Book Review: The immersed interface method. Numerical solutions of PDEs involving interfaces and irregular domains

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The immersed interface method. Numerical solutions of PDEs involving interfaces and irregular domains

Contents Preface Introduction xv 1 1.1 A one-dimensional model problem 2 1.2 A two-dimensional example of heat propagation in a heterogeneous material 3 1.3 Examples of irregular domains and free boundary problems 5 1.4 The scope of the monograph and the methodology 5 1.4.1 Jump conditions 7 1.4.2 The choice of grids 7 1.5 A minireview of some popular finite difference methods for interface pro...

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An Immersed Interface Method for the Incompressible Navier-Stokes Equations in Irregular Domains

We present an immersed interface method for the incompressible Navier Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the no-slip condition on the boundary is satisfied, singular forces are applied on the fluid at the immersed boundary. The forces are related to the jumps in pr...

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In 1993, Li and Mayo [3] gave a finite-difference method with second order accuracy for solving the heat equations involving interfaces with constant coefficients and discontinuous sources. In this paper, we expand their result by presenting a finite-difference method which allows each coefficient to take different values in different sub-regions of the interface. Our method is useful in physic...

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Conditional expected values in Markov chains are solutions to a set of associated backward differential equations, which may be ordinary or partial depending on the number of relevant state variables. This paper investigates the validity of these differential equations by locating the points of non-smoothness of the state-wise conditional expected values, and it presents a numerical method for ...

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ژورنال

عنوان ژورنال: Mathematics of Computation

سال: 2007

ISSN: 0025-5718,1088-6842

DOI: 10.1090/s0025-5718-07-01996-5