An introduction to computational engineering with matlab
This book strives to provide a concise introduction to computational engineering by introducing a wider range of numerical methods commonly used in computational modelling and scientific computing. These methods include finite difference methods, finite volume methods, finite element methods, virtua...
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| Hlavní autor: | |
|---|---|
| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
| Vydáno: |
Cambridge, UK
Cambridge International Science Publishing Ltd
2006
Camridge International Science Cambridge International Science Publishing |
| Vydání: | 1 |
| Témata: | |
| ISBN: | 1904602525, 9781904602521 |
| On-line přístup: | Získat plný text |
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- An introduction to computational engineering with matlab -- Preface -- Acknowledgements -- Summary -- About the Author -- Contents -- I Mathematical Foundations -- Chapter 1: Introduction -- Chapter 2: Vectors and Matrices -- Chapter 3: Differential Equations -- II Numerical Methods -- Chapter 4: Finite Difference Method -- Chapter 5: Hyperbolic Equations -- Chapter 6: Parabolic/Elliptical Equations -- Chapter 7: Pattern Formation -- Chapter 8: Finite Volume Method -- Chapter 9: Finite Element Method -- Chapter 10: Heat Conduction -- Chapter 11: Time-Dependent Problems -- III Advanced Topics -- Chapter 12: Optimization in Engineering -- Chapter 13: Cellular Automata -- Chapter 14: Engineering Applications -- Chapter 15: Scientific Packages -- Index.
- 10.4 A Simple Program: 1-D Heat Conduction -- 10.5 2-D Heat Transfer -- 11. Time-Dependent Problems -- 11.1 The Time Dimension -- 11.2 Time-Stepping -- 11.3 1-D Transient Heat Transfer -- 11.4 Wave Equation -- 12. Optimization in Engineering -- 12.1 Introduction -- 12.2 Bioinspired Algorithms -- 12.2.1 Genetic Algorithms -- 12.2.2 Neural Networks -- 12.2.3 Virtual Bee Algorithms -- 12.2.4 Cellular Automata -- 12.2.5 Optimization -- 12.2.6 No Free Lunch Theorems -- 12.3 Engineering Optimization -- 12.3.1 Function and Multilevel Optimization -- 12.3.2 Multi-Peaked Functions -- 12.3.3 Inverse Analysis -- 13. Cellular Automata -- 13.1 Introduction -- 13.2 Cellular Automata -- 13.2.1 Fundamentals of Cellular Automaton -- 13.2.2 Finite State Cellular Automata -- 13.2.3 Stochastic Cellular Automata -- 13.2.4 Reversible Cellular Automata -- 13.3 Cellular Automata and PDEs -- 13.3.1 Rule-Based and Equation-Based ? -- 13.3.2 Finite Difference and Cellular Automata -- 13.3.3 Differential Equations for CAs -- 13.4 Simulations via Cellular Automata -- 13.4.1 CA for Reaction-Diffusion Systems -- 13.4.2 CA for the Wave Equation -- 14. Engineering Applications -- 14.1 Combustion -- 14.2 Consolidation -- 14.2.1 Nonlinear Consolidation Equation -- 14.3 Heat Transfer of Carbon Nanotubes -- 14.3.1 Carbon Nanotubes -- 14.3.2 Governing Equations -- 14.3.3 Heat Transfer of a Nanotube -- 14.4 Nonlinear Calcium Waves -- 14.4.1 Calcium Functioning -- 14.4.2 Two-Pool Models -- 14.4.3 Stochastic Cellular Automaton -- 14.5 Fracture Dynamics and Structures -- 14.5.1 Element-Free Method -- 14.5.2 Cracking in Elastic Media -- 14.5.3 Fracture in Structures -- 15. Scientific Packages -- 15.1 Pre-Processing -- 15.2 The Solvers -- 15.3 Post-Processing -- 15.4 Make Sense of Your Results -- 15.5 The New Ways -- Index
- Intro -- Preface -- Acknowledgements -- Summary -- About the Author -- Contents -- 1. Introduction -- 1.1 Computational Engineering -- 1.2 DIY Philosophy -- 1.3 How to Use the Book -- 2. Vectors and Matrices -- 2.1 Vector Analysis -- 2.1.1 Vectors -- 2.1.2 Dot Product and Norm -- 2.1.3 Cross Product -- 2.1.4 Differentiation of Vectors -- 2.1.5 Three Basic Operators -- 2.1.6 Some Important Theorems -- 2.2 Matrix Algebra -- 2.2.1 Matrix -- 2.2.2 Determinant -- 2.2.3 Inverse -- 2.2.4 Solution of linear systems -- 3. Differential Equations -- 3.1 Ordinary Differential Equations -- 3.1.1 First Order ODE -- 3.1.2 Higher Order ODEs -- 3.2 Partial Differential Equations -- 3.2.1 First Order Partial Differential Equation -- 3.2.2 Classification of Second-Order Equations -- 3.2.3 Classic PDEs -- 3.2.4 Other PDEs -- 4. Finite Difference Method -- 4.1 Introduction -- 4.2 Integration of ODEs -- 4.2.1 Euler Scheme -- 4.2.2 Leap-Frog Method -- 4.2.3 Runge-Kutta Method -- 4.2.4 Belousov-Zhabotinsky Oscillator -- 5. Hyperbolic Equations -- 5.1 First-Order Hyperbolic Equation -- 5.2 Second Order Wave Equation -- 5.3 Sine-Gordon Equation -- 6. Parabolic/Elliptical Equations -- 6.1 Parabolic Equation -- 6.2 Elliptical Equation -- 7. Pattern Formation -- 7.1 Pattern Formation -- 7.2 Reaction-Diffusion System -- 8. Finite Volume Method -- 8.1 Introduction -- 8.2 Elliptic Equations -- 8.3 Parabolic Equations -- 8.4 Hyperbolic Equations -- 8.5 Heat Conduction: A Case Study -- 9. Finite Element Method -- 9.1 Finite Element Formulation -- 9.1.1 Weak Formulation -- 9.1.2 Shape Functions -- 9.2 Elasticity -- 9.2.1 Plane Stress and Plane Strain -- 9.2.2 Plane Stress and Plane Strain -- 9.2.3 Implementation -- 10. Heat Conduction -- 10.1 Basic Formulation -- 10.2 Element-by-Element Assembly -- 10.3 Application of Boundary Conditions