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The Immersed Interface Method

The Immersed Interface Method
Numerical Solutions of PDEs Involving Interfaces and Irregular Domains

$105.00 (C)

Part of Frontiers in Applied Mathematics

  • Date Published: July 2006
  • 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: 9780898716092

$ 105.00 (C)
Paperback

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  • This text provides an introduction to the immersed interface method (IIM), a powerful numerical method for solving interface problems and problems defined on irregular domains for which analytic solutions are rarely available. It provides a complete description of the IIM, discusses recent progress in the area, and describes numerical methods for a number of classic interface problems. It also contains many numerical examples that can be used as benchmark problems for numerical methods designed for interface problems on irregular domains. Particular topics include the IIM's applications to Stefan problems and unstable crystal growth, incompressible Stokes and Navier-Stokes flows with moving interfaces, an inverse problem identifying unknown shapes in a region, a nonlinear interface problem of magnetorheological fluids containing iron particles, and other problems. The book also contains several applications of free boundary and moving interface problems, including examples from physics, computational fluid mechanics, mathematical biology, material science, and other fields.

    • Introduces the reader to the Immersed Interface Method (IIM)
    • Discusses recent progress in the area
    • Includes a complete description of the IIM
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    Reviews & endorsements

    'Most everything ever published on the topic is described … A tour de force on immersed interface methods.' Loyce Adams, University of Washington

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    Product details

    • Date Published: July 2006
    • format: Paperback
    • isbn: 9780898716092
    • length: 184 pages
    • dimensions: 254 x 177 x 19 mm
    • weight: 0.6kg
    • 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

    Preface
    1. Introduction
    2. The IIM for one-dimensional elliptic interface problems
    3. The IIM for two-dimensional elliptic interface problems
    4. The IIM for three-dimensional elliptic interface problems
    5. Removing source singularities for certain interface problems
    6. Augmented strategies
    7. The fourth-order IIM
    8. The immersed finite element methods
    9. The IIM for parabolic interface problems
    10. The IIM for Stokes and Navier-Stokes equations
    11. Some applications of the IIM
    Bibliography
    Index.

  • Authors

    Zhilin Li, North Carolina State University

    Kazufumi Ito, North Carolina State University

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