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The Immersed Interface Method - Numerical Solutions of PDEs Involving Interfaces and Irregular Domains (Paperback)
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The Immersed Interface Method - Numerical Solutions of PDEs Involving Interfaces and Irregular Domains (Paperback)
Series: Frontiers in Applied Mathematics, No. 33
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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, and the source
terms are often singular to re?ect source/sink distributions along
codimensional interfaces. Because of these irregularities, the
solutions to the differential equations are typically nonsmooth or
even discontinuous. 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
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. The IIM is a sharp interface method that has
been coupled with evolution schemes such as the level set and front
tracking methods and has been used in both finite difference and
finite element formulations to solve several moving interface and
free boundary problems. In particular, the authors discuss 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 ?uids
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. The IIM, which is based on uniform or adaptive
Cartesian/polar/spherical grids or triangulations, is simple enough
to be implemented by researchers and graduate students with a
reasonable background in differential equations and numerical
analysis yet powerful enough to solve complicated problems with
high-order accuracy. Since interfaces or irregular boundaries are
one dimension lower than solution domains, the extra costs in
dealing with interfaces or irregular boundaries are generally
insigni?cant, and many software packages based on uniform
Cartesian/polar/spherical grids, such as the FFT and fast Poisson
solvers, can be applied easily with the IIM. The most recent IIM
computer codes and packages are available online.
General
Imprint: |
Society For Industrial & Applied Mathematics,U.S.
|
Country of origin: |
United States |
Series: |
Frontiers in Applied Mathematics, No. 33 |
Release date: |
June 2006 |
Authors: |
Zhilin Li
• Kazufumi Ito
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Series editors: |
H.T. Banks
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Dimensions: |
229 x 152 x 19mm (L x W x T) |
Format: |
Paperback - Trade
|
Pages: |
348 |
ISBN-13: |
978-0-89871-609-2 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Numerical analysis
|
LSN: |
0-89871-609-8 |
Barcode: |
9780898716092 |
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