Journal Article10.1016/J.JCP.2003.12.003
A decomposed immersed interface method for variable coefficient elliptic equations with non-smooth and discontinuous solutions
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TL;DR: In this article, a second order accurate finite difference method is presented for solving two-dimensional variable coefficient elliptic equations on Cartesian grids, in which the coefficients, the source term, the solution and its derivatives may be nonsmooth or discontinuous across an interface.
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About: This article is published in Journal of Computational Physics. The article was published on 10 Jun 2004. The article focuses on the topics: Finite difference method & Discretization.
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Citations
High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
TL;DR: This paper introduces a novel high order interface scheme, the matched interface and boundary (MIB) method, for solving elliptic equations with discontinuous coefficients and singular sources on Cartesian grids by appropriate use of auxiliary line and/or fictitious points.
400
Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces
Sining Yu,Y. C. Zhou,Guo-Wei Wei +2 more
TL;DR: This work generalizes the matched interface and boundary method previously designed for solving elliptic problems with curved interfaces to the aforementioned problems, and introduces primary and secondary fictitious values to deal with sharp-edged interfaces.
205
Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
Sining Yu,Guo-Wei Wei +1 more
TL;DR: The three-dimensional MIB generalization of the previous 2D higher-order matched interface and boundary method for solving elliptic equations with discontinuous coefficients and non-smooth interfaces is reported, extensively validated in terms of the order of accuracy, the speed of convergence, the number of iterations and CPU time.
148
An interface-fitted mesh generator and virtual element methods for elliptic interface problems ☆
TL;DR: A simple and efficient interface-fitted mesh generation algorithm which can produce a semi-structured interface- fitted mesh in two and three dimensions quickly is developed in this paper.
146
Solving elliptic problems with discontinuities on irregular domains - the Voronoi Interface Method
TL;DR: A simple method is introduced, dubbed the Voronoi Interface Method, to solve Elliptic problems with discontinuities across the interface of irregular domains, which produces a linear system that is symmetric positive definite with only its right-hand-side affected by the jump conditions.
86
References
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Stanley Osher,James A. Sethian +1 more
TL;DR: The PSC algorithm as mentioned in this paper approximates the Hamilton-Jacobi equations with parabolic right-hand-sides by using techniques from the hyperbolic conservation laws, which can be used also for more general surface motion problems.
14K
A continuum method for modeling surface tension
TL;DR: In this paper, a force density proportional to the surface curvature of constant color is defined at each point in the transition region; this force-density is normalized in such a way that the conventional description of surface tension on an interface is recovered when the ratio of local transition-reion thickness to local curvature radius approaches zero.
9.4K
Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. Final report
S. Osher,J.A. Sethian +1 more
- 01 Sep 1987
TL;DR: New numerical algorithms are devised (PSC algorithms) for following fronts propagating with curvature-dependent speed, providing methods that accurately capture the formation of sharp gradients and cusps in the moving fronts.
8.3K
A level set approach for computing solutions to incompressible two-phase flow
TL;DR: A level set method for capturing the interface between two fluids is combined with a variable density projection method to allow for computation of two-phase flow where the interface can merge/break and the flow can have a high Reynolds number.
4.7K
A level set approach for computing solutions to incompressible two- phase flow II
Mark Sussman,Emad Fatemi,Stanley Osher,Peter Smereka +3 more
- 01 Jun 1995
TL;DR: In this article, a level set method for capturing the interface between two fluids is combined with a variable density projection method to allow for computation of two-phase flow where the interface can merge/break and the flow can have a high Reynolds number.