Wave and Scattering Methods for Numerical SimulationScattering-based numerical methods are increasingly applied to the numerical simulation of distributed time-dependent physical systems. These methods, which possess excellent stability and stability verification properties, have appeared in various guises as the transmission line matrix (TLM) method, multidimensional wave digital (MDWD) filtering and digital waveguide (DWN) methods. This text provides a unified framework for all of these techniques and addresses the question of how they are related to more standard numerical simulation techniques. Covering circuit/scattering models in electromagnetics, transmission line modelling, elastic dynamics, as well as time-varying and nonlinear systems, this book highlights the general applicability of this technique across a variety of disciplines, as well as the inter-relationships between simulation techniques and digital filter design.
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Contents
| 1 | |
2 Wave Digital Filters | 25 |
3 Multidimensional Wave Digital Networks | 53 |
4 Digital Waveguide Networks | 115 |
5 Extensions of Digital Waveguide Networks | 169 |
6 Scattering Methods A Unified Perspective | 205 |
7 Applications to Vibrating Systems | 223 |
8 Timevarying and Nonlinear Systems | 261 |
9 Concluding Remarks | 289 |
A Finite Difference Schemes for the Wave Equation | 297 |
B Eigenvalue and Steady State Problems | 325 |
| 333 | |
| 355 | |
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1)D transmission line acoustic tube adaptor admittances algorithm approximation bidirectional delay lines boundary conditions capacitance capacitor Chapter circuit elements coefficients computational coordinates defined density derived discrete discussed in Section domain eigenvalues electrical network energy FDTD Fettweis finite difference scheme frequency grid functions grid point grid spacing group velocity gyrator immittances impedance inductance inductor interleaved l2 norm linear lossless lumped matrix MD-passive MDKC MDWD network N-port nonlinear numerical integration numerical methods one-port operation parallel junction parallel-plate system passive phase velocity port resistances positive problem region scattering junctions scattering methods self-loop series junctions shown in Figure simulation solution spatial spectral mappings stability bound step structure symmetric hyperbolic system of PDEs time-varying transformation transmission line transmission line equations trapezoid rule two-port unit element vector voltage voltage waves wave digital filters wave equation wave variables waveguide mesh
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