Stefan Bilbao

Wave and Scattering Methods for Numerical Simulation

• Gebundenes Buch

Produktbeschreibung

Physical phenomena, such as the vibration in acoustic instruments, for example, can usually be modelled in terms of partial differential equations. Various methods exist for doing this and the ultimate choice of method is often a trade-off between the accuracy of the solution provided and the computational power required to achieve it. This book presents a unified treatment of a family of methods that have evolved independently and offers a numerical simulation method that may be applied to a range of distributed systems in diverse simulation environments. The author investigates the relationship between this method and other techniques such as wave digital filters, and develops a unified general numerical simulation method that can be applied to a range of distributed systems in electromagnetics, acoustics, and mechanics.

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Reliable prediction through modelling forms the basis of engineering design. Circuit-based methods for the numerical integration of partial differential equations offer electronic and electrical engineers a simple and verifiable technique for defining efficient and stable models. The digital waveguide method, traditionally popular in the field of sound synthesis, becomes less reliable when applied to multidimensional systems and/or non-ideal media.
_ Provides a comprehensive overview of circuit-based numerical integration methods.
_ Presents a unified simulation method with potential applications in electromagnetics, acoustics, mechanics and digital signal processing.
_ The first book to cover these important simulation techniques in the English language.
_ Extends the application of traditional EE techniques to problems in civil and mechanical engineering bringing together four distinct research communities: wave digital filters, digital waveguide mesh, transmission line matrix, and general finite differences.

The author investigates the relationship between this method and other techniques such as wave digital filters, and develops a unified general numerical simulation method that can be applied to a range of distributed systems in electromagnetics, acoustics and mechanics.

Produktdetails

• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 380
• Erscheinungstermin: 2. Juli 2004
• Englisch
• Abmessung: 250mm x 175mm x 25mm
• Gewicht: 865g
• ISBN-13: 9780470870174
• ISBN-10: 0470870176
• Artikelnr.: 12965057

Autorenporträt

Stefan Bilbao received his BA in Physics at Harvard University ('92), then spent two years at the Institut de Recherche et Coordination Acoustique Musicale (IRCAM) in Paris as a student intern. He then completed the MSc and PhD degrees in Electrical Engineering at Stanford University ('96 and '01, respectively), while working at the Center for Computer Research in Music and Acoustics (CCRMA). His current research interests include the application of digital filtering and numerical simulation techniques to the physical modeling of musical instruments.

Inhaltsangabe

Preface. Foreword. 1. Introduction. 1.1 An Overview of Scattering Methods.
1.2 Questions. 2. Wave Digital Filters. 2.1 Classical Network Theory. 2.2
Wave Digital Elements and Connections. 2.3 Wave Digital Filters and Finite
Differences. 3. Multidimensional Wave Digital Filters. 3.1 Symmetric
Hyperbolic Systems. 3.2 Coordinate Changes and Grid Generation. 3.3
MD-passivity. 3.4 MD Circuit Elements. 3.5 The (1 +1)D Advection Equation.
3.6 The (1 +1)D Transmission Line. 3.7 The (2 +1)D Parallel-plate System.
3.8 Finite-difference Interpretation. 3.9 Initial Conditions. 3.10 Boundary
Conditions. 3.11 Balanced Forms. 3.12 Higher-order Accuracy. 4. Digital
Waveguide Networks. 4.1 FDTD and TLM. 4.2 Digital Waveguides. 4.3 The (1
+1)D Transmission Line. 4.4 The (2 +1)D Parallel-plate System. 4.5 Initial
Conditions. 4.6 Music and Audio Applications of Digital Waveguides. 5.
Extensions of Digital Waveguide Networks. 5.1 Alternative Grids in (2 +1)D.
5.2 The (3 + 1)D Wave Equation and Waveguide Meshes. 5.3 The Waveguide Mesh
in General Curvilinear Coordinates. 5.4 Interfaces between Grids. 6.
Incorporating the DWN into the MDWD Framework. 6.1 The (1 +1)D Transmission
Line Revisited. 6.2 Alternative MDKC for the (2 + 1)D Parallel-plate
System. 6.3 Higher-order Accuracy Revisited. 6.4 Maxwell's Equations. 7.
Applications to Vibrating Systems. 7.1 Beam Dynamics. 7.2 Plates. 7.3
Cylindrical Shells. 7.4 Elastic Solids. 8. Time-varying and Nonlinear
Systems. 8.1 Time-varying and Nonlinear Circuit Elements. 8.2 Linear
Time-varying Distributed Systems. 8.3 Lumped Nonlinear Systems in Musical
Acoustics. 8.4 From Wave Digital Principles to Relativity Theory. 8.5
Burger's Equation. 8.6 The Gas Dynamics Equations. 9. Concluding Remarks.
9.1 Answers. 9.2 Questions. A. Finite Difference Schemes for the Wave
Equation. A.1 Von Neumann Analysis of Difference Schemes. A.2 Finite
Difference Schemes for the (2 + 1)D Wave Equation. A.3 Finite Difference
Schemes for the (3 + 1)D Wave Equation. B. Eigenvalue and Steady State
Problems. B.1 Introduction. B.2 Abstract Time Domain Models. B.3 Typical
Eigenvalue Distribution of a Discretized PDE. B.4 Excitation and Filtering.
B.5 Partial Similarity Transform. B.6 Steady State Problems. B.7
Generalization to Multiple Eigenvalues. B.8 Numerical Example.
Bibliography. Index.