Solving PDEs in C++
Society for Industrial & Applied Mathematics,U.S. (Verlag)
978-0-89871-601-6 (ISBN)
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This comprehensive book 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). 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. It introduces a unified approach for the implementation of complex mathematical objects, such as unstructured mesh, sparse matrix, and multigrid hierarchy, often used in numerical modeling, where the high level of abstraction available in C++ is particularly useful, Included is all the required background in programming, PDEs, and numerical methods, and an elementary background in linear algebra and calculus. Useful exercises and solutions conclude each chapter.
Preface; Part I. Programming: 1. Introduction to C; 2. Introduction to C++; 3. Data structures; Part II. The Object-Oriented Approach: 4. Object-oriented programming; 5. Algorithms and their object-oriented implementation; 6. Object-oriented analysis; Part III. Partial Differential Equations and Their Discretization: 7. The convection-diffusion equation; 8. Stability analysis; 9. Nonlinear equations; 10. Application in image processing; Part IV. The Finite-Element Discretization Method: 11. The weak formulation; 12. Linear finite elements; 13. Unstructured finite-element meshes; 14. Adaptive mesh refinement; 15. High-order finite elements; Part V. The Numerical Solution of Large Sparse Linear Systems of Equations: 16. Sparse matrices and their implementation; 17. Iterative methods for large sparse linear systems; 18. Parallelism; Part VI. Applications: 19. Diffusion equations; 20. The linear elasticity equations; 21. The Stokes equations; 22. Electromagnetic waves; Appendix; Bibliography; Index.
Reihe/Serie | Computational Science and Engineering ; Vol.1 |
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Verlagsort | New York |
Sprache | englisch |
Maße | 176 x 255 mm |
Gewicht | 900 g |
Themenwelt | Mathematik / Informatik ► Informatik ► Programmiersprachen / -werkzeuge |
Mathematik / Informatik ► Mathematik ► Analysis | |
ISBN-10 | 0-89871-601-2 / 0898716012 |
ISBN-13 | 978-0-89871-601-6 / 9780898716016 |
Zustand | Neuware |
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