Fundamentals of Scientific Computing

Author: Bertil Gustafsson
Publisher: Springer Science & Business Media
ISBN: 3642194958
Release Date: 2011-06-11
Genre: Mathematics

The book of nature is written in the language of mathematics -- Galileo Galilei How is it possible to predict weather patterns for tomorrow, with access solely to today’s weather data? And how is it possible to predict the aerodynamic behavior of an aircraft that has yet to be built? The answer is computer simulations based on mathematical models – sets of equations – that describe the underlying physical properties. However, these equations are usually much too complicated to solve, either by the smartest mathematician or the largest supercomputer. This problem is overcome by constructing an approximation: a numerical model with a simpler structure can be translated into a program that tells the computer how to carry out the simulation. This book conveys the fundamentals of mathematical models, numerical methods and algorithms. Opening with a tutorial on mathematical models and analysis, it proceeds to introduce the most important classes of numerical methods, with finite element, finite difference and spectral methods as central tools. The concluding section describes applications in physics and engineering, including wave propagation, heat conduction and fluid dynamics. Also covered are the principles of computers and programming, including MATLAB®.

Scientific Computing

Author: Michael T. Heath
Publisher: McGraw-Hill Europe
ISBN: 0071244891
Release Date: 2005
Genre: Numerical analysis

This Auditing practice set incorporates both the cycles and the risk approach using the audit risk model. Students will learn to design and prepare the current year's working papers and assemble the completed case. Taking about 30 hours to complete, this practice set can be used with any Auditing textbook.

Mathematical Principles for Scientific Computing and Visualization

Author: Gerald Farin
Publisher: CRC Press
ISBN: 9781568813219
Release Date: 2008-10-21
Genre: Mathematics

This non-traditional introduction to the mathematics of scientific computation describes the principles behind the major methods, from statistics, applied mathematics, scientific visualization, and elsewhere, in a way that is accessible to a large part of the scientific community. Introductory material includes computational basics, a review of coordinate systems, an introduction to facets (planes and triangle meshes) and an introduction to computer graphics. The scientific computing part of the book covers topics in numerical linear algebra (basics, solving linear system, eigen-problems, SVD, and PCA) and numerical calculus (basics, data fitting, dynamic processes, root finding, and multivariate functions). The visualization component of the book is separated into three parts: empirical data, scalar values over 2D data, and volumes.

Scientific Computing

Author: Timo Heister
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 9783110386806
Release Date: 2015-05-19
Genre: Mathematics

Nowadays most mathematics done in practice is done on a computer. In engineering it is necessary to solve more than 1 million equations simultaneously, and computers can be used to reduce the calculation time from years to minutes or even seconds. This book explains: How can we approximate these important mathematical processes? How accurate are our approximations? How efficient are our approximations?

Practical Scientific Computing

Author: Muhammad Ali
Publisher: Elsevier
ISBN: 9780857092267
Release Date: 2011-02-26
Genre: Mathematics

Scientific computing is about developing mathematical models, numerical methods and computer implementations to study and solve real problems in science, engineering, business and even social sciences. Mathematical modelling requires deep understanding of classical numerical methods. This essential guide provides the reader with sufficient foundations in these areas to venture into more advanced texts. The first section of the book presents numEclipse, an open source tool for numerical computing based on the notion of MATLAB®. numEclipse is implemented as a plug-in for Eclipse, a leading integrated development environment for Java programming. The second section studies the classical methods of numerical analysis. Numerical algorithms and their implementations are presented using numEclipse. Practical scientific computing is an invaluable reference for undergraduate engineering, science and mathematics students taking numerical methods courses. It will also be a useful handbook for postgraduate researchers and professionals whose work involves scientific computing. An invaluable reference for undergraduate engineering, science and mathematics students taking numerical methods courses Guides the reader through developing a deep understanding of classical numerical methods Features a comprehensive analysis of numEclipse including numerical algorithms and their implementations

Scientific Computing Computer Arithmetic and Validated Numerics

Author: Marco Nehmeier
Publisher: Springer
ISBN: 9783319317694
Release Date: 2016-04-08
Genre: Computers

This book constitutes the refereed post proceedings of the 16th International Symposium, SCAN 2014, held in Würzburg, Germany, in September 2014. The 22 full papers presented were carefully reviewed and selected from 60 submissions. The main concerns of research addressed by SCAN conferences are validation, verification or reliable assertions of numerical computations. Interval arithmetic and other treatments of uncertainty are developed as appropriate tools.

Scientific Computing and Applications

Author: Peter Minev
Publisher: Nova Publishers
ISBN: 1590330277
Release Date: 2001
Genre: Mathematics

Contents: An Optimal Order Multilevel Preconditioner with Respect to Problem and Discretisation Parameters; 3D Numerical Simulation of Drop Coalescence; Fully Implicit Implementation of Boundary Conditions in Operator-Splitting Methods for Steady Incompressible Navier-Stokes Equations; Point-Distributed Algorithms on Locally Refined Grids for Second Order Elliptic Equations; Anisotropic Mesh Adaptation Through Hierarchical Error Estimators; Operator Splitting for Compressible Miscible Displacement in Porous Media; On Smoothers in Parallel Coupled Multigrid Methods for Incompressible Navier-Stokes Equations; Time-Evolving Interfaces in a Stokes Flow; Adaptive Finite Volume Element Method for Convection-Diffusion-Reaction Problems in 3-D; A Rectangular Immersed Finite Element Space for Interface Problems; Convergence Analysis For Quadrilateral Rotated Q1 Elements; A Spectral Solver for the Three-Dimensional Navier-Stokes Equations in Velocity-Vorticity Formulation; B-spline Collocation Methods for Elasticity Problems; Moving Mesh Finite Element Methods Based on Harmonic Maps; Interface Solvers and Preconditioners of Domain Decomposition Type for Multiphase Flow in Multiblock Porous M

Scientific Computing in Electrical Engineering

Author: Angelo Marcello Anile
Publisher: Springer Science & Business Media
ISBN: 9783540328629
Release Date: 2007-01-10
Genre: Technology & Engineering

This book is a collection of papers presented at the last Scientific Computing in Electrical Engineering (SCEE) Conference, held in Sicily, in 2004. The series of SCEE conferences aims at addressing mathematical problems which have a relevancy to industry. The areas covered at SCEE-2004 were: Electromagnetism, Circuit Simulation, Coupled Problems and General mathematical and computational methods.

Scientific Computing with MATLAB

Author: Alfio Quarteroni
Publisher: Springer Science & Business Media
ISBN: 9783642593390
Release Date: 2012-12-06
Genre: Computers

This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer solution of certain classes of mathematical problems are illustrated. The authors 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 differential equations. To make the presentation concrete and appealing, the programming environment Matlab is adopted as a faithful companion.

Combinatorial Scientific Computing

Author: Uwe Naumann
Publisher: CRC Press
ISBN: 9781439827352
Release Date: 2012-01-25
Genre: Computers

Combinatorial Scientific Computing explores the latest research on creating algorithms and software tools to solve key combinatorial problems on large-scale high-performance computing architectures. It includes contributions from international researchers who are pioneers in designing software and applications for high-performance computing systems. The book offers a state-of-the-art overview of the latest research, tool development, and applications. It focuses on load balancing and parallelization on high-performance computers, large-scale optimization, algorithmic differentiation of numerical simulation code, sparse matrix software tools, and combinatorial challenges and applications in large-scale social networks. The authors unify these seemingly disparate areas through a common set of abstractions and algorithms based on combinatorics, graphs, and hypergraphs. Combinatorial algorithms have long played a crucial enabling role in scientific and engineering computations and their importance continues to grow with the demands of new applications and advanced architectures. By addressing current challenges in the field, this volume sets the stage for the accelerated development and deployment of fundamental enabling technologies in high-performance scientific computing.

Scientific Computing An Introduction using Maple and MATLAB

Author: Walter Gander
Publisher: Springer Science & Business
ISBN: 9783319043258
Release Date: 2014-04-23
Genre: Mathematics

Scientific computing is the study of how to use computers effectively to solve problems that arise from the mathematical modeling of phenomena in science and engineering. It is based on mathematics, numerical and symbolic/algebraic computations and visualization. This book serves as an introduction to both the theory and practice of scientific computing, with each chapter presenting the basic algorithms that serve as the workhorses of many scientific codes; we explain both the theory behind these algorithms and how they must be implemented in order to work reliably in finite-precision arithmetic. The book includes many programs written in Matlab and Maple – Maple is often used to derive numerical algorithms, whereas Matlab is used to implement them. The theory is developed in such a way that students can learn by themselves as they work through the text. Each chapter contains numerous examples and problems to help readers understand the material “hands-on”.

Modern Software Tools for Scientific Computing

Author: A. Bruaset
Publisher: Springer Science & Business Media
ISBN: 9781461219866
Release Date: 2012-12-06
Genre: Computers

Looking back at the years that have passed since the realization of the very first electronic, multi-purpose computers, one observes a tremendous growth in hardware and software performance. Today, researchers and engi neers have access to computing power and software that can solve numerical problems which are not fully understood in terms of existing mathemati cal theory. Thus, computational sciences must in many respects be viewed as experimental disciplines. As a consequence, there is a demand for high quality, flexible software that allows, and even encourages, experimentation with alternative numerical strategies and mathematical models. Extensibil ity is then a key issue; the software must provide an efficient environment for incorporation of new methods and models that will be required in fu ture problem scenarios. The development of such kind of flexible software is a challenging and expensive task. One way to achieve these goals is to in vest much work in the design and implementation of generic software tools which can be used in a wide range of application fields. In order to provide a forum where researchers could present and discuss their contributions to the described development, an International Work shop on Modern Software Tools for Scientific Computing was arranged in Oslo, Norway, September 16-18, 1996. This workshop, informally referred to as Sci Tools '96, was a collaboration between SINTEF Applied Mathe matics and the Departments of Informatics and Mathematics at the Uni versity of Oslo.

Scientific Computing with Python 3

Author: Claus Fuhrer
Publisher: Packt Publishing Ltd
ISBN: 9781786463647
Release Date: 2016-12-23
Genre: Computers

An example-rich, comprehensive guide for all of your Python computational needs About This Book Your ultimate resource for getting up and running with Python numerical computations Explore numerical computing and mathematical libraries using Python 3.x code with SciPy and NumPy modules A hands-on guide to implementing mathematics with Python, with complete coverage of all the key concepts Who This Book Is For This book is for anyone who wants to perform numerical and mathematical computations in Python. It is especially useful for developers, students, and anyone who wants to use Python for computation. Readers are expected to possess basic a knowledge of scientific computing and mathematics, but no prior experience with Python is needed. What You Will Learn The principal syntactical elements of Python The most important and basic types in Python The essential building blocks of computational mathematics, linear algebra, and related Python objects Plot in Python using matplotlib to create high quality figures and graphics to draw and visualize your results Define and use functions and learn to treat them as objects How and when to correctly apply object-oriented programming for scientific computing in Python Handle exceptions, which are an important part of writing reliable and usable code Two aspects of testing for scientific programming: Manual and Automatic In Detail Python can be used for more than just general-purpose programming. It is a free, open source language and environment that has tremendous potential for use within the domain of scientific computing. This book presents Python in tight connection with mathematical applications and demonstrates how to use various concepts in Python for computing purposes, including examples with the latest version of Python 3. Python is an effective tool to use when coupling scientific computing and mathematics and this book will teach you how to use it for linear algebra, arrays, plotting, iterating, functions, polynomials, and much more. Style and approach This book takes a concept-based approach to the language rather than a systematic introduction. It is a complete Python tutorial and introduces computing principles, using practical examples to and showing you how to correctly implement them in Python. You'll learn to focus on high-level design as well as the intricate details of Python syntax. Rather than providing canned problems to be solved, the exercises have been designed to inspire you to think about your own code and give you real-world insight.