Numerical Approximation Methods

Modern fluid dynamics is a combination of traditional methods of theory and analysis and newer methods of computation and numerical simulation. Fluid Dynamics with a Computational Perspective synthesizes traditional theory and modern computation. It is neither a book on methods of computation, nor a book on analysis; it is about fluid dynamics. The book is ideal for a course on fluid dynamics. Early chapters review the laws of fluid mechanics and survey computational methodology, following chapters study flows in which the Reynolds number increases from creeping flow to turbulence, followed by a thorough discussion of compressible flow and interfaces. Whereas all significant equations and their solutions are presented, their derivations are informal. References for detailed derivations are provided. A chapter on intermediate Reynolds number flows provides illustrative case studies by pure computation. Elsewhere, computations and theory are interwoven.

This book presents both deterministic methods and stochastic methods with numerous applications from physics. Coverage includes numerical differentiation and integration, monte-carlo (MC) methods, dat

Complexity science is the study of systems with many interdependent components. Such systems - and the self-organization and emergent phenomena they manifest - lie at the heart of many challenges of global importance. This book is a coherent introduction to the mathematical methods used to understand complexity, with plenty of examples and real-world applications. It starts with the crucial concepts of self-organization and emergence, then tackles complexity in dynamical systems using differential equations and chaos theory. Several classes of models of interacting particle systems are studied with techniques from stochastic analysis, followed by a treatment of the statistical mechanics of complex systems. Further topics include numerical analysis of PDEs, and applications of stochastic methods in economics and finance. The book concludes with introductions to space-time phases and selfish routing. The exposition is suitable for researchers, practitioners and students in complexity sci

This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers

First published in 2007, this second edition describes the computational methods used in theoretical physics. New sections were added to cover finite element methods and lattice Boltzmann simulation, density functional theory, quantum molecular dynamics, Monte Carlo simulation, and diagonalisation of one-dimensional quantum systems. It covers many different areas of physics research and different computational methodologies, including computational methods such as Monte Carlo and molecular dynamics, various electronic structure methodologies, methods for solving partial differential equations, and lattice gauge theory. Throughout the book the relations between the methods used in different fields of physics are emphasised. Several new programs are described and can be downloaded from www.cambridge.org/9781107677135. The book requires a background in elementary programming, numerical analysis, and field theory, as well as undergraduate knowledge of condensed matter theory and statistica

This monograph addresses fundamental aspects of mathematical modeling and numerical solution methods of electromagnetic problems involving low frequencies. It includes a large list of industrial appli

With strong numerical and computational focus, this book serves as an essential resource on the methods for functional neuroimaging analysis, diffusion weighted image analysis, and longitudinal VBM an

Mechanics of Materials uniformly incorporates the fundamentals into analytical methods, modeling approaches, numerical methods, experimental procedures, and design techniques in a systematic manner th

This book offers comprehensive treatment of both the mathematical framework and the numerical methods for flexible multibody dynamics, from a theoretical as well as practical point-of-view.

A comprehensive introduction to various numerical methods used in computational finance todayQuantitative skills are a prerequisite for anyone working in finance or beginning a career in the field, as

Iterative algorithms often rely on approximate evaluation techniques, which may include statistical estimation, computer simulation or functional approximation. This volume presents methods for the st

Updated and revised, this second edition outlines theoretical concepts, simple models and numerical methods for modeling the general circulation of the atmosphere. New topics include the recent progre

This book covers the basics of mechanical vibration and rotordynamics, presenting numerical models and analysis methods, loads, pressure fluctuations, instability of hydraulic machines and a system fo

An in-depth guide to understanding wind effects on cable supported bridges, this book uses analytical, numerical and experimental methods to give readers a practical understanding. It is structured to

A comprehensive manual on the efficient modeling and analysis of photonic devices through building numerical codes, this book provides graduate students and researchers with the theoretical background and MATLAB programs necessary for them to start their own numerical experiments. Beginning by summarizing topics in optics and electromagnetism, the book discusses optical planar waveguides, linear optical fiber, the propagation of linear pulses, laser diodes, optical amplifiers, optical receivers, finite-difference time-domain method, beam propagation method and some wavelength division devices, solitons, solar cells and metamaterials. Assuming only a basic knowledge of physics and numerical methods, the book is ideal for engineers, physicists and practising scientists. It concentrates on the operating principles of optical devices, as well as the models and numerical methods used to describe them.

The masses of neutron stars are limited by an instability to gravitational collapse and an instability driven by gravitational waves limits their spin. Their oscillations are relevant to x-ray observations of accreting binaries and to gravitational wave observations of neutron stars formed during the coalescence of double neutron-star systems. This volume includes more than forty years of research to provide graduate students and researchers in astrophysics, gravitational physics and astronomy with the first self-contained treatment of the structure, stability and oscillations of rotating neutron stars. This monograph treats the equations of stellar equilibrium; key approximations, including slow rotation and perturbations of spherical and rotating stars; stability theory and its applications, from convective stability to the r-mode instability; and numerical methods for computing equilibrium configurations and the nonlinear evolution of their oscillations. The presentation of fundamen

The principles of signal processing are fundamental to the operation of many everyday devices. This book introduces the basic theory of digital signal processing, with emphasis on real-world applications. Sampling, quantization, the Fourier transform, filters, Bayesian methods and numerical considerations are covered, then developed to illustrate how they are used in audio, image, and video processing and compression, and in communications. The book concludes with methods for the efficient implementation of algorithms in hardware and software. Intuitive arguments rather than mathematical ones are used wherever possible, and links between various signal processing techniques are stressed. The advantages and disadvantages of different approaches are presented in the context of real-world examples, enabling the reader to choose the best solution to a given problem. With over 200 illustrations and over 130 exercises (including solutions), this book will appeal to practitioners working in s

Stochastic Dynamics of Marine Structures is a text for students and a reference for professionals on the basic theory and methods used for stochastic modelling and analysis of marine structures subjected to environmental loads. The first part of the book provides a detailed introduction to the basic dynamic analysis of structures, serving as a foundation for later chapters on stochastic response analysis. This includes an extensive chapter on the finite element method. A careful introduction to stochastic modelling is provided, which includes such concepts as stochastic process, variance spectrum, random environmental processes, response spectrum, response statistics and short- and long-term extreme value models. The second part of the book offers detailed discussion of limit state design approaches, fatigue design methods, the equations of motion for dynamic structures and numerical solution techniques. The final chapter highlights methods for prediction of extreme values from measure

This scholarly text provides an introduction to the numerical methods used to model partial differential equations, with focus on atmospheric and oceanic flows. The book covers both the essentials of

This judicious selection of articles combines mathematical and numerical methods to apply parameter estimation and optimum experimental design in a range of contexts. These include fields as diverse a

Aimed at graduates and researchers, and requiring only a basic knowledge of multi-variable calculus, this introduction to computer-based partial differential equation (PDE) modeling provides readers with the practical methods necessary to develop and use PDE mathematical models in biomedical engineering. Taking an applied approach, rather than using abstract mathematics, the reader is instructed through six biomedical example applications, each example characterized by step-by-step discussions of established numerical methods and implemented in reliable computer routines. Adopting this technique, the reader will understand how PDE models are formulated, implemented and tested. Supported by a set of rigorously tested general purpose PDE routines online, and with enhanced understanding through animations, this book will be ideal for anyone faced with interpreting large experimental data sets that need to be analyzed with PDE models in biomedical engineering.

There is a certain body of knowledge and methods that finds application in most branches of fluid mechanics. This book aims to supply a proper theoretical understanding that will permit sensible simplifications to be made in the formulation of problems, and enable the reader to develop analytical models of practical significance. Such analyses can be used to guide more detailed experimental and numerical investigations. As in most technical subjects, such understanding is acquired by detailed study of highly simplified 'model problems'. The first part (Chapters 1-4) is concerned entirely with the incompressible flow of a homogeneous fluid. It was written for the Boston University introductory graduate level course 'Advanced Fluid Mechanics'. The remaining Chapters 5 and 6 deal with dispersive waves and acoustics, and are unashamedly inspired by James Lighthill's masterpiece, Waves in Fluids.

Computational aeroacoustics (CAA) is a relatively new research area. CAA algorithms have developed rapidly and the methods have been applied in many areas of aeroacoustics. The objective of CAA is not simply to develop computational methods but also to use these methods to solve practical aeroacoustics problems and to perform numerical simulation of aeroacoustic phenomena. By analysing the simulation data, an investigator can determine noise generation mechanisms and sound propagation processes. This is both a textbook for graduate students and a reference for researchers in CAA and as such is self-contained. No prior knowledge of numerical methods for solving partial differential equations (PDEs) is needed, however, a general understanding of partial differential equations and basic numerical analysis is assumed. Exercises are included and are designed to be an integral part of the chapter content. In addition, sample computer programs are included to illustrate the implementation of

This book treats the classical problem of gravitational physics within Einstein's theory of general relativity. It presents basic principles and equations needed to describe rotating fluid bodies, as well as black holes in equilibrium. It then goes on to deal with a number of analytically tractable limiting cases, placing particular emphasis on the rigidly rotating disc of dust. The book concludes by considering the general case using powerful numerical methods that are applied to various models, including the classical example of equilibrium figures of constant density. Researchers in general relativity, mathematical physics, and astrophysics will find this a valuable reference book on the topic. A related website containing codes for calculating various figures of equilibrium is available at www.cambridge.org/9781107407350.

Bennett's Transport by Advection and Diffusion provides analytical and numerical tools to aid problem solving in every topic area of the text. These tools foster use of generalized methods in the exer

This book presents a broad exposition of analytical and numerical methods for modeling composite materials, laminates, polycrystals and other heterogeneous solids, with emphasis on connections between

This textbook provides engineers with the capability, tools and confidence to solve real-world heat transfer problems. It includes many advanced topics, such as Bessel functions, Laplace transforms, separation of variables, Duhamel's theorem and complex combination, as well as high order explicit and implicit numerical integration algorithms. These analytical and numerical solution methods are applied to topics not considered in most textbooks. Examples include heat exchangers involving fluids with varying specific heats or phase changes; heat exchangers in which axial conduction is a concern; and regenerators. Derivations of important results are presented completely, without skipping steps, which reduces student frustration and improves readability and retention. The examples are not trivial 'textbook' exercises; they are rather complex and timely real-world problems that are inherently interesting. This book integrates the computational software packages Maple, MATLAB®, FEHT and Eng

This text provides a comprehensive and self-contained guide for the numerical solution of PDEs using C++ for students, engineers and researchers who want to use advanced programming tools to solve pro

Discrete Element Methods (DEM) is a numerical technique for analysing the mechanics and physics of particulate systems. Originated in the late seventies for analysing geotechnical problems, it has se

The long-awaited revision of the bestseller on heat conductionHeat Conduction, Third Edition is an update of the classic text on heat conduction, replacing some of the coverage of numerical methods wi

??????Stationarity and Convergence in Reduce-or-Retreat Minimization presents and analyzes a unifying framework for a wide variety of numerical methods in optimization. The author’s “reduce-or-retreat

This book was first published in 2005. When an oceanic tidal wave that is primarily active on the water surface passes an ocean shelf or a region with a seamount, it is split into a less energetic surface wave and other internal modes with different wavelengths and propagation speeds. This cascading process, from the barotropic tides to the baroclinic components, leads to the transformation of tidal energy into turbulence and heat, an important process for the dynamics of the lower ocean. Baroclinic Tides demonstrates the analytical and numerical methods used to study the generation and evolution of baroclinic tides and, by comparison with experiments and observational data, shows how to distinguish and interpret internal waves. Strongly non-linear solitary internal waves, which are generated by internal tidal waves at the final stage of their evolution, are investigated in detail. This book is intended for researchers and graduate students of physical oceanography, geophysical fluid d

Noise pollution around airports, trains, and industries increasingly attracts environmental concern and regulation. Designers and researchers have intensified the use of large-eddy simulation (LES) for noise reduced industrial design and acoustical research. This 2007 book, written by 30 experts, presents the theoretical background of acoustics and of LES, followed by details about numerical methods, e.g. discretization schemes, boundary conditions, coupling aspects. Industrially relevant, hybrid RANS/LES techniques for acoustic source predictions are presented in detail. Many applications are featured ranging from simple geometries for mixing layers and jet flows to complex wing and car geometries. Selected applications include scientific investigations at industrial and university research institutions.

Control and automation of water systems in one of the branches of fluid mechanics and hydraulics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Comp

Filtering and system identification are powerful techniques for building models of complex systems. This 2007 book discusses the design of reliable numerical methods to retrieve missing information in models derived using these techniques. Emphasis is on the least squares approach as applied to the linear state-space model, and problems of increasing complexity are analyzed and solved within this framework, starting with the Kalman filter and concluding with the estimation of a full model, noise statistics and state estimator directly from the data. Key background topics, including linear matrix algebra and linear system theory, are covered, followed by different estimation and identification methods in the state-space model. With end-of-chapter exercises, MATLAB simulations and numerous illustrations, this book will appeal to graduate students and researchers in electrical, mechanical and aerospace engineering. It is also useful for practitioners. Additional resources for this title,

Computational Modeling of Multiphase Geomaterials discusses how numerical methods play a very important role in geotechnical engineering and in the related activity of computational geotechnics. It sh

This is a modern textbook for courses in continuum mechanics. It provides both the theoretical framework and the numerical methods required to model the behaviour of continuous materials. This self-contained textbook is tailored for advanced undergraduate or first-year graduate students with numerous step-by-step derivations and worked-out examples. The author presents both the general continuum theory and the mathematics needed to apply it in practice. The derivation of constitutive models for ideal gases, fluids, solids and biological materials, and the numerical methods required to solve the resulting differential equations, are also detailed. Specifically, the text presents the theory and numerical implementation for the finite difference and the finite element methods in the Matlab® programming language. It includes thirteen detailed Matlab® programs illustrating how constitutive models are used in practice.

Giving a detailed overview of the subject, this book takes in the results and methods that have arisen since the term 'self-organised criticality' was coined twenty years ago. Providing an overview of numerical and analytical methods, from their theoretical foundation to the actual application and implementation, the book is an easy access point to important results and sophisticated methods. Starting with the famous Bak-Tang-Wiesenfeld sandpile, ten key models are carefully defined, together with their results and applications. Comprehensive tables of numerical results are collected in one volume for the first time, making the information readily accessible to readers. Written for graduate students and practising researchers in a range of disciplines, from physics and mathematics to biology, sociology, finance, medicine and engineering, the book gives a practical, hands-on approach throughout. Methods and results are applied in ways that will relate to the reader's own research.

Michael A. Matt constructs two trivariate local Lagrange interpolation methods which yield optimal approximation order and Cr macro-elements based on the Alfeld and the Worsey-Farin split of a tetrahe

Essentials of Electromagnetics for Engineering, first published in 2000, provides a clearly written introduction to the key physical and engineering principles of electromagnetics. Throughout the book, the author describes the intermediate steps in mathematical derivations that many other textbooks leave out. The author begins by examining Coulomb's law and simple electrostatics, covering in depth the concepts of fields and potentials. He then progresses to magnetostatics and Maxwell's equations. This approach leads naturally to a discussion of electrodynamics and the treatment of wave propagation, waveguides, transmission lines, and antennas. At each stage, the author stresses the physical principles underlying the mathematical results. Many homework exercises are provided, including several in Matlab and Mathematica formats. The book contains a separate chapter on numerical methods in electromagnetics, and a broad range of worked examples to illustrate important concepts. It is suita