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Author: Joel Franklin
Publisher: Cambridge University Press
ISBN: 1107067855
Category : Science
Languages : en
Pages : 419
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Book Description
There is an increasing need for undergraduate students in physics to have a core set of computational tools. Most problems in physics benefit from numerical methods, and many of them resist analytical solution altogether. This textbook presents numerical techniques for solving familiar physical problems where a complete solution is inaccessible using traditional mathematical methods. The numerical techniques for solving the problems are clearly laid out, with a focus on the logic and applicability of the method. The same problems are revisited multiple times using different numerical techniques, so readers can easily compare the methods. The book features over 250 end-of-chapter exercises. A website hosted by the author features a complete set of programs used to generate the examples and figures, which can be used as a starting point for further investigation. A link to this can be found at www.cambridge.org/9781107034303.
Author: Joel Franklin
Publisher: Cambridge University Press
ISBN: 1107067855
Category : Science
Languages : en
Pages : 419
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Book Description
There is an increasing need for undergraduate students in physics to have a core set of computational tools. Most problems in physics benefit from numerical methods, and many of them resist analytical solution altogether. This textbook presents numerical techniques for solving familiar physical problems where a complete solution is inaccessible using traditional mathematical methods. The numerical techniques for solving the problems are clearly laid out, with a focus on the logic and applicability of the method. The same problems are revisited multiple times using different numerical techniques, so readers can easily compare the methods. The book features over 250 end-of-chapter exercises. A website hosted by the author features a complete set of programs used to generate the examples and figures, which can be used as a starting point for further investigation. A link to this can be found at www.cambridge.org/9781107034303.
Author: Philipp Scherer
Publisher: Springer Science & Business Media
ISBN: 3319004018
Category : Science
Languages : en
Pages : 456
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Book Description
This textbook presents basic and advanced computational physics in a very didactic style. It contains very-well-presented and simple mathematical descriptions of many of the most important algorithms used in computational physics. The first part of the book discusses the basic numerical methods. The second part concentrates on simulation of classical and quantum systems. Several classes of integration methods are discussed including not only the standard Euler and Runge Kutta method but also multi-step methods and the class of Verlet methods, which is introduced by studying the motion in Liouville space. A general chapter on the numerical treatment of differential equations provides methods of finite differences, finite volumes, finite elements and boundary elements together with spectral methods and weighted residual based methods. The book gives simple but non trivial examples from a broad range of physical topics trying to give the reader insight into not only the numerical treatment but also simulated problems. Different methods are compared with regard to their stability and efficiency. The exercises in the book are realised as computer experiments.
Author: Paul Harrison
Publisher: John Wiley & Sons
ISBN: 9780471495635
Category : Science
Languages : en
Pages : 230
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Book Description
Eine gut verständliche Einführung in moderne naturwissenschaftliche Rechenmethoden! Nur geringe physikalische Vorkenntnisse voraussetzend, vermittelt der Autor Grundlagen und komplexere Ansätze anhand vieler Beispiele und ausgesprochen praxisnaher Übungsaufgaben. Besprochen werden alle Rechenmethoden, die im Grundstudium erlernt werden sollen, hinsichtlich ihrer Leistungsfähigkeit und ihrer Anwendungsgebiete.
Author: George Rawitscher
Publisher: Springer
ISBN: 3319427032
Category : Science
Languages : en
Pages : 227
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Book Description
This monograph presents fundamental aspects of modern spectral and other computational methods, which are not generally taught in traditional courses. It emphasizes concepts as errors, convergence, stability, order and efficiency applied to the solution of physical problems. The spectral methods consist in expanding the function to be calculated into a set of appropriate basis functions (generally orthogonal polynomials) and the respective expansion coefficients are obtained via collocation equations. The main advantage of these methods is that they simultaneously take into account all available information, rather only the information available at a limited number of mesh points. They require more complicated matrix equations than those obtained in finite difference methods. However, the elegance, speed, and accuracy of the spectral methods more than compensates for any such drawbacks. During the course of the monograph, the authors examine the usually rapid convergence of the spectral expansions and the improved accuracy that results when nonequispaced support points are used, in contrast to the equispaced points used in finite difference methods. In particular, they demonstrate the enhanced accuracy obtained in the solutionof integral equations. The monograph includes an informative introduction to old and new computational methods with numerous practical examples, while at the same time pointing out the errors that each of the available algorithms introduces into the specific solution. It is a valuable resource for undergraduate students as an introduction to the field and for graduate students wishing to compare the available computational methods. In addition, the work develops the criteria required for students to select the most suitable method to solve the particular scientific problem that they are confronting.
Author: Stephen Jardin
Publisher: CRC Press
ISBN: 1439810958
Category : Computers
Languages : en
Pages : 364
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Book Description
Assuming no prior knowledge of plasma physics or numerical methods, Computational Methods in Plasma Physics covers the computational mathematics and techniques needed to simulate magnetically confined plasmas in modern magnetic fusion experiments and future magnetic fusion reactors. Largely self-contained, the text presents the basic concepts neces
Author: Benjamin A. Stickler
Publisher: Springer
ISBN: 3319272659
Category : Science
Languages : en
Pages : 409
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Book Description
This new edition is a concise introduction to the basic methods of computational physics. Readers will discover the benefits of numerical methods for solving complex mathematical problems and for the direct simulation of physical processes. The book is divided into two main parts: Deterministic methods and stochastic methods in computational physics. Based on concrete problems, the first part discusses numerical differentiation and integration, as well as the treatment of ordinary differential equations. This is extended by a brief introduction to the numerics of partial differential equations. The second part deals with the generation of random numbers, summarizes the basics of stochastics, and subsequently introduces Monte-Carlo (MC) methods. Specific emphasis is on MARKOV chain MC algorithms. The final two chapters discuss data analysis and stochastic optimization. All this is again motivated and augmented by applications from physics. In addition, the book offers a number of appendices to provide the reader with information on topics not discussed in the main text. Numerous problems with worked-out solutions, chapter introductions and summaries, together with a clear and application-oriented style support the reader. Ready to use C++ codes are provided online.
Author: Timothy J. Barth
Publisher: Springer Science & Business Media
ISBN: 366203882X
Category : Mathematics
Languages : en
Pages : 594
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Book Description
The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining chal lenges facing the field of computational fluid dynamics. In structural me chanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the com putation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order ac curacy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence sug gests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Cen ter. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18,1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25,1998 at the NASA Ames Research Center in the United States.
Author: Maria Fyta
Publisher: Morgan & Claypool Publishers
ISBN: 168174418X
Category : Computers
Languages : en
Pages : 166
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Book Description
Computational Approaches in Physics reviews computational schemes which are used in the simulations of physical systems. These range from very accurate ab initio techniques up to coarse-grained and mesoscopic schemes. The choice of the method is based on the desired accuracy and computational efficiency. A bottom-up approach is used to present the various simulation methods used in Physics, starting from the lower level and the most accurate methods, up to particle-based ones. The book outlines the basic theory underlying each technique and its complexity, addresses the computational implications and issues in the implementation, as well as present representative examples. A link to the most common computational codes, commercial or open source is listed in each chapter. The strengths and deficiencies of the variety of techniques discussed in this book are presented in detail and visualization tools commonly used to make the simulation data more comprehensive are also discussed. In the end, specific techniques are used as bridges across different disciplines. To this end, examples of different systems tackled with the same methods are presented. The appendices include elements of physical theory which are prerequisites in understanding the simulation methods.
Author: Julius Chang
Publisher: Elsevier
ISBN: 0323154824
Category : Science
Languages : en
Pages : 348
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Book Description
Methods in Computational Physics, Volume 17: General Circulation Models of the Atmosphere is a five-chapter text that covers the fundamentals and application of general circulation models to solving practical problems related to the atmosphere. The first chapter describes the various options in modeling physical processes and computational procedures. The next two chapters illustrate the influence of practical considerations to the compromise between a detailed physical description and reasonable computing time. Other chapters outline the computational details of two different numerical schemes for general circulation models. These chapters particularly provide an in-depth analysis of finite difference methods by proceeding from general considerations of homogeneous incompressible flow to the fine details of the particular numerical scheme. The final chapter discusses the fundamentals of the alternative spectral method for a multilevel spectral model that illustrates the capability of that approach. This book is of value to geoscientists, mathematicians, and physicists.
Author: Gideon Gilat
Publisher: Elsevier
ISBN: 032315008X
Category : Science
Languages : en
Pages : 445
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Book Description
Methods in Computational Physics, Volume 15: Vibrational Properties of Solids explores the application of computational methods to delineate microscopic vibrational behavior. This book is composed of nine chapters that further illustrate the utility of these methods to ordered lattices, quantum solids, impurity modes, surface modes, and amorphous solids. The opening chapters present the basic theoretical models and their computational aspects for different solids of diverse chemical nature, together with some methods of automation and computation in the highly sophisticated experiments in inelastic scattering of neutrons. These topics are followed by a discussion on how group theoretical methods treated by computers can yield the proper symmetry assignments of phonon eigenvalues and eigenstates. Considerable chapters are devoted to the different applications of traditional lattice dynamics, each having its own computational ramification. Other chapters survey the properties of solids that mostly involve integrations over the Brillouin zone. The last chapter concerns the dynamic or time-dependent aspect of lattice dynamics, namely, the calculation of thermal and electric conductivities in some models of solids. This book is of great benefit to geoscientists, physicists, and mathematicians.
