The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains (Frontiers in Applied Mathematics)

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9780898716092: The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains (Frontiers in Applied Mathematics)

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.

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Book Description:

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.

About the Author:

Zhilin Li is a Professor in the Department of Mathematics and Center for Research in Scientific Computing at North Carolina State University.

Kazufumi Ito is a Professor in the Department of Mathematics and Center for Research in Scientific Computing at North Carolina State University.

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Zhilin Li, Kazufumi Ito
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Li, Zhilin/ Ito, Kazufumi
Published by Society for Industrial & Applied (2006)
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