New Book on Numerical PDE for interface problems and irregualr domains.

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

Authors: Zhilin Li and Kazufumi Ito

North Carolina State University

2006 / xvi + 332 pages / Softcover

ISBN-10: 0-89871-609-8 List Price $85.00 /
SIAM Member Price $59.50 / Order Code FR33

Order information:

On-line: http://www.ec-securehost.com/SIAM/FR33.html

Interface problems arise when there are two different materials, such as water and oil, or the same material at different states, such as water and ice. If partial or ordinary differential equations are used to model these applications, the parameters in the governing equations are typically discontinuous across the interface separating the two materials or states.

As a result, many standard numerical methods based on the assumption of  smoothness of solutions do not work or work poorly for interface problems.

The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains 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. This book gives 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.

Audience: This book will be a useful resource for mathematicians, numerical analysts, engineers, graduate students, and anyone who uses numerical methods to solve computational problems, particularly problems with fixed and moving interfaces, free boundary problems, and problems on irregular domains.

Contents:

Preface;
Chapter 1: Introduction;
Chapter 2: The IIM for One-Dimensional Elliptic Interface Problems;
Chapter 3: The IIM for Two-Dimensional Elliptic Interface Problems;
Chapter 4: The IIM for Three-Dimensional Elliptic Interface Problems;
Chapter 5: Removing Source Singularities for Certain Interface Problems;
Chapter 6: Augmented Strategies;
Chapter 7: The Fourth-Order IIM;
Chapter 8: The Immersed Finite Element Methods;
Chapter 9: The IIM for Parabolic Interface Problems;
Chapter 10: The IIM for Stokes and Navier-Stokes Equations;
Chapter 11: Some Applications of the IIM