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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‘Most everything ever published on the topic is described … A tour de force on immersed interface methods.’ Loyce Adams, Department of Applied Mathematics, University of Washington
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.
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Inside This Book
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First Sentence:
Fixed or moving interface problems, free boundary problems, and problems defined on irregular domains have many applications but are challenging. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
grid refinement analysis, principle preserving scheme, elliptic interface problems, immersed finite element methods, irregular grid points, squares interpolation scheme, noninterface element, nonlinear interface problems, homogeneous jump conditions, certain interface problems, flux jump condition, cosine delta function, sharp interface method, moving interface problems, finite difference coefficients, known jump conditions, augmented approach, initial level set function, immersed interface method, spline package, central finite difference scheme, discrete delta function, augmented variable, augmented method, finite difference stencil Key Phrases - Capitalized Phrases (CAPs): (learn more)
The Immersed Finite Element Methods, Two-Dimensional Elliptic Interface Problems, Three-Dimensional Elliptic Interface Problems, Using the Taylor, Parabolic Interface Problems, The Dirichlet, Simulations of Stefan, Augmented Strategies New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Fixed or moving interface problems, free boundary problems, and problems defined on irregular domains have many applications but are challenging. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
grid refinement analysis, principle preserving scheme, elliptic interface problems, immersed finite element methods, irregular grid points, squares interpolation scheme, noninterface element, nonlinear interface problems, homogeneous jump conditions, certain interface problems, flux jump condition, cosine delta function, sharp interface method, moving interface problems, finite difference coefficients, known jump conditions, augmented approach, initial level set function, immersed interface method, spline package, central finite difference scheme, discrete delta function, augmented variable, augmented method, finite difference stencil Key Phrases - Capitalized Phrases (CAPs): (learn more)
The Immersed Finite Element Methods, Two-Dimensional Elliptic Interface Problems, Three-Dimensional Elliptic Interface Problems, Using the Taylor, Parabolic Interface Problems, The Dirichlet, Simulations of Stefan, Augmented Strategies New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 46
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- Partial Differential Equations (Applied Mathematical Sciences) (v. 1) by Fritz John in Front Matter, and Back Matter
- Multigrid Methods (Frontiers in Applied Mathematics) by Stephen F. McCormick in Front Matter, and Back Matter
- Computational Frameworks for the Fast Fourier Transform (Frontiers in Applied Mathematics) by Charles Van Loan in Front Matter
- Analysis and control of nonlinear infinite dimensional systems, Volume 190 (Mathematics in Science and Engineering) by Barbu in Back Matter
- Computational Methods in Partial Differential Equations (Introductory mathematics for scientists & engineers) by Richard A. Mitchell in Back Matter
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