Object-Oriented Implementation of Numerical Methods

Object-Oriented Implementation of Numerical Methods
Author: Didier H. Besset
Publisher: Morgan Kaufmann
Total Pages: 800
Release: 2001
Genre: Computers
ISBN: 9781558606791
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"There are few books that show how to build programs of any kind. One common theme is compiler building, and there are shelves full of them. There are few others. It's an area, or a void, that needs filling. this book does a great job of showing how to build numerical analysis programs." -David N. Smith, IBM T J Watson Research Center Numerical methods naturally lend themselves to an object-oriented approach. Mathematics builds high- level ideas on top of previously described, simpler ones. Once a property is demonstrated for a given concept, it can be applied to any new concept sharing the same premise as the original one, similar to the ideas of reuse and inheritance in object-oriented (OO) methodology. Few books on numerical methods teach developers much about designing and building good code. Good computing routines are problem-specific. Insight and understanding are what is needed, rather than just recipes and black box routines. Developers need the ability to construct new programs for different applications. Object-Oriented Implementation of Numerical Methods reveals a complete OO design methodology in a clear and systematic way. Each method is presented in a consistent format, beginning with a short explanation and following with a description of the general OO architecture for the algorithm. Next, the code implementations are discussed and presented along with real-world examples that the author, an experienced software engineer, has used in a variety of commercial applications. Features: Reveals the design methodology behind the code, including design patterns where appropriate, rather than just presenting canned solutions. Implements all methods side by side in both Java and Smalltalk. This contrast can significantly enhance your understanding of the nature of OO programming languages. Provides a step-by-step pathway to new object-oriented techniques for programmers familiar with using procedural languages such as C or Fortran for numerical methods. Includes a chapter on data mining, a key application of numerical methods.

Solving PDEs in C++

Solving PDEs in C++
Author: Yair Shapira
Publisher:
Total Pages: 500
Release: 2006
Genre: C++ (Computer program language)
ISBN: 9780898718959
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This comprehensive book introduces the C and C++ programming languages and shows how to use them in the numerical solution of partial differential equations (PDEs). It leads the reader through the entire solution process, from the original PDE, through the discretization stage, to the numerical solution of the resulting algebraic system. The well-debugged and tested code segments implement the numerical methods efficiently and transparently. Basic and advanced numerical methods are introduced and implemented easily and efficiently in a unified object-oriented approach. The high level of abstraction available in C++ is particularly useful in the implementation of complex mathematical objects, such as unstructured mesh, sparse matrix, and multigrid hierarchy, often used in numerical modeling. This book introduces a unified approach for the implementation of these objects. Solving PDEs in C++ contains all the required background in programming, PDEs, and numerical methods; only an elementary background in linear algebra and calculus is required. For the more advanced reader, there is also material on stability analysis and weak formulation. The final parts of the book demonstrate the object-oriented approach in advanced applications. Audience: researchers, engineers, and advanced students. It can be used as a textbook in courses in C++ with applications, C++ in engineering, numerical analysis, and numerical PDEs at the advanced undergraduate and graduate levels. Because it is self-contained, the book is also suitable for self-study by researchers and students in applied and computational science and engineering.

Solving PDEs in C++

Solving PDEs in C++
Author: Yair Shapira
Publisher: SIAM
Total Pages: 775
Release: 2012-06-07
Genre: Computers
ISBN: 1611972167
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In this much-expanded second edition, author Yair Shapira presents new applications and a substantial extension of the original object-oriented framework to make this popular and comprehensive book even easier to understand and use. It not only introduces the C and C++ programming languages, but also shows how to use them in the numerical solution of partial differential equations (PDEs). The book leads readers through the entire solution process, from the original PDE, through the discretization stage, to the numerical solution of the resulting algebraic system. The high level of abstraction available in C++ is particularly useful in the implementation of complex mathematical objects, such as unstructured mesh, sparse matrix, and multigrid hierarchy, often used in numerical modeling. The well-debugged and tested code segments implement the numerical methods efficiently and transparently in a unified object-oriented approach.

Computing for Numerical Methods Using Visual C++

Computing for Numerical Methods Using Visual C++
Author: Shaharuddin Salleh
Publisher: John Wiley & Sons
Total Pages: 468
Release: 2007-12-14
Genre: Technology & Engineering
ISBN: 0470192623
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A visual, interdisciplinary approach to solving problems in numerical methods Computing for Numerical Methods Using Visual C++ fills the need for a complete, authoritative book on the visual solutions to problems in numerical methods using C++. In an age of boundless research, there is a need for a programming language that can successfully bridge the communication gap between a problem and its computing elements through the use of visual-ization for engineers and members of varying disciplines, such as biologists, medical doctors, mathematicians, economists, and politicians. This book takes an interdisciplinary approach to the subject and demonstrates how solving problems in numerical methods using C++ is dominant and practical for implementation due to its flexible language format, object-oriented methodology, and support for high numerical precisions. In an accessible, easy-to-follow style, the authors cover: Numerical modeling using C++ Fundamental mathematical tools MFC interfaces Curve visualization Systems of linear equations Nonlinear equations Interpolation and approximation Differentiation and integration Eigenvalues and Eigenvectors Ordinary differential equations Partial differential equations This reader-friendly book includes a companion Web site, giving readers free access to all of the codes discussed in the book as well as an equation parser called "MyParser" that can be used to develop various numerical applications on Windows. Computing for Numerical Methods Using Visual C++ serves as an excellent reference for students in upper undergraduate- and graduate-level courses in engineering, science, and mathematics. It is also an ideal resource for practitioners using Microsoft Visual C++.

Mathematical Objects in C++

Mathematical Objects in C++
Author: Yair Shapira
Publisher: CRC Press
Total Pages: 609
Release: 2009-06-19
Genre: Computers
ISBN: 9781439811481
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Emphasizing the connection between mathematical objects and their practical C++ implementation, this book provides a comprehensive introduction to both the theory behind the objects and the C and C++ programming. Object-oriented implementation of three-dimensional meshes facilitates understanding of their mathematical nature. Requiring no prerequisites, the text covers discrete mathematics, data structures, and computational physics, including high-order discretization of nonlinear equations. Exercises and solutions make the book suitable for classroom use and a supporting website supplies downloadable code.

Numerical Methods and Software Tools in Industrial Mathematics

Numerical Methods and Software Tools in Industrial Mathematics
Author: A. Tveito
Publisher: Springer Science & Business Media
Total Pages: 404
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461219841
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13. 2 Abstract Saddle Point Problems . 282 13. 3 Preconditioned Iterative Methods . 283 13. 4 Examples of Saddle Point Problems 286 13. 5 Discretizations of Saddle Point Problems. 290 13. 6 Numerical Results . . . . . . . . . . . . . 295 III GEOMETRIC MODELLING 299 14 Surface Modelling from Scattered Geological Data 301 N. P. Fremming, @. Hjelle, C. Tarrou 14. 1 Introduction. . . . . . . . . . . 301 14. 2 Description of Geological Data 302 14. 3 Triangulations . . . . . . . . 304 14. 4 Regular Grid Models . . . . . 306 14. 5 A Composite Surface Model. 307 14. 6 Examples . . . . . . 312 14. 7 Concluding Remarks. . . . . 314 15 Varioscale Surfaces in Geographic Information Systems 317 G. Misund 15. 1 Introduction. . . . . . . . . . . . . . . 317 15. 2 Surfaces of Variable Resolution . . . . 318 15. 3 Surface Varioscaling by Normalization 320 15. 4 Examples . . . 323 15. 5 Final Remarks . . . . . . . . . . . . . 327 16 Surface Modelling from Biomedical Data 329 J. G. Bjaalie, M. Dtllhlen, T. V. Stensby 16. 1 Boundary Polygons. . . . . . . . . . . 332 16. 2 Curve Approximation . . . . . . . . . 333 16. 3 Reducing Twist in the Closed Surface 336 16. 4 Surface Approximation. 337 16. 5 Open Surfaces. . . . 339 16. 6 Examples . . . . . . 340 16. 7 Concluding Remarks 344 17 Data Reduction of Piecewise Linear Curves 347 E. Arge, M. Dtllhlen 17. 1 Introduction. . . . . . . . . . . 347 17. 2 Preliminaries . . . . . . . . . . 349 17. 3 The Intersecting Cones Method 351 17. 4 The Improved Douglas Method 353 17. 5 Numerical Examples . . . . . . 360 17. 6 Resolution Sorting . . . . . . . . . . . . . . . . . . 361 18 Aspects of Algorithms for Manifold Intersection 365 T. Dokken 18. 1 Introduction . . . . . . . . . . . . . . . 365 18. 2 Basic Concepts Used . . . . . . . . . .

Numerical Algorithms

Numerical Algorithms
Author: Justin Solomon
Publisher: CRC Press
Total Pages: 400
Release: 2015-06-24
Genre: Computers
ISBN: 1482251892
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Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig

Software Engineering: A Hands-On Approach

Software Engineering: A Hands-On Approach
Author: Roger Y. Lee
Publisher: Springer Science & Business Media
Total Pages: 302
Release: 2013-07-04
Genre: Computers
ISBN: 9462390061
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This textbook provides a progressive approach to the teaching of software engineering. First, readers are introduced to the core concepts of the object-oriented methodology, which is used throughout the book to act as the foundation for software engineering and programming practices, and partly for the software engineering process itself. Then, the processes involved in software engineering are explained in more detail, especially methods and their applications in design, implementation, testing, and measurement, as they relate to software engineering projects. At last, readers are given the chance to practice these concepts by applying commonly used skills and tasks to a hands-on project. The impact of such a format is the potential for quicker and deeper understanding. Readers will master concepts and skills at the most basic levels before continuing to expand on and apply these lessons in later chapters.

Concurrent Object-Oriented Programming and Petri Nets

Concurrent Object-Oriented Programming and Petri Nets
Author: Gul A. Agha
Publisher: Springer
Total Pages: 548
Release: 2003-06-29
Genre: Computers
ISBN: 3540453970
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Concurrency and distribution have become the dominant paradigm and concern in computer science. Despite the fact that much of the early research in object-oriented programming focused on sequential systems, objects are a natural unit of distribution and concurrency - as elucidated early on by research on the Actor model. Thus, models and theories of concurrency, the oldest one being Petri nets, and their relation to objects are an attractive topic of study. This book presents state-of-the-art results on Petri nets and concurrent object-oriented programming in a coherent and competent way. The 24 thoroughly reviewed and revised papers are organized in three sections. The first consists of long papers, each presenting a detailed approach to integrating Petri nets and object-orientation. Section II includes shorter papers with emphasis on concrete examples to demonstrate the approach. Finally, section III is devoted to papers which significantly build on the Actor model of computation.

Geomechanics and Geodynamics of Rock Masses

Geomechanics and Geodynamics of Rock Masses
Author: Vladimir Litvinenko
Publisher: CRC Press
Total Pages: 1908
Release: 2018-05-15
Genre: Technology & Engineering
ISBN: 0429868588
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Geomechanics and Geodynamics of Rock Masses contains contributions presented at EUROCK 2018, the 2018 International Symposium of the International Society for Rock Mechanics (ISRM 2018, Saint Petersburg, Russia, 22-26 May 2018). Dedicated to recent advances and achievements in the fields of geomechanics and geotechnology, the main topics of the book include: - Physical and mechanical properties of fractured rock (laboratory testing and rock properties, field measurements and site investigations) - Geophysics in rock mechanics - Rock mass strength and failure - Nonlinear problems in rock mechanics - Effect of joint water on the behavior of rock foundation - Numerical modeling and back analysis - Mineral resources development: methods and rock mechanics problems - Rock mechanics and underground construction in mining, hydropower industry and civil engineering - Rock mechanics in petroleum engineering - Geodynamics and monitoring of rock mass behavior - Risks and hazards - Geomechanics of technogenic deposits Geomechanics and Geodynamics of Rock Masses will be of interest to researchers and professionals involved in the various branches of rock mechanics and rock engineering. EUROCK 2018, organized by the Saint Petersburg Mining University, is a continuation of the successful series of ISRM symposia in Europe, which began in 1992 in Chester, UK.