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Solving PDEs in C++

Solving PDEs in C++
Numerical Methods in a Unified Object-Oriented Approach

2nd Edition

$160.00 (P)

Part of Computational Science and Engineering

  • Author: Yair Shapira, Computer Science Department, Technion, Israel Institute of Technology, Haifa, Israel
  • Date Published: August 2012
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9781611972160

$ 160.00 (P)
Paperback

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  • This text provides a comprehensive guide for the numerical solution of PDEs using C++ within an object-oriented approach. The high level of abstraction available in C++ is particularly useful in the implementation of complex mathematical objects, such as unstructured meshes, sparse matrices and multigrid hierarchies, often used in numerical modeling. Assuming only an elementary knowledge of calculus and linear algebra, the reader is given a full introduction to programming, PDEs and numerical methods. The learning process is illuminated further by practical examples alongside exercises and solutions that are found at the end of each chapter. This massively expanded second edition contains a wealth of new material, including sections on cryptography, image processing and solution of nonlinear PDEs, accompanied by new reader-friendly code. This book is ideal for students, engineers and researchers who want to use advanced numerical programming methods to solve problems in applied science and engineering.

    • A complete introduction to the topic
    • The reader is guided through the entire process of solving PDEs in C++
    • Each chapter ends with exercises and solutions to advance the reader's understanding
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    Product details

    • Edition: 2nd Edition
    • Date Published: August 2012
    • format: Paperback
    • isbn: 9781611972160
    • length: 800 pages
    • dimensions: 255 x 175 x 41 mm
    • weight: 1.38kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    List of figures
    List of tables
    Preface
    Part I. Elementary Background in Programming:
    1. Concise introduction to C
    2. Concise introduction to C++
    3. Data structures used in the present algorithms
    Part II. Object-Oriented Programming:
    4. From Wittgenstein–Lacan's theory to the object-oriented implementation of graphs and matrices
    5. FFT and other algorithms in numerics and cryptography
    6. Object-oriented analysis of nonlinear ordinary differential equations
    Part III. Partial Differential Equations and their Discretization:
    7. The convection-diffusion equation
    8. Some stability analysis
    9. About nonlinear conservation laws
    10. Application in image processing
    Part IV. The Finite Element Discretization Method:
    11. About the weak formulation
    12. Some background in linear finite elements
    13. Unstructured finite-element meshes
    14. Adaptive mesh refinement
    15. Towards high-order finite elements
    Part V. The Numerical Solution of Large Sparse Linear Systems of Algebraic Equations:
    16. Sparse matrices and their object-oriented implementation
    17. Iterative methods for the numerical solution of large sparse linear systems of algebraic equations
    18. Towards parallelism
    Part VI. Applications in Two Spatial Dimensions:
    19. Diffusion equations
    20. The linear elasticity equations
    21. The Stokes equations
    22. Application in electromagnetic waves
    23. Multigrid for nonlinear equations and for the fusion problem in image processing
    Part VII. Applications in Three Spatial Dimensions:
    24. Polynomials in three independent variables
    25. The Helmholtz equation: error estimate
    26. Adaptive finite elements in three spatial dimensions
    27. Application in nonlinear optics: the nonlinear Helmholtz equation in three spatial dimensions
    28. High-order finite elements in three spatial dimensions
    29. Application in the nonlinear Maxwell equations
    30. Towards inverse problems
    31. Application in the Navier–Stokes equations
    Appendix. Solutions to selected exercises
    Bibliography
    Index.

  • Author

    Yair Shapira, Computer Science Department, Technion, Israel Institute of Technology, Haifa, Israel
    Yair Shapira is engaged in research in the Computer Science Department, Technion – Israel Institute of Technology, Haifa, Israel. His main research interests are multigrid, preconditioning and numerical methods. He is author of the books Matrix-Based Multigrid: Theory and Applications, 2nd Edition (2008) and Mathematical Objects in C++: Computational Tools in a Unified Object-Oriented Approach (2009).

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