Computational Acoustics : Theory and Implementation.

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 Green´s Function -- 4.7.1 Green´s Function in Free Space -- 4.7.2 Mode Expansion of Green´s 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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.