Wave and Scattering Methods for Numerical Simulation
Wave and Scattering Methods for Numerical Simulation
复制标题
用于数值模拟的波和散射方法
DOI：
10.1002/0470870192
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发表时间：
2004
影响因子：
8
通讯作者：
S. Bilbao
中科院分区：
文献类型：
--
作者：
S. Bilbao
Preface.Foreword.1。引言。1.1散射方法概述。1.1.1对无源性的评述。1.1.2案例研究：Kelly-Lochbaum数字语音合成模式。1.1.3数字波导网络。1.1.4一般方法：多维电路表示和波数字滤波器。1.2问题。2。波数字滤波器。2.1经典网络理论。2.1.1 n端口。2.1.2功率和无源性。2.1.3 Kirchhoff定律。2.1.4电路元件。2.2波数字元件和连接。2.2.1双线性变换。2.2.2波变量。2.2.3伪功率和伪无源性。2.2.4波数字元件。2.2.5适配器。2.2.6信号和系数量化。2.2.7矢量波变量。2.3波数字滤波器和有限差分。多维波数字Filters.3.1对称双曲Systems.3.2坐标变化和网格坐标Changes.3.2.2 Generation.3.2.1结构坐标的变化(1 + 1)D.3.2.3坐标变化高Dimensions.3.3 MD-passivity.3.4 MD电路Elements.3.4.1 MD Inductor.3.4.2 OtherMD Elements.3.4.3离散谱Domain.3.4.4其他光谱Mappings.3.5(1 + 1)维平流Equation.3.5.1多维基尔霍夫Circuit.3.5.2 Stability.3.5.33.6.1 (1 +1)D传输线方程的MDKC。3.6.3能量解释。3.6.4 (1 +1)D传输线MDWD网络。3.6.5简化网络。3.7 (2 +1)D平行板系统。3.7.1 MDKC和MDWD网络。3.8有限差分解释。3.8.1 MDWD网络作为多步方案。3.8.2数值相速度和寄生性模式。3.9初始条件。3.10边界条件。3.10.1 MDKC边界建模。3.11平衡形式。3.12高阶精度。数字波导网络。4.1 FDTD和TLM.4.2数字波导。4.2.1双向延迟线。4.2.2阻抗。4.2.3波动方程解释。4.2.4波量不同定义注。4.2.5散射结。4.2.6矢量波导和散射结。4.2.7过渡注。4.3 (1+1)D传输线。4.3.1一阶系统和波动方程。4.3.2中心差分格式和网格分割。4.3.3 A (1+1)D波导网络。4.3.4波导网络和波动方程。4.3.5交错波导网络。4.3.6变系数。4.3.7结合损耗和源。4.3.8数值相速度和色散。4.3.9边界条件。4.4 (2 +1)D平行板系统。4.4.1定义方程和中心差分。4.4.2波导网格。4.4.3在波导网格的标准形式中降低计算复杂度和内存要求。4.4.4边界条件。4.5初始条件。4.6音乐和音频数字波导的应用。数字波导网络的扩展。5.1（2 +1）中的可选网格D.5.1.1六边形和三角形网格。5.1.2径向坐标下的波导网格。5.2 (3 +1)D波方程和波导网格。5.3一般曲线坐标下的波导网格。5.4网格之间的接口。5.4.1跨界面的网格密度加倍。5.4.2网格密度逐步加倍。5.4.3网格密度四倍。5.4.4连接直线网格和径向网格。5.4.5（3 +1）中的网格密度加倍+ 1) D.5.4.6 Note.6。将DWN纳入MDWD框架。6.1重新审视（1+1）D传输线。6.1.1多维单元单元。6.1.2多维单元单元的混合形式。6.1.3 (1+1)D传输线的替代MDKC。6.2 (2 +1)D平行板系统的替代MDKC。6.3重新审视高阶精度。6.4麦克斯韦方程组。振动系统的应用。7.1波束动力学。7.1.1 Timoshenko系统的MDKC和MDWDF。7.1.2 Timoshenko系统的波导网络。7.1.3 dwn中的边界条件。7.1.4仿真：均匀和变截面面积波束的Timoshenko系统。7.1.5通过平衡改进Timoshenko系统的MDKC。7.2板。7.2.1 Mindlin系统的MDKC和散射网络。7.2.2 Mindlin板的边界终止。7.2.3仿真：等厚变厚板的Mindlin系统。7.3圆柱壳。7.3.1膜壳。7.3.2 Naghdi-Cooper系统II公式。7.4弹性固体。7.4.1 Navier系统的散射网络。7.4.2边界条件。时变与非线性系统。8.1时变与非线性电路元件。8.1.1集总元件。8.1.2分布式元件。8.2线性时变分布式系统。8.2.1时变传输线模型。8.3音乐声学中的集总非线性系统。8.3.1钢琴锤。8.3.2单簧片。8.4从波数字原理到相对论。8.4.1挑战的起源。8.4.2牛顿极限原理。8.4.3牛顿第二定律。8.4.4牛顿第三定律及其他8.4.5运动电磁场。8.4.6 Bertozzi实验。8.5 Burger方程。8.6气体动力学方程。8.6.1气体动力学方程的MDKC和MDWDF。8.6.2替代MDKC和散射网络。8.6.3熵变量。结束语。9.1回答。9.2问题。波动方程的有限差分格式。a .1差分格式的Von Neumann分析。a .1.1一步格式。a .1.2多步格式。a .1.3矢量格式。a .1.4数值相速度（2 + 1）D波方程的有限差分格式。a .2.1直线格式。a .2.2插值直线格式。a .2.3三角形格式。a .2.4六边形格式。a .2.5高阶精度注（3 + 1）D波动方程的有限差分格式。a .3.1三次直线格式。a .3.2八面体格式。a .3.3 (3 + 1)D插值直线格式。a .3.4四面体格式。特征值与稳态问题Introduction.B.2时间域模型[b]离散化偏微分方程的典型特征值分布激励和滤波。b .5部分相似变换稳态问题多特征值的概化。b .8数值Example.Bibliography.Index。
Preface.Foreword.1. Introduction.1.1 An Overview of Scattering Methods.1.1.1 Remarks on Passivity.1.1.2 Case Study: The Kelly-Lochbaum Digital Speech Synthesis Mode.1.1.3 Digital Waveguide Networks.1.1.4 A General Approach: Multidimensional Circuit Representations and Wave Digital Filters.1.2 Questions.2. Wave Digital Filters.2.1 Classical Network Theory.2.1.1 N-ports.2.1.2 Power and Passivity.2.1.3 Kirchhoff's Laws.2.1.4 Circuit Elements.2.2 Wave Digital Elements and Connections.2.2.1 The Bilinear Transform.2.2.2 Wave Variables.2.2.3 Pseudopower and Pseudopassivity.2.2.4 Wave Digital Elements.2.2.5 Adaptors.2.2.6 Signal and Coefficient Quantization.2.2.7 VectorWave Variables.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.3.2.1 Structure of Coordinate Changes.3.2.2 Coordinate Changes in (1 +1)D.3.2.3 Coordinate Changes in Higher Dimensions.3.3 MD-passivity.3.4 MD Circuit Elements.3.4.1 The MD Inductor.3.4.2 OtherMD Elements.3.4.3 Discretization in the Spectral Domain.3.4.4 Other Spectral Mappings.3.5 The (1 +1)D Advection Equation.3.5.1 A Multidimensional Kirchhoff Circuit.3.5.2 Stability.3.5.3 An Upwind Form.3.6 The (1 +1)D Transmission Line.3.6.1 MDKC for the (1 + 1)D Transmission Line Equations.3.6.2 Digression: The Inductive Lattice Two-port.3.6.3 Energetic Interpretation.3.6.4 A MDWD Network for the (1 + 1)D Transmission Line.3.6.5 Simplified Networks.3.7 The (2 +1)D Parallel-plate System.3.7.1 MDKC and MDWD Network.3.8 Finite-difference Interpretation.3.8.1 MDWD Networks as Multistep Schemes.3.8.2 Numerical Phase Velocity and Parasitic Modes.3.9 Initial Conditions.3.10 Boundary Conditions.3.10.1 MDKC Modeling of Boundaries.3.11 Balanced Forms.3.12 Higher-order Accuracy.4. Digital Waveguide Networks.4.1 FDTD and TLM.4.2 Digital Waveguides.4.2.1 The Bidirectional Delay Line.4.2.2 Impedance.4.2.3 Wave Equation Interpretation.4.2.4 Note on the Different Definitions of Wave Quantities.4.2.5 Scattering Junctions.4.2.6 Vector Waveguides and Scattering Junctions.4.2.7 Transitional Note.4.3 The (1 +1)D Transmission Line.4.3.1 First-order System and the Wave Equation .4.3.2 Centered Difference Schemes and Grid Decimation.4.3.3 A (1+1)D Waveguide Network.4.3.4 Waveguide Network and the Wave Equation.4.3.5 An Interleaved Waveguide Network.4.3.6 Varying Coefficients.4.3.7 Incorporating Losses and Sources.4.3.8 Numerical Phase Velocity and Dispersion.4.3.9 Boundary Conditions.4.4 The (2 +1)D Parallel-plate System.4.4.1 Defining Equations and Centered Differences.4.4.2 The Waveguide Mesh.4.4.3 Reduced Computational Complexity and Memory Requirements in the Standard Form of the Waveguide Mesh.4.4.4 Boundary Conditions.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.5.1.1 Hexagonal and Triangular Grids.5.1.2 The Waveguide Mesh in Radial Coordinates.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.5.4.1 Doubled Grid Density Across an Interface.5.4.2 Progressive Grid Density Doubling.5.4.3 Grid Density Quadrupling.5.4.4 Connecting Rectilinear and Radial Grids.5.4.5 Grid Density Doubling in (3 +1)D.5.4.6 Note.6. Incorporating the DWN into the MDWD Framework.6.1 The (1 +1)D Transmission Line Revisited.6.1.1 Multidimensional Unit Elements.6.1.2 Hybrid Form of the Multidimensional Unit Element.6.1.3 Alternative MDKC for the (1+1)D Transmission Line.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.7.1.1 MDKC and MDWDF for Timoshenko's System.7.1.2 Waveguide Network for Timoshenko's System.7.1.3 Boundary Conditions in the DWN.7.1.4 Simulation: Timoshenko's System for Beams of Uniform and Varying Cross-sectional Areas.7.1.5 Improved MDKC for Timoshenko's System via Balancing.7.2 Plates.7.2.1 MDKCs and Scattering Networks for Mindlin's System.7.2.2 Boundary Termination of the Mindlin Plate.7.2.3 Simulation: Mindlin's System for Plates of Uniform and Varying Thickness.7.3 Cylindrical Shells.7.3.1 The Membrane Shell.7.3.2 The Naghdi-Cooper System II Formulation.7.4 Elastic Solids.7.4.1 Scattering Networks for the Navier System.7.4.2 Boundary Conditions.8. Time-varying and Nonlinear Systems.8.1 Time-varying and Nonlinear Circuit Elements.8.1.1 Lumped Elements.8.1.2 Distributed Elements.8.2 Linear Time-varying Distributed Systems.8.2.1 A Time-varying Transmission Line Model.8.3 Lumped Nonlinear Systems in Musical Acoustics.8.3.1 Piano Hammers.8.3.2 The Single Reed.8.4 From Wave Digital Principles to Relativity Theory.8.4.1 Origin of the Challenge.8.4.2 The Principle of Newtonian Limit.8.4.3 Newton's Second Law.8.4.4 Newton's Third Law and Some Consequences.8.4.5 Moving Electromagnetic Field.8.4.6 The Bertozzi Experiment.8.5 Burger's Equation.8.6 The Gas Dynamics Equations.8.6.1 MDKC and MDWDF for the Gas Dynamics Equations.8.6.2 An Alternate MDKC and Scattering Network.8.6.3 Entropy Variables.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.1.1 One-step Schemes.A.1.2 Multistep Schemes.A.1.3 Vector Schemes.A.1.4 Numerical Phase Velocity.A.2 Finite Difference Schemes for the (2 + 1)D Wave Equation.A.2.1 The Rectilinear Scheme.A.2.2 The Interpolated Rectilinear Scheme.A.2.3 The Triangular Scheme.A.2.4 The Hexagonal Scheme.A.2.5 Note on Higher-order Accuracy.A.3 Finite Difference Schemes for the (3 + 1)D Wave Equation.A.3.1 The Cubic Rectilinear Scheme.A.3.2 The Octahedral Scheme.A.3.3 The (3 + 1)D Interpolated Rectilinear Scheme.A.3.4 The Tetrahedral Scheme.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.