Continuous System Simulation
暫譯: 連續系統模擬

François E. Cellier, Ernesto Kofman

Continuous System Simulation
  • 出版商: Demos Medical Publis
  • 出版日期: 2006-03-15
  • 售價: $1,250
  • 貴賓價: 9.8 折 $1,225
  • 語言: 英文
  • 頁數: 644
  • 裝訂: Hardcover
  • ISBN: 0387261028
  • ISBN-13: 9780387261027
  • 相關分類: Computer-networks

    • 下單後立即進貨 (約5~7天)

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Continuous System Simulation describes systematically and methodically how mathematical models of dynamic systems, usually described by sets of either ordinary or partial differential equations possibly coupled with algebraic equations, can be simulated on a digital computer.

Modern modeling and simulation environments relieve the occasional user from having to understand how simulation really works. Once a mathematical model of a process has been formulated, the modeling and simulation environment compiles and simulates the model, and curves of result trajectories appear magically on the user’s screen. Yet, magic has a tendency to fail, and it is then that the user must understand what went wrong, and why the model could not be simulated as expected.

Continuous System Simulation is written by engineers for engineers, introducing the partly symbolical and partly numerical algorithms that drive the process of simulation in terms that are familiar to simulation practitioners with an engineering background, and yet, the text is rigorous in its approach and comprehensive in its coverage, providing the reader with a thorough and detailed understanding of the mechanisms that govern the simulation of dynamical systems.

Continuous System Simulation is a highly software-oriented text, based on MATLAB. Homework problems, suggestions for term project, and open research questions conclude every chapter to deepen the understanding of the student and increase his or her motivation.

Continuous System Simulation is the first text of its kind that has been written for an engineering audience primarily. Yet due to the depth and breadth of its coverage, the book will also be highly useful for readers with a mathematics background. The book has been designed to accompany senior and graduate students enrolled in a simulation class, but it may also serve as a reference and self-study guide for modeling and simulation practitioners.

 

Table of Contents

Introduction, Scope, Definitions.- Modeling and Simulation: A Circuit Example.- Modeling vs. Simulation.- Time and Again.- Simulation as a Problem Solving Tool.- Simulation Software: Today and Tomorrow.-

Basic Principles of Numerical Integration.- Introduction.- The Approximation Accuracy.- Euler Integration.- The Domain of Numerical Stability.- The Newton Iteration.- Semi–analytic Algorithms.- Spectral Algorithms.-

Single–step Integration Methods.- Introduction.- Runge–Kutta Algorithms.- Stability Domains of RK Algorithms.- Stiff Systems.- Extrapolation Techniques.- Marginally Stable Systems.- Backinterpolation Methods.- Accuracy Considerations.- Step–size and Order Control.-

Multi–step Integration Methods.- Introduction.- Newton–Gregory Polynomials.- Numerical Integration Through Polynomial Extrapolation.- Explicit Adams–Bashforth Formulae.- Implicit Adams–Moulton Formulae.- Adams–Bashforth–Moulton Predictor–Corrector Formulae.- Backward Difference Formulae.- Nyström and Milne Algorithms.- In Search for Stiffly–stable Methods.- High–order Backward Difference Formulae.- Newton Iteration.- Step–size and Order Control.- The Startup Problem.- The Readout Problem.-

Second Derivative Systems.- Introduction.- Conversion of Second–derivative Models to State–space Form.- Velocity–free Models.- Linear Velocity Models.- Nonlinear Velocity Models.- Stability and Damping of Godunov Scheme.- Explicit and Implicit Godunov Algorithms of Different Orders.- The Newmark Algorithm.-

Partial Differential Equations.- Introduction.- The Method of Lines.- Parabolic PDEs.- Hyperbolic PDEs.- Shock Waves.- Upwind Discretization.- Grid–width Control.- PDEs in Multiple Space Dimensions.- Elliptic PDEs and Invariant Embedding.- Finite Element Approximations.-

Differential Algebraic Equations.- Introduction.- Causalization of Equations.- Algebraic Loops.- The Tearing Algorithm.- The Relaxation Algorithm.- Structural Singularities.- Structural Singularity Elimination.- The Solvability Issue.-

Differential Algebraic Equation Solvers.- Introduction.- Multi-step Formulae.- Single–step Formulae.- DASSL.- Inline Integration.- Inlining Implicit Runge–Kutta Algorithms.- Stiffly Stable Step–size Control of Radau IIA.- Stiffly Stable Step–size Control of Lobatto IIIC.- Inlining Partial Differential Equations.- Overdetermined DAEs.- Electronic Circuit Simulators.- Multibody System Dynamics Simulators.- Chemical Process Dynamics Simulators.-

Simulation of Discontinuous Systems.- Introduction.- Basic Difficulties.- Time Events.- Simulation of Sampled–data Systems.- State Events (1. Multiple Zero Crossings, 2. Single Zero Crossings, Single–step Algorithms, 3. Single Zero Crossings, Multi-step Algorithms, 4. Non–essential State Events).- Consistent Initial Conditions.- Object–oriented Descriptions of Discontinuities ( 1. The Computational Causality of if–Statements, 2. Multi–valued Functions).- The Switch Equation.- Ideal Diodes and Parameterized Curve Descriptions.- Variable Structure Models.- Mixed–mode Integration.- State Transition Diagrams.- Petri Nets.-

Real–time Simulation.- Introduction.- The Race Against Time.- Suitable Numerical Integration Methods.- Linearly Implicit Methods.- Multi–rate Integration.- Inline Integration.- Mixed–mode Integration.- Discontinuous Systems.- Simulation Architecture.- Overruns.-

Discrete Event Simulation.- Introduction.- Space Discretization: A Simple Example.- Discrete Event Systems and DEVS.- Coupled DEVS Models.- Simulation of DEVS Models.- DEVS and Continuous Systems Simulation.- Quantized State Systems.-

Quantization-based Integration.- Introduction.- Convergence, Accuracy, and Stability in QSS.- Choosing Quantum and Hysteresis Width.- Input Signals in the QSS Method.- Startup and Output Interpolation.- Second-order QSS.- Algebraic Loops in QSS Methods.- DAE Simulation with QSS Methods.- Discontinuity Handling.- Real-time Simulation.- Open Problems in Quantization–based Methods.
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Cellier, Francois E.
Kofman, Ernesto

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商品描述(中文翻譯)

描述

《連續系統模擬》系統性且有條理地描述了如何在數位計算機上模擬動態系統的數學模型，這些模型通常由一組常微分方程或偏微分方程組成，可能還結合了代數方程。

現代建模和模擬環境使偶爾使用者不必了解模擬的實際運作方式。一旦過程的數學模型被建立，建模和模擬環境便會編譯並模擬該模型，結果的曲線會神奇地出現在使用者的螢幕上。然而，魔法有時會失效，這時使用者必須了解問題出在哪裡，以及為什麼模型無法如預期那樣被模擬。

《連續系統模擬》是由工程師為工程師撰寫的，介紹了部分符號化和部分數值的算法，這些算法以模擬實務者熟悉的術語推動模擬過程，然而，文本在其方法上是嚴謹的，並且在其涵蓋範圍上是全面的，為讀者提供了對於支配動態系統模擬機制的徹底和詳細的理解。

《連續系統模擬》是一部高度以軟體為導向的文本，基於 MATLAB。每章結尾都有作業問題、學期專案建議和開放研究問題，以加深學生的理解並提高其動機。

《連續系統模擬》是首部專為工程讀者撰寫的同類書籍。然而，由於其涵蓋的深度和廣度，這本書對於具有數學背景的讀者也將非常有用。本書旨在輔助修讀模擬課程的高年級和研究生，但也可作為建模和模擬實務者的參考和自學指南。

目錄

引言、範圍、定義。- 建模與模擬：一個電路範例。- 建模與模擬的區別。- 時間與再次。- 模擬作為問題解決工具。- 模擬軟體：今天與明天。-

數值積分的基本原則。- 引言。- 近似精度。- 歐拉積分。- 數值穩定性的範疇。- 牛頓迭代。- 半解析算法。- 頻譜算法。-

單步積分方法。- 引言。- 龍格-庫塔算法。- RK算法的穩定性範疇。- 剛性系統。- 外推技術。- 邊際穩定系統。- 反插值方法。- 精度考量。- 步長與階數控制。-

多步積分方法。- 引言。- 牛頓-格雷戈里多項式。- 通過多項式外推的數值積分。- 顯式亞當斯-巴什福斯公式。- 隱式亞當斯-莫爾頓公式。- 亞當斯-巴什福斯-莫爾頓預測-修正公式。- 向後差分公式。- Nyström和Milne算法。- 尋找剛性穩定方法。- 高階向後差分公式。- 牛頓迭代。- 步長與階數控制。- 啟動問題。- 讀出問題。-

二階導數系統。- 引言。- 將二階導數模型轉換為狀態空間形式。- 無速度模型。- 線性速度模型。- 非線性速度模型。- Godunov方案的穩定性與阻尼。- 不同階數的顯式與隱式Godunov算法。- Newmark算法。-

偏微分方程。- 引言。- 線法。- 拋物型PDE。- 超波型PDE。- 衝擊波。- 順風離散化。- 網格寬度控制。- 多維空間中的PDE。- 橢圓型PDE與不變嵌入。- 有限元素近似。-

微分代數方程。- 引言。- 方程的因果化。- 代數迴路。- 撕裂算法。- 放鬆算法。- 結構奇異性。- 結構奇異性消除。- 可解性問題。-

微分代數方程求解器。- 引言。- 多步公式。- 單步公式。- DASSL。- 內聯積分。- 內聯隱式龍格-庫塔算法。- Radau IIA的剛性穩定步長控制。- Lobatto IIIC的剛性穩定步長控制。- 內聯偏微分方程。- 過度確定的DAE。- 電子電路模擬器。- 多體系統動力學模擬器。- 化學過程動力學模擬器。-

不連續系統的模擬。- 引言。- 基本困難。- 時間事件。- 樣本數據系統的模擬。- 狀態事件（1. 多重零交叉，2. 單一零交叉，單步算法，3. 單一零交叉，多步算法，4. 非必要狀態事件）。- 一致的初始條件。- 不連續性的物件導向描述（1. if語句的計算因果性，2. 多值函數）。- 開關方程。- 理想二極體與參數化曲線描述。- 可變結構模型。- 混合模式積分。- 狀態轉換圖。- Petri網。-

即時模擬。- 引言。- 與時間的賽跑。- 合適的數值積分方法。- 線性隱式方法。- 多速率積分。- 內聯積分。- 混合模式積分。- 不連續系統。- 模擬架構。- 超限。-

離散事件模擬。- 引言。- 空間離散化：一個簡單的例子。- 離散事件系統與DEVS。- 耦合DEVS模型。- DEVS模型的模擬。- DEVS與連續系統模擬。- 量化狀態系統。-

基於量化的積分。- 引言。- QSS中的收斂、精度與穩定性。- 選擇量子與滯後寬度。- QSS方法中的輸入信號。- 啟動與輸出插值。- 二階QSS。- QSS方法中的代數迴路。- 使用QSS方法的DAE模擬。- 不連續性處理。- 即時模擬。- 基於量化方法的開放問題。

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Cellier, Francois E.
Kofman, Ernesto

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計算科學與工程
計算機科學
工程
數學
計算數學

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