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2584 results in Computational Science

Page 94 of 130

  • Non-variational computation of the eigenstates of Dirac operators with radially symmetric potentials

  • Part of
  • Lyonell Boulton, Nabile Boussaid
  • Journal:
    LMS Journal of Computation and Mathematics / Volume 13 / January 2010
    Published online by Cambridge University Press:
    01 January 2010, pp. 10-32
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  • We discuss a novel strategy for computing the eigenvalues and eigenfunctions of the relativistic Dirac operator with a radially symmetric potential. The virtues of this strategy lie in the fact that it avoids completely the phenomenon of spectral pollution and it always provides two-sided estimates for the eigenvalues with explicit error bounds on both eigenvalues and eigenfunctions. We also discuss convergence rates of the method and illustrate our results with various numerical experiments.

  • On the combinatorial classification of toric log del Pezzo surfaces

  • Part of
  • Alexander M. Kasprzyk, Maximilian Kreuzer, Benjamin Nill
  • Journal:
    LMS Journal of Computation and Mathematics / Volume 13 / January 2010
    Published online by Cambridge University Press:
    01 January 2010, pp. 33-46
    • Article
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  • Toric log del Pezzo surfaces correspond to convex lattice polygons containing the origin in their interior and having only primitive vertices. Upper bounds on the volume and on the number of boundary lattice points of these polygons are derived in terms of the index ℓ. Techniques for classifying these polygons are also described: a direct classification for index two is given, and a classification for all ℓ≤16 is obtained.

  • On complete interpolating sequences and sampling expansions

  • Part of
  • Kevin Smith
  • Journal:
    LMS Journal of Computation and Mathematics / Volume 13 / January 2010
    Published online by Cambridge University Press:
    01 January 2010, pp. 1-9
    • Article
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  • Complete interpolating sequences for L2(−π,π) are considered under the condition that the real parts of the sequence are a subsequence of the scaled integers xℤ, x>0. It is found that this condition leads to very specific and restrictive conditions on the existence and structure of complete interpolating sequences for L2(−π,π). Further general results in the case of bunched sampling of Bernstein functions are also given.

The Theory of Composites
  • Graeme W. Milton
  • Published online:
    07 December 2009
    Print publication:
    06 May 2002
  • Some of the greatest scientists including Poisson, Faraday, Maxwell, Rayleigh, and Einstein have contributed to the theory of composite materials. Mathematically, it is the study of partial differential equations with rapid oscillations in their coefficients. Although extensively studied for more than a hundred years, an explosion of ideas in the last five decades (and particularly in the last three decades) has dramatically increased our understanding of the relationship between the properties of the constituent materials, the underlying microstructure of a composite, and the overall effective (electrical, thermal, elastic) moduli which govern the macroscopic behavior. This renaissance has been fueled by the technological need for improving our knowledge base of composites, by the advance of the underlying mathematical theory of homogenization, by the discovery of new variational principles, by the recognition of how important the subject is to solving structural optimization problems, and by the realization of the connection with the mathematical problem of quasiconvexification. This 2002 book surveys these exciting developments at the frontier of mathematics.

Computational Methods for Multiphase Flow
  • Edited by Andrea Prosperetti, Grétar Tryggvason
  • Published online:
    07 December 2009
    Print publication:
    29 March 2007
  • Thanks to high-speed computers and advanced algorithms, the important field of modelling multiphase flows is an area of rapid growth. This one-stop account – now in paperback, with corrections from the first printing – is the ideal way to get to grips with this topic, which has significant applications in industry and nature. Each chapter is written by an acknowledged expert and includes extensive references to current research. All of the chapters are essentially independent and so the book can be used for a range of advanced courses and the self-study of specific topics. No other book covers so many topics related to multiphase flow, and it will therefore be warmly welcomed by researchers and graduate students of the subject across engineering, physics, and applied mathematics.

Spectral Methods for Time-Dependent Problems
  • Jan S. Hesthaven, Sigal Gottlieb, David Gottlieb
  • Published online:
    04 December 2009
    Print publication:
    11 January 2007
  • Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested 2007 introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of spectral methods, allowing the reader to understand the techniques through numerous examples as well as more rigorous developments. They provide a detailed treatment of methods based on Fourier expansions and orthogonal polynomials (including discussions of stability, boundary conditions, filtering, and the extension from the linear to the nonlinear situation). Computational solution techniques for integration in time are dealt with by Runge-Kutta type methods. Several chapters are devoted to material not previously covered in book form, including stability theory for polynomial methods, techniques for problems with discontinuous solutions, round-off errors and the formulation of spectral methods on general grids. These will be especially helpful for practitioners.

Simulating Hamiltonian Dynamics
  • Benedict Leimkuhler, Sebastian Reich
  • Published online:
    04 December 2009
    Print publication:
    14 February 2005
  • Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of the book for self-instruction or as a text for a graduate course on the subject.

A Practical Guide to Pseudospectral Methods
  • Bengt Fornberg
  • Published online:
    03 December 2009
    Print publication:
    26 January 1996
  • Partial differential equations arise in almost all areas of science, engineering, modeling, and forecasting. During the last two decades pseudospectral methods have emerged as successful alternatives to better known computational procedures, (e.g. finite difference and finite element methods of numerical solution), in several key application areas. These areas include computational fluid dynamics, wave motion, and weather forecasting. This book explains how, when and why this pseudospectral approach works. In order to make the subject accessible to students as well as researchers and engineers, the subject is presented using illustrations, examples, heuristic explanations, and algorithms rather than rigorous theoretical arguments. This book will be of interest to graduate students, scientists and engineers interested in applying pseudospectral methods to real problems.

Automata Theory with Modern Applications
  • James A. Anderson
  • Published online:
    02 December 2009
    Print publication:
    22 June 2006
  • Recent applications to biomolecular science and DNA computing have created a new audience for automata theory and formal languages. This is the only introductory book to cover such applications. It begins with a clear and readily understood exposition of the fundamentals that assumes only a background in discrete mathematics. The first five chapters give a gentle but rigorous coverage of basic ideas as well as topics not found in other texts at this level, including codes, retracts and semiretracts. Chapter 6 introduces combinatorics on words and uses it to describe a visually inspired approach to languages. The final chapter explains recently-developed language theory coming from developments in bioscience and DNA computing. With over 350 exercises (for which solutions are available), many examples and illustrations, this text will make an ideal contemporary introduction for students; others, new to the field, will welcome it for self-learning.

Iterative Krylov Methods for Large Linear Systems
  • Henk A. van der Vorst
  • Published online:
    24 November 2009
    Print publication:
    17 April 2003
  • Computational simulation of scientific phenomena and engineering problems often depends on solving linear systems with a large number of unknowns. This book gives insight into the construction of iterative methods for the solution of such systems and helps the reader to select the best solver for a given class of problems. The emphasis is on the main ideas and how they have led to efficient solvers such as CG, GMRES, and BI-CGSTAB. The author also explains the main concepts behind the construction of preconditioners. The reader is encouraged to gain experience by analysing numerous examples that illustrate how best to exploit the methods. The book also hints at many open problems and as such it will appeal to established researchers. There are many exercises that motivate the material and help students to understand the essential steps in the analysis and construction of algorithms.

Orthogonal Rational Functions
  • Adhemar Bultheel, Pablo Gonzalez-Vera, Erik Hendriksen, Olav Njastad
  • Published online:
    22 October 2009
    Print publication:
    13 February 1999
  • This book generalises the classical theory of orthogonal polynomials on the complex unit circle, or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. The first part treats the case where these poles are all outside the unit disk or in the lower half plane. Classical topics such as recurrence relations, numerical quadrature, interpolation properties, Favard theorems, convergence, asymptotics, and moment problems are generalised and treated in detail. The same topics are discussed for the different situation where the poles are located on the unit circle or on the extended real line. In the last chapter, several applications are mentioned including linear prediction, Pisarenko modelling, lossless inverse scattering, and network synthesis. This theory has many applications in theoretical real and complex analysis, approximation theory, numerical analysis, system theory, and in electrical engineering.

Object-Oriented Programming via Fortran 90/95
  • Ed Akin
  • Published online:
    15 October 2009
    Print publication:
    13 January 2003
  • Learn how to write technical applications in a modern object-oriented approach, using Fortran 90 or 95. This book will teach you how to stop focusing on the traditional procedural abilities of Fortran and to employ the principles of object-oriented programming to produce clear, highly efficient executable codes. Get ready now to take advantage of all the features of the finalized, fully object-oriented Fortran 200X! In addition to covering the OOP methodologies the book also covers the basic foundation of the language and good programming skills, making the book valuable also as a good migration tool for experienced Fortran programmers who want to smoothly pick up the OOP paradigm. The author highlights common themes by using comparisons with Matlab and C++ and uses numerous cross-referenced examples to convey all concepts quickly and clearly. Complete code for the examples is included on the book's web page.

Numerical Simulation of Reactive Flow
  • 2nd edition
  • Elaine S. Oran, Jay P. Boris
  • Published online:
    09 October 2009
    Print publication:
    06 November 2000
  • Reactive flows encompass a broad range of physical phenomena, interacting over many different time and space scales. Such flows occur in combustion, chemical lasers, the earth's oceans and atmosphere, and stars and interstellar space. Despite the obvious physical differences in these flows, there is a striking similarity in the forms of their descriptive equations. Thus, the considerations and procedures for constructing numerical models of these systems are also similar, and these similarities can be exploited. Moreover, using the latest technology, what were once difficult and expensive computations can now be done on desktop computers. This book takes account of the explosive growth in computer technology and the greatly increased capacity for solving complex reactive flow problems that have occurred since the first edition of Numerical Simulation of Reactive Flow was published in 1987. It presents algorithms useful for reactive flow simulations, describes trade-offs involved in their use, and gives guidance for building and using models of complex reactive flows.

Geometry and Topology for Mesh Generation
  • Herbert Edelsbrunner
  • Published online:
    03 October 2009
    Print publication:
    28 May 2001
  • The book combines topics in mathematics (geometry and topology), computer science (algorithms), and engineering (mesh generation). The motivation for these topics is the difficulty, both conceptually and in the technical execution, of combining elements of combinatorial and of numerical algorithms. Mesh generation is a topic where a meaningful combination of these different approaches to problem solving is inevitable. The book develops methods from both areas that are amenable to combination, and explains breakthrough solutions to meshing that fit into this category. This book emphasizes topics that are elementary, attractive, useful, interesting, and lend themselves to teaching, making it an ideal graduate text for courses on mesh generation.

Identification and Control of Mechanical Systems
  • Jer-Nan Juang, Minh Q. Phan
  • Published online:
    02 September 2009
    Print publication:
    06 August 2001
  • The control of vibrating systems is a significant issue in the design of aircraft, spacecraft, bridges and high-rise buildings. This 2001 book discusses the control of vibrating systems, integrating structural dynamics, vibration analysis, modern control and system identification. Integrating these subjects is an important feature in that engineers will need only one book, rather than several texts or courses, to solve vibration control problems. The book begins with a review of basic mathematics needed to understand subsequent material. Chapters then cover more recent and valuable developments in aerospace control and identification theory, including virtual passive control, observer and state-space identification, and data-based controller synthesis. Many practical issues and applications are addressed, with examples showing how various methods are applied to real systems. Some methods show the close integration of system identification and control theory from the state-space perspective, rather than from the traditional input-output model perspective of adaptive control. This text will be useful for advanced undergraduate and beginning graduate students in aerospace, mechanical and civil engineering, as well as for practising engineers.

High-Order Methods for Incompressible Fluid Flow
  • M. O. Deville, P. F. Fischer, E. H. Mund
  • Published online:
    24 August 2009
    Print publication:
    15 August 2002
  • High-order numerical methods provide an efficient approach to simulating many physical problems. This book considers the range of mathematical, engineering, and computer science topics that form the foundation of high-order numerical methods for the simulation of incompressible fluid flows in complex domains. Introductory chapters present high-order spatial and temporal discretizations for one-dimensional problems. These are extended to multiple space dimensions with a detailed discussion of tensor-product forms, multi-domain methods, and preconditioners for iterative solution techniques. Numerous discretizations of the steady and unsteady Stokes and Navier-Stokes equations are presented, with particular attention given to enforcement of incompressibility. Advanced discretizations, implementation issues, and parallel and vector performance are considered in the closing sections. Numerous examples are provided throughout to illustrate the capabilities of high-order methods in actual applications. Computer scientists, engineers and applied mathematicians interested in developing software for solving flow problems will find this book a valuable reference.

Schwarz-Christoffel Mapping
  • Tobin A. Driscoll, Lloyd N. Trefethen
  • Published online:
    20 August 2009
    Print publication:
    20 June 2002
  • This book provides a comprehensive look at the Schwarz-Christoffel transformation, including its history and foundations, practical computation, common and less common variations, and many applications in fields such as electromagnetism, fluid flow, design and inverse problems, and the solution of linear systems of equations. It is an accessible resource for engineers, scientists, and applied mathematicians who seek more experience with theoretical or computational conformal mapping techniques. The most important theoretical results are stated and proved, but the emphasis throughout remains on concrete understanding and implementation, as evidenced by the 76 figures based on quantitatively correct illustrative examples. There are over 150 classical and modern reference works cited for readers needing more details. There is also a brief appendix illustrating the use of the Schwarz-Christoffel Toolbox for MATLAB, a package for computation of these maps.

Generalized Riemann Problems in Computational Fluid Dynamics
  • Matania Ben-Artzi, Joseph Falcovitz
  • Published online:
    20 August 2009
    Print publication:
    10 April 2003
  • Numerical simulation of compressible, inviscid time-dependent flow is a major branch of computational fluid dynamics. Its primary goal is to obtain accurate representation of the time evolution of complex flow patterns, involving interactions of shocks, interfaces, and rarefaction waves. The Generalized Riemann Problem (GRP) algorithm, developed by the authors for this purpose, provides a unifying 'shell' which comprises some of the most commonly used numerical schemes of this process. This monograph gives a systematic presentation of the GRP methodology, starting from the underlying mathematical principles, through basic scheme analysis and scheme extensions (such as reacting flow or two-dimensional flows involving moving or stationary boundaries). An array of instructive examples illustrates the range of applications, extending from (simple) scalar equations to computational fluid dynamics. Background material from mathematical analysis and fluid dynamics is provided, making the book accessible to both researchers and graduate students of applied mathematics, science and engineering.

Curve and Surface Reconstruction
  • Algorithms with Mathematical Analysis
  • Tamal K. Dey
  • Published online:
    20 August 2009
    Print publication:
    16 October 2006
  • Many applications in science and engineering require a digital model of a real physical object. Advanced scanning technology has made it possible to scan such objects and generate point samples on their boundaries. This book, first published in 2007, shows how to compute a digital model from this point sample. After developing the basics of sampling theory and its connections to various geometric and topological properties, the author describes a suite of algorithms that have been designed for the reconstruction problem, including algorithms for surface reconstruction from dense samples, from samples that are not adequately dense and from noisy samples. Voronoi- and Delaunay-based techniques, implicit surface-based methods and Morse theory-based methods are covered. Scientists and engineers working in drug design, medical imaging, CAD, GIS, and many other areas will benefit from this first book on the subject.

Page 94 of 130