Download or read book Computational Methods in Transport Verification and Validation written by Frank Graziani and published by Springer Science & Business Media. This book was released on 2008-08-09 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this book deals with a cross cutting issue affecting all transport disciplines, whether it be photon, neutron, charged particle or neutrino transport. That is, verification and validation. In this book, we learn what the astrophysicist, atmospheric scientist, mathematician or nuclear engineer do to assess the accuracy of their code. What convergence studies, what error analysis, what problems do each field use to ascertain the accuracy of their transport simulations.

Download or read book Verification and Validation in Computational Science and Engineering written by Patrick J. Roache and published by . This book was released on 1998 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book AIAA Guide for the Verification and Validation of Computational Fluid Dynamics Simulations written by American Institute of Aeronautics and Astronautics and published by AIAA (American Institute of Aeronautics & Astronautics). This book was released on 1998 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document defines a number of key terms, discusses fundamental concepts, and specifies general procedures for conducting verification and validation of computational fluid dynamics simulations. It's goal is to provide a foundation for the major issues and concepts in verification and validation. However, it does not recommend standards in these areas because a number of important issues are not yet resolved.

Download or read book Advanced Computational Methods in Science and Engineering written by Barry Koren and published by Springer Science & Business Media. This book was released on 2010-04-29 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the present book is to show, in a broad and yet deep way, the state of the art in computational science and engineering. Examples of topics addressed are: fast and accurate numerical algorithms, model-order reduction, grid computing, immersed-boundary methods, and specific computational methods for simulating a wide variety of challenging problems, problems such as: fluid-structure interaction, turbulent flames, bone-fracture healing, micro-electro-mechanical systems, failure of composite materials, storm surges, particulate flows, and so on. The main benefit offered to readers of the book is a well-balanced, up-to-date overview over the field of computational science and engineering, through in-depth articles by specialists from the separate disciplines.

Download or read book Programming for Computations Python written by Svein Linge and published by Springer Nature. This book was released on 2019-10-30 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is published open access under a CC BY 4.0 license. This book presents computer programming as a key method for solving mathematical problems. This second edition of the well-received book has been extensively revised: All code is now written in Python version 3.6 (no longer version 2.7). In addition, the two first chapters of the previous edition have been extended and split up into five new chapters, thus expanding the introduction to programming from 50 to 150 pages. Throughout the book, the explanations provided are now more detailed, previous examples have been modified, and new sections, examples and exercises have been added. Also, a number of small errors have been corrected. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style employed is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows students to write simple programs for solving common mathematical problems with numerical methods in the context of engineering and science courses. The emphasis is on generic algorithms, clean program design, the use of functions, and automatic tests for verification.

Download or read book Introduction to Numerical Methods for Variational Problems written by Hans Petter Langtangen and published by Springer Nature. This book was released on 2019-09-26 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.

Download or read book Exercises in Numerical Linear Algebra and Matrix Factorizations written by Tom Lyche and published by Springer Nature. This book was released on 2020-11-02 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: To put the world of linear algebra to advanced use, it is not enough to merely understand the theory; there is a significant gap between the theory of linear algebra and its myriad expressions in nearly every computational domain. To bridge this gap, it is essential to process the theory by solving many exercises, thus obtaining a firmer grasp of its diverse applications. Similarly, from a theoretical perspective, diving into the literature on advanced linear algebra often reveals more and more topics that are deferred to exercises instead of being treated in the main text. As exercises grow more complex and numerous, it becomes increasingly important to provide supporting material and guidelines on how to solve them, supporting students’ learning process. This book provides precisely this type of supporting material for the textbook “Numerical Linear Algebra and Matrix Factorizations,” published as Vol. 22 of Springer’s Texts in Computational Science and Engineering series. Instead of omitting details or merely providing rough outlines, this book offers detailed proofs, and connects the solutions to the corresponding results in the textbook. For the algorithmic exercises the utmost level of detail is provided in the form of MATLAB implementations. Both the textbook and solutions are self-contained. This book and the textbook are of similar length, demonstrating that solutions should not be considered a minor aspect when learning at advanced levels.

Download or read book Numerical Techniques for Global Atmospheric Models written by Peter H. Lauritzen and published by Springer Science & Business Media. This book was released on 2011-03-29 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys recent developments in numerical techniques for global atmospheric models. It is based upon a collection of lectures prepared by leading experts in the field. The chapters reveal the multitude of steps that determine the global atmospheric model design. They encompass the choice of the equation set, computational grids on the sphere, horizontal and vertical discretizations, time integration methods, filtering and diffusion mechanisms, conservation properties, tracer transport, and considerations for designing models for massively parallel computers. A reader interested in applied numerical methods but also the many facets of atmospheric modeling should find this book of particular relevance.

Download or read book Numerical Linear Algebra and Matrix Factorizations written by Tom Lyche and published by Springer Nature. This book was released on 2020-03-02 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them. Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones. The main characteristics of this book are as follows: It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results. Further, its respective parts can be used independently, making it suitable for self-study. The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.

Download or read book Optimization with PDE Constraints written by Ronald Hoppe and published by Springer. This book was released on 2014-09-11 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on PDE Constrained Optimization contains contributions on the mathematical analysis and numerical solution of constrained optimal control and optimization problems where a partial differential equation (PDE) or a system of PDEs appears as an essential part of the constraints. The appropriate treatment of such problems requires a fundamental understanding of the subtle interplay between optimization in function spaces and numerical discretization techniques and relies on advanced methodologies from the theory of PDEs and numerical analysis as well as scientific computing. The contributions reflect the work of the European Science Foundation Networking Programme ’Optimization with PDEs’ (OPTPDE).

Download or read book Finite Difference Computing with PDEs written by Hans Petter Langtangen and published by Springer. This book was released on 2017-06-21 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.

Download or read book Scientific Computing with MATLAB and Octave written by Alfio Quarteroni and published by Springer Science & Business Media. This book was released on 2010-05-30 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface to the First Edition This textbook is an introduction to Scienti?c Computing. We will illustrate several numerical methods for the computer solution of c- tain classes of mathematical problems that cannot be faced by paper and pencil. We will show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions by polynomials and construct accurate approximations for the solution of di?erential equations. With this aim, in Chapter 1 we will illustrate the rules of the game thatcomputersadoptwhenstoringandoperatingwith realandcomplex numbers, vectors and matrices. In order to make our presentation concrete and appealing we will 1 adopt the programming environment MATLAB as a faithful c- panion. We will gradually discover its principal commands, statements and constructs. We will show how to execute all the algorithms that we introduce throughout the book. This will enable us to furnish an - mediate quantitative assessment of their theoretical properties such as stability, accuracy and complexity. We will solve several problems that will be raisedthrough exercises and examples, often stemming from s- ci?c applications.

Download or read book Frontiers in Numerical Analysis Durham 2010 written by James Blowey and published by Springer Science & Business Media. This book was released on 2012-01-10 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains detailed lecture notes on four topics at the forefront of current research in computational mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to gain quickly an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research are given. This book is also suitable for professional mathematicians who require a succint and accurate account of recent research in areas parallel to their own, and graduates in mathematical sciences.

Download or read book Numerical Geometry Grid Generation and Scientific Computing written by Vladimir A. Garanzha and published by Springer Nature. This book was released on 2021-09-25 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of these conference proceedings is on research, development, and applications in the fields of numerical geometry, scientific computing and numerical simulation, particularly in mesh generation and related problems. In addition, this year’s special focus is on Delaunay triangulations and their applications, celebrating the 130th birthday of Boris Delaunay. In terms of content, the book strikes a balance between engineering algorithms and mathematical foundations. It presents an overview of recent advances in numerical geometry, grid generation and adaptation in terms of mathematical foundations, algorithm and software development and applications. The specific topics covered include: quasi-conformal and quasi-isometric mappings, hyperelastic deformations, multidimensional generalisations of the equidistribution principle, discrete differential geometry, spatial and metric encodings, Voronoi-Delaunay theory for tilings and partitions, duality in mathematical programming and numerical geometry, mesh-based optimisation and optimal control methods. Further aspects examined include iterative solvers for variational problems and algorithm and software development. The applications of the methods discussed are multidisciplinary and include problems from mathematics, physics, biology, chemistry, material science, and engineering.

Download or read book Recent Advances in Algorithmic Differentiation written by Shaun Forth and published by Springer Science & Business Media. This book was released on 2012-07-30 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings represent the state of knowledge in the area of algorithmic differentiation (AD). The 31 contributed papers presented at the AD2012 conference cover the application of AD to many areas in science and engineering as well as aspects of AD theory and its implementation in tools. For all papers the referees, selected from the program committee and the greater community, as well as the editors have emphasized accessibility of the presented ideas also to non-AD experts. In the AD tools arena new implementations are introduced covering, for example, Java and graphical modeling environments or join the set of existing tools for Fortran. New developments in AD algorithms target the efficiency of matrix-operation derivatives, detection and exploitation of sparsity, partial separability, the treatment of nonsmooth functions, and other high-level mathematical aspects of the numerical computations to be differentiated. Applications stem from the Earth sciences, nuclear engineering, fluid dynamics, and chemistry, to name just a few. In many cases the applications in a given area of science or engineering share characteristics that require specific approaches to enable AD capabilities or provide an opportunity for efficiency gains in the derivative computation. The description of these characteristics and of the techniques for successfully using AD should make the proceedings a valuable source of information for users of AD tools.

Download or read book Scientific Computing written by Bertil Gustafsson and published by Springer. This book was released on 2018-10-03 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the most significant computational methods and the history of their development. It begins with the earliest mathematical / numerical achievements made by the Babylonians and the Greeks, followed by the period beginning in the 16th century. For several centuries the main scientific challenge concerned the mechanics of planetary dynamics, and the book describes the basic numerical methods of that time. In turn, at the end of the Second World War scientific computing took a giant step forward with the advent of electronic computers, which greatly accelerated the development of numerical methods. As a result, scientific computing became established as a third scientific method in addition to the two traditional branches: theory and experimentation. The book traces numerical methods’ journey back to their origins and to the people who invented them, while also briefly examining the development of electronic computers over the years. Featuring 163 references and more than 100 figures, many of them portraits or photos of key historical figures, the book provides a unique historical perspective on the general field of scientific computing – making it a valuable resource for all students and professionals interested in the history of numerical analysis and computing, and for a broader readership alike.

Download or read book Numerical Mathematics and Advanced Applications ENUMATH 2013 written by Assyr Abdulle and published by Springer. This book was released on 2014-11-25 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers a selection of invited and contributed lectures from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) held in Lausanne, Switzerland, August 26-30, 2013. It provides an overview of recent developments in numerical analysis, computational mathematics and applications from leading experts in the field. New results on finite element methods, multiscale methods, numerical linear algebra and discretization techniques for fluid mechanics and optics are presented. As such, the book offers a valuable resource for a wide range of readers looking for a state-of-the-art overview of advanced techniques, algorithms and results in numerical mathematics and scientific computing.