The Explicit-Jump Immersed Interface Method: Finite Difference Methods for PDEs with Piecewise Smooth Solutions

By Andreas Wiegmann, K. Bube. SIAM Journal on Numerical Analysis, 2000

308 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/46c93c980868aa5dd09338262bca6faed73c3993

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In Computational Mechanics

1. Yanping Lin
2. Xiaoming He
3. Tao Lin
4. Anita T. Layton
5. Zhilin Li
6. Ming-Chih Lai
7. Sheng Xu
8. Zhijian Wang

In Electrical and Electronic Engineering

1. Yanping Lin
2. Xiaoming He
3. Tao Lin
4. James A. Sethian
5. Anita T. Layton
6. G. Wei
7. J. Thomas Beale
8. Sheng Xu

Citations in the corpus

• Approximation capability of a bilinear immersed finite element space (2008, methodology): “Since then, FD methods such as the Cartesian grid method, embedded boundary method, cut-cell methods, etc., have been developed, and they have been used to treat Euler ∞ows [3, 25, 28, 42, 56], Navier-Stokes ∞ow [20, 23, 43], and of course, the interface problems involving the fundamental elliptic o”
• An immersed interface method for simulating the interaction of a fluid with moving boundaries (2006, methodology): “Later, it was extended to one-dimensional nonlinear parabolic equations [36], Poisson equations with Neumann boundary conditions [37,8], and the twodimensional incompressible Navier–Stokes equations [19,16].”
• ON THE ACCURACY OF FINITE DIFFERENCE METHODS FOR ELLIPTIC PROBLEMS WITH INTERFACES (2006, methodology): “We now describe the derivation of (2–10) as in Mayo’s method [32; 34; 31], the related work of Wiegmann and Bube [37], or the immersed interface method of LeVeque and Li [24; 27; 26].”
• A Fictitious domain approach with spread interface for elliptic problems with general boundary conditions (2007, methodology): “methods can be found in this group: truncated domains methods [6,7], immersed interface methods (I.I.M.) [8, 9 ], penalty methods [1,2,10,11,12,4], ctitious domain methods with Lagrange multipliers [13,14,15], an adapted Galerkin method proposed in [16], and recent work on a ctitious model with ux a”
• Evolution, implementation, and application of level set and fast marching methods for advancing fronts (2001, methodology): “This explicit jump immersed interface method (see [ 100 ]) is a finite difference technique on uniform grids, after LeVeque and Li’simmersed interface method([42]), that is capable of dealing with non-grid-aligned boundaries with the same truncation error as interior differences.”
• High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources (2006, methodology): “The linear systems in two IIMs [ 51 ,5] are all symmetric and diagonally dominant, allowing the use of conventional fast Poisson solvers.”
• An augmented approach for Stokes equations with a discontinuous viscosity and singular forces (2007, methodology): “While augmented approaches have been developed for elliptic interface problems or problems defined on irregular domain problems in [3,8,10,20,23,24,40], and for dealing with the pressure boundary condition in [22], the augmented approach proposed in this paper provides a way to get a second order im”
• Digital rock physics benchmarks - part II: Computing effective properties (2013, methodology): “One method used to calculate the permeability from rock microstructure images is the Explicit Jump (EJ) method (Wiegmann and Bube, 2000).”
• A Bilinear Immersed Finite Volume Element Method For the Diffusion Equation with Discontinuous Coefficient (2009, methodology): “Along this direction, Peskin’s immersed boundary method [71,72] is one of the early representative ideas followed by many publications with applications in numerous fields [3,21,26,28,31,35,42,45,49–51,53,55,65,80,81,84,85].”