This book is a description of why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described. The focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, Convection-Diffusion problem, Stokes problem and Navier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite and nonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughout the book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory " provided by the software. Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduate level.
The authors' intended audience is at the level of graduate students and researchers, and we believe that the text offers a valuable contribution to all finite element researchers who would like to broadened both their fundamental and applied knowledge of the field. - Spencer J. Sherwin and Robert M. Kirby, Fluid Mechanics, Vol 557, 2006.
This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods. Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems. The underlying theory is illustrated by numerous examples and there are around 300 exercises, designed to promote and test understanding. They are starred according to level of difficulty. Solutions to odd-numbered exercises are available to all readers while even-numbered solutions are available to authorised instructors. Written in an informal yet rigorous style, Essential Partial Differential Equations is designed for mathematics undergraduates in their final or penultimate year of university study, but will be equally useful for students following other scientific and engineering disciplines in which PDEs are of practical importance. The only prerequisite is a familiarity with the basic concepts of calculus and linear algebra.
The subject of this book is the efficient solution of partial differential equations (PDEs) that arise when modelling incompressible fluid flow. The first part covers the Poisson and the Stokes equations. For each PDE, there is a chapter concerned with finite element discretization and a companion chapter concerned with efficient iterative solution of the algebraic equations obtained from discretization. Chapter 5 describes the basics of PDE-constrained optimization. The second part of the book is a more advanced introduction to the numerical analysis of incompressible flows.
The time is Earth Year 2333 AD--a year at the beginning of a horrible new reality for civilization. The location is the city of Chicago, one of the last cities in the United States that remains. But it, too, has suffered great devastation. Death and destruction have been directed on it by the other cities that were caught up in what turned out to be a self-destructive competition to gain preeminence. Most of the people are gone, and the believers that remain in Chicago are thrust into survival mode. Marduk, a vicious leader of the forces loyal to the Leader, sees the remnant as a threat and makes his personal goal to wipe them out. Victor Steinhouse and his friends are all that stand in his way. But who will win this contest of wills? And what will it cost? And will the believers glorify God as they deal with such opposition? Yet the bigger question remains: Is faith all you really need when faith is all you have?
Writing in the tradition of Pinocchio, Hans Christian Anderson Award winner David Almond brings his ineffable touch to a warm and wistful story that shows anything is possible with imagination and trust. “You’re a mystery, aren’t you, Puppet? But isn’t everything a mystery? Not just you, but every single thing that exists.” What should a puppet master do when he’s old and alone and all his puppets are gone? Silvester decides to make one last puppet. But this one is different. When the old man speaks to him, Puppet speaks back. And then he starts to walk . . . While Silvester shows Puppet the town, the playground, and other wonders the world holds, Puppet in turn helps Silvester to make a new friend and share his puppet-making skills with the next generation. With themes of compassion and creativity, threaded with David Almond’s inimitable humor, this wonder-filled story of creation and the circle of life, illustrated with wordless black-and-white spreads by award-winning artist Lizzy Stewart, is destined to become a modern-day classic.
Much has been written about the 302 British and Commonwealth soldiers who were executed for military offences during the First World War, but there is usually only a passing reference to those who took part – the members of the firing squad, the officer in charge, the medical officer and the padre. What are their stories? Through extensive research, David Johnson explores the controversial story of the men forced to shoot their fellow Tommies, examining how they were selected, how they were treated before, during and after the executions and why there were so many procedural variations in the way that the executions were conducted.
A long overdue update, this edition of Introduction to Magnetism and Magnetic Materials is a complete revision of its predecessor. While it provides relatively minor updates to the first two sections, the third section contains vast updates to reflect the enormous progress made in applications in the past 15 years, particularly in magnetic recordin
Many historians of insurance have commented on the disconnect between the rise of English life insurance companies in the early eighteenth century and the mathematics behind the sound pricing of life insurance products that was developed at about the same time. Insurance and annuity promoters typically ignored this mathematical work. Bellhouse explores this issue, and shows that the early mathematical work was not motivated by insurance but instead by the fair valuation of life contingent contracts related to property. Even the work of the mathematician James Dodson in the creation of the Equitable Life Assurance Society, offering sound actuarially based premiums, did not change the industry in any significant way. The tipping point was a crisis in 1770 in which the philosopher and mathematician Richard Price, as well as other mathematicians, showed that a dozen or more recently formed annuity societies could not meet their financial obligations and were inviable.
Archaeological surveys of the Fenland of eastern England were initiated in the 1930s after it became clear that centuries of drainage and cultivation had seriously reduced the archaeological deposits. These studies were among the first to take a multi-disciplinary aproach to archaeological work, and continued with new work in the 1980s when intensive surveys were made of the wetlands of Cambridgeshire, Lincolnshire, Norfolk and Suffolk. During the eight years of the Fenland Survey (1981-88), fieldworkers walked 250,000 hectares and initiated palaeoenvironemental investigations allied to a radiocarbon dating programme. At the end of the survey, in 1989-90, the survey results were evaluated and a programme of field investigations undertaken. This volume is a synopsis of that work. It provides an introduction to the traditional Fenland, as perceived by both ancient and modern geographers, explorers, and historians, and a summary of the complex environmental history of the region. It is presented broadly according to the traditional archaeological periods - Mesolithic to medieval - but it also provides an overview of cultural continuity and of the response to changing conditions over 6000 years of history. It concludes with some reflections on the present condition of the Fenland and the response of the archaeological community to the threats posted by recent agricultural and other practices.
2009 Outstanding Academic Title, Choice This acclaimed textbook is the most comprehensive available in the field of forest ecology. Designed for advanced students of forest science, ecology, and environmental studies, it is also an essential reference for forest ecologists, foresters, and land managers. The authors provide an inclusive survey of boreal, temperate, and tropical forests with an emphasis on ecological concepts across scales that range from global to landscape to microscopic. Situating forests in the context of larger landscapes, they reveal the complex patterns and processes observed in tree-dominated habitats. The updated and expanded second edition covers • Conservation • Ecosystem services • Climate change • Vegetation classification • Disturbance • Species interactions • Self-thinning • Genetics • Soil influences • Productivity • Biogeochemical cycling • Mineralization • Effects of herbivory • Ecosystem stability
What happened to the culture of common law and English barristers in the long eighteenth century? In this wide-ranging sequel to Gentlemen and Barristers: The Inns of Court and the English Bar, 1680-1730, David Lemmings not only anatomizes the barristers and their world; he also explores the popular reputation and self-image of the law and lawyers in the context of declining popular participation in litigation, increased parliamentary legislation, and the growth of theimperial state. He shows how the bar survived and prospered in a century of low recruitment and declining work, but failed to fulfil the expectations of an age of Enlightenment and Reform. By contrast with the important role played by the common law, and lawyers, in seventeenth-century England and in colonialAmerica, it appears that the culture and services of the barristers became marginalized as the courts concentrated on elite clients, and parliament became the primary point of contact between government and population. In his conclusion the author suggests that the failure of the bar and the judiciary to follow Blackstones mid-century recommendations for reforming legal culture and delivering the Englishmans birthrights significantly assisted the growth of parliamentary absolutism ingovernment.
Thank you for visiting our website. Would you like to provide feedback on how we could improve your experience?
This site does not use any third party cookies with one exception — it uses cookies from Google to deliver its services and to analyze traffic.Learn More.