Wave and Scattering Methods for Numerical Simulation

Informationen zum Autor 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. Klappentext 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. Zusammenfassung 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. Inhaltsverzeichnis Preface xi Foreword xv 1 Introduction 1 1.1 An Overview of Scattering Methods 3 1.1.1 Remarks on Passivity 3 1.1.2 Case Study: The Kelly-Lochbaum Digital Speech Synthesis Model 4 1.1.3 Digital Waveguide Networks 12 1.1.4 A General Approach: Multidimensional Circuit Representations and Wave Digital Filters 18 1.2 Questions 24 2 Wave Digital Filters 25 2.1 Classical Network Theory 27 2.1.1 N-ports 27 2.1.2 Power and Passivity 28 2.1.3 Kirchhoff's Laws 30 2.1.4 Circuit Elements 31 2.2 Wave Digital Elements and Connections 32 2.2.1 The Bilinear Transform 33 2.2.2 Wave Variables 35 ...

List of contents

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.

Report

"...remarkable...the book is to be highly recommended..." (International Journal of Numerical Modelling, Vol 18 (4) July 2005)

Product details

• Authors: S Bilbao, Stefan Bilbao, Stefan (Queen''s University Bilbao, Bilbao Stefan
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 21.05.2004
• EAN: 9780470870174
• ISBN: 978-0-470-87017-4
• No. of pages: 380
• Subjects: Natural sciences, medicine, IT, technology > Technology > Electronics, electrical engineering, communications engineering; Elektromagnetismus, Elektroakustik, Electrical & Electronics Engineering, Elektrotechnik u. Elektronik, Schaltkreise - Theorie u. Entwurf, Circuit Theory & Design, Electromagnetic Theory