Li and Ito, both affiliated with the Department of Mathematics and the Center for Scientific Computing at North Carolina State University, introduce the immersed interface method (IIM), a numerical method for solving materials interface problems and problems defined on irregular domains. They offer a complete description of the IIM, discuss recent progress in the area, and describe numerical methods for classic interface problems. They also supply many numerical examples that can be used as benchmarks for numerical methods designed for interface problems on irregular domains. Several applications of free boundary and moving interface problems from various fields are given. The book is for mathematicians, numerical analysts, engineers, graduate students, and anyone who uses numerical methods to solve computational problems.
Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)

Li and Ito, both affiliated with the Department of Mathematics and the Center for Scientific Computing at North Carolina State University, introduce the immersed interface method (IIM), a numerical method for solving materials interface problems and problems defined on irregular domains. They offer a complete description of the IIM, discuss recent progress in the area, and describe numerical methods for classic interface problems. They also supply many numerical examples that can be used as benchmarks for numerical methods designed for interface problems on irregular domains. Several applications of free boundary and moving interface problems from various fields are given. The book is for mathematicians, numerical analysts, engineers, graduate students, and anyone who uses numerical methods to solve computational problems. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)

This book provides an introduction to the immersed interface method (IIM), a numerical method for solving interface problems and problems defined on irregular domains, where analytic solutions are rarely available. Included is a complete description of the IIM, discussions on progress and a description of numerical methods for interface problems.

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.