagation in inhomogeneous and anisotropic fluid medium from a source and scattering from objects. Written for both students and working engineers, this book features a unique pedagogical approach to acquainting readers with innovative numerical methods for developing computational procedures for solving problems in acoustics and for understanding linear acoustic propagation and scattering. Chapters follow a consistent format, beginning with a presentation of modelling paradigms, followed by descriptions of numerical methods appropriate to each paradigm. Along the way important implementation issues are discussed and examples are provided, as are exercises and references to suggested readings. Classic methods and approaches are explored throughout, along with comments on modern advances and novel modeling approaches.' -Bridges the gap between theory and implementation, and features examples illustrating the use of the methods described -Provides complete derivations and explanations of recent research trends in order to provide readers with a deep understanding of novel techniques and methods -Features a systematic presentation appropriate for advanced students as well as working professionals -References, suggested reading and fully worked problems are provided throughout' An indispensable learning tool/reference that readers will find useful throughout their academic and professional careers, this book is both a supplemental text for graduate students in physics and engineering interested in acoustics and a valuable working resource for engineers in an array of industries, including defense, medicine, architecture, civil engineering, aerospace, biotech, and more.

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.