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Advanced Topics in Computational Partial Differential Equations

Numerical Methods and Diffpack Programming

  • Textbook
  • © 2003

Overview

Editors:
  1. Hans Petter Langtangen

    1. Simula Research Laboratory, Lysaker, Fornebu, Norway

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  2. Aslak Tveito

    1. Simula Research Laboratory, Lysaker, Fornebu, Norway

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • Outstanding CSE textbook with real applications
  • Graduate level book suitable for CSE courses
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Computational Science and Engineering (LNCSE, volume 33)

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Table of contents (15 chapters)

  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

    • Ã…. ØdegÃ¥rd, 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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Keywords

About this book

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.

Editors and Affiliations

  • Simula Research Laboratory, Lysaker, Fornebu, Norway

    Hans Petter Langtangen, Aslak Tveito

Bibliographic Information

  • Book Title: Advanced Topics in Computational Partial Differential Equations

  • Book Subtitle: Numerical Methods and Diffpack Programming

  • Editors: Hans Petter Langtangen, Aslak Tveito

  • Series Title: Lecture Notes in Computational Science and Engineering

  • DOI: https://doi.org/10.1007/978-3-642-18237-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2003

  • Softcover ISBN: 978-3-540-01438-6Published: 29 October 2003

  • eBook ISBN: 978-3-642-18237-2Published: 22 September 2012

  • Series ISSN: 1439-7358

  • Series E-ISSN: 2197-7100

  • Edition Number: 1

  • Number of Pages: XIX, 663

  • Number of Illustrations: 13 b/w illustrations

  • Topics: Analysis, Computational Science and Engineering, Partial Differential Equations

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