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

This book provides an introduction to the immersed interface method (IIM).

Zhilin Li (Author), Kazifumi Ito (Author)

9780898716092

Paperback / softback, published 30 June 2006

348 pages
25.6 x 18 x 2.2 cm, 0.632 kg

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

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.

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.

Subject Areas: Miscellaneous items [WZ]