Advanced Topics in Computational Partial Differential Equations

1. Front Matter

   Pages I-XIX

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2. Parallel Computing

   • X. Cai, E. Acklam, H. P. Langtangen, A. Tveito

   Pages 1-55

3. Overlapping Domain Decomposition Methods

   • X. Cai

   Pages 57-95

4. Software Tools for Multigrid Methods

   • K.-A. Mardal, G. W. Zumbusch, H. P. Langtangen

   Pages 97-151

5. Mixed Finite Elements

   • K.-A. Mardal, H. P. Langtangen

   Pages 153-197

6. Systems of PDEs and Block Preconditioning

   • K.-A. Mardal, J. Sundnes, H. P. Langtangen, A. Tveito

   Pages 199-236

7. Fully Implicit Methods for Systems of PDEs

   • Å. Ødegård, H. P. Langtangen, A. Tveito

   Pages 237-256

8. Stochastic Partial Differential Equations

   • H. P. Langtangen, H. Osnes

   Pages 257-320

9. Using Diffpack from Python Scripts

   • H. P. Langtangen, K.-A. Mardal

   Pages 321-360

10. Performance Modeling of PDE Solvers

    • X. Cai, A. M. Bruaset, H. P. Langtangen, G. T. Lines, K. Samuelsson, W. Shen et al.

    Pages 361-399

11. Electrical Activity in the Human Heart

    • J. Sundnes, G. T. Lines, P. Grøttum, A. Tveito

    Pages 401-449

12. Mathematical Models of Financial Derivatives

    • O. Skavhaug, B. F. Nielsen, A. Tveito

    Pages 451-482

13. Numerical Methods for Financial Derivatives

    • O. Skavhaug, B. F. Nielsen, A. Tveito

    Pages 483-506

14. Finite Element Modeling of Elastic Structures

    • T. Thorvaldsen, H. P. Langtangen, H. Osnes

    Pages 507-576

15. Simulation of Aluminum Extrusion

    • K. M. Okstad, T. Kvamsdal

    Pages 577-609

16. Simulation of Sedimentary Basins

    • A. Kjeldstad, H. P. Langtangen, J. Skogseid, K. Bjørlykke

    Pages 611-658

17. Back Matter

    Pages 659-663

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This book is about solving partial differential equations (PDEs). Such equa­ tions are used to model a wide range ofphenomena in virtually all fields ofsci­ ence and technology. Inthe last decade, the general availability of extremely powerful computers has shifted the focus in computational mathematics from simplified model problems to much more sophisticated models resembling in­ tricate features of real life. This change challenges our knowledge in computer science and in numerical analysis. The main objective ofthe present book is to teach modern,advanced tech­ niques for numerical PDE solution. The book also introduces several models arising in fields likefinance, medicine, material technology, and geology. Inor­ der to read this book, you must have a basic knowledge of partial differential equations and numerical methods for solving such equations. Furthermore, some background in finite element methods is required. You do not need to know Diffpack, although this programming environment is used in examples throughout the text. Basically, this book is about models, methods, and how to implement the methods. For the implementation part it is natural for us to use Diffpack as the programming environment, because making a PDE solver in Diffpack requires little amount of programming and because Diff­ pack has support for the advanced numerical methods treated in this book. Most chapters have a part on models and methods, and a part on imple­ mentation and Diffpack programming. The exposition is designed such that readers can focus only on the first part, if desired.

• Boundary value problem
• finite element method
• finite element methods
• object-oriented programming
• parallel computing
• partial differential equation
• partial differential equations

• Simula Research Laboratory, Lysaker, Fornebu, Norway

  Hans Petter Langtangen, Aslak Tveito

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