Cambridge International Science Publishing

AN INTRODUCTION INTO COMPUTATIONAL ENGINEERING WITH MATLAB

Xin-She Yang
Department of Engineering
University of Cambridge, United Kingdom


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270 pages

June 2006

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 Modern engineering design and modelling involve substantial amount of computer simulations using efficient numerical methods and visualization tools. The performance and feasibility of the designed products are simulated using sophisticated scientific tools such as finite element analysis and computational fluid dynamics. This emerging interdisciplinary technology for the modelling and design in engineering and science is essentially forming what is now called computational engineering. It is becoming the third component, complementing the traditional theoretical and experimental approaches to problem-solving. Many companies use it to design new products and to find solutions to challenging problems so as to increase their competitiveness in international markets. 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, virtual bee algorithms, and cellular automata. It also covers a wide spectrum of advanced topics in engineering applications, and these advanced topics include elasticity, heat conduction, reaction-diffusion system, optimisation, stochastic cellular automata, combustion, consolidation, heat transfer of carbon nanotubes, and pattern formation. The accompanied concise Matlab programs, no more than 100 lines each, demonstrate how each numerical method works. The animation and visualization of the results provide a first hand experience to the readers, especially for undergraduates and graduates, to master the fundamentals of the numerical methods. These Matlab programs can also be modified by the readers to carry out their own modelling and simulations. This book can serve as an introductory textbook and prepare the readers to learn more advanced topics in scientific computing.

About the Author
Xin-She Yang received his D.Phil in applied mathematics from the University of Oxford. He is currently a research fellow at the University of Cambridge. Dr Yang has published extensively in various international journals, book chapters, and conference proceedings. His research interests include asymptotic analysis, bioinspired algorithms, combustion, computational engineering, mathematical modelling, optimisation, gravity, solar eclipse, scientific programming and pattern formation.
Contents
This book is organised into three parts. Part I is a brief introduction to the fundamentals of mathematics that will be used in the book. Part II concerns the major conventional numerical methods, and Part III covers the advanced topics in engineering applications.
Part I:
Chapters 1 to 3
Chapter 1 is the introduction to the general areas of computational engineering and how to use programs in the book.
Chapter 2 concerns briefly vector and matrix analysis, such as the dot product and cross products of vectors and basic matrix algebra.
Chapter 3 reviews the ordinary differential equations and partial differential equations. It also introduces some of important PDEs used in the book.

Part II: Chapters 4 to 11
Chapter 4 introduces the numerical integration of ordinary differential equations, and it includes the Euler scheme, Runge-Kutta methd. The Belousov-Zhanbotinsky oscillation is used as an example for Matlab implementation.
Chapter 5 introduces the finite difference methods for the hyperbolic equations, and these include the wave equation and Sine-Gordon equation as examples.
Chapter 6 discusses the finite difference methods for the parabolic and elliptical equations. The elliptical equations are considered as the special case of parabolic equations as steady states.
Chapter 7 uses the finite difference methods discussed so far to solve non-linear reaction-diffusion systems and to simulate pattern formation.
Chapter 8 formulates briefly the finite volume methods for three types of classical equations and applies it to study heat transfer problems.
Chapter 9 discusses the popular finite element methods using weak formulation and shape functions. The elasticity problem is used as an example for Matlab implementation.
Chapter 10 concerns steady-state heat transfer problems. It discusses the finite element procedure in detail such as the assembly of the stiffness matrix, the application of boundary conditions, and the solution procedure.
Chapter 11 introduces the time-dependent problems such as transient heat transfer. It covers the time-stepping schemes and uses the wave equation as the example for discussion. Part III:
Chapters 12 to 15 Chapter 12 introduces the advanced topics of optimisation in engineering. It briefly introduces several popular bioinspired algorithms such as genetic algorithms, and virtual bee algorithms. The virtual bees algorithms are then used for Matlab implementation.
Chapter 13 provides the alternative methods for computer simulations, and the cellular automaton method is discussed in detail. The reaction-diffusion equations are used for implementation.
Chapter 14 covers several advanced topics in engineering applications, and these topics include combustion, consolidation, heat transfer of carbon nanotubes, biological calcium waves, and fracture and crack propagation in structures.
Chapter 15 broadens the view of computer modelling to cover the general features of scientific packages either commercial or free software packages.