I want this title to be available as an eBook

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

2nd Edition

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

Rate & review

Paperback

Add to wishlist

Looking for an inspection copy?

This title is not currently available on inspection

Description

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
Read more
Customer reviews

Not yet reviewed
Be the first to review

Log in to review

Review was not posted due to profanity
×

, create a review

(If you're not , sign out)

Please enter the right captcha value

Please enter a star rating.

Your review must be a minimum of 12 words.

How do you rate this item?

Reviews must contain at least 12 words about the product.

×

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).