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Introductory Remarks
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Wave and Scattering Methods
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Higher-order Accuracy
Digital Waveguide Networks
Subsections
Introductory Remarks
FDTD and TLM
Digital Waveguides
The Bidirectional Delay Line
Impedance
Wave Equation Interpretation
Note on the Different Definitions of Wave Quantities
Scattering Junctions
Vector Waveguides and Scattering Junctions
Vector/Scalar Waveguide Coupling
Music and Audio Applications of Digital Waveguides
Transitional Note
The (1+1)D Transmission Line
First-order System and the Wave Equation
Centered Difference Schemes and Grid Decimation
A (1+1)D Waveguide Network
Waveguide Network and the Wave Equation
Comment on Numerical Instability
An Interleaved Waveguide Network
Varying Coefficients
Type I: Voltage-centered Network
Type II: Current-centered Network
Type III: Mixed Network
Comment: Passivity and Stability
Incorporating Losses and Sources
Numerical Phase Velocity and Dispersion
Boundary Conditions
The (2+1)D Parallel-plate System
Defining Equations and Centered Differences
The Waveguide Mesh
Losses, Sources, and Spatially-varying Coefficients
Type I: Voltage-centered Mesh
Type II: Current-centered Mesh
Type III: Mixed Mesh
Reduced Computational Complexity and Memory Requirements in the Standard Form of the Waveguide Mesh
Boundary Conditions
Grid Arrangement Requiring Voltage and Tangential Current Density Component on Boundary
Grid Arrangement with Normal Current Density Component Required on Boundary
Initial Conditions
Alternative Grids in (2+1)D
Hexagonal and Triangular Grids
The Waveguide Mesh in Radial Coordinates
Type I: Voltage-Centered Mesh
Type II: Current-Centered Mesh
Central Gridpoint in a Radial Mesh
Simulation: Circular Region with Varying Inductance
The (3+1)D Wave Equation and Waveguide Meshes
The Waveguide Mesh in General Curvilinear Coordinates
Interfaces Between Grids
Doubled Grid Density Across an Interface
Corners
Simulation
Progressive Grid Density Doubling
Grid Density Quadrupling
Connecting Rectilinear and Radial Grids
Simulation: Solving the Acoustic Wave Equation in a U-Shaped Tube
Grid Density Doubling in (3+1)D
Note
Incorporating the DWN into the MDWD Framework
Multidimensional Unit Elements
Hybrid Form of the Multidimensional Unit Element
Alternative MDKC for the (1+1)D Transmission Line
Alternative MDKC for (2+1)D Parallel-plate System
Higher-order Accuracy Revisited
Maxwell's Equations
Phase and Group Velocity
Scattering Networks for Maxwell's Equations
Stefan Bilbao 2002-01-22
