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

By Ronald Fedkiw. Mathematics of Computation, 2007

436 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/dc7f106117b9252f344aa88ef3362af3d21e43c7

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In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

Extended smoothed boundary method for solving partial differential equations with general boundary conditions on complex boundaries (2009, background): “Various studies have examined optimal discretization of the Dirac delta function [7, 8, 11, 12].”
A high‐order hybridizable discontinuous Galerkin method for elliptic interface problems (2013, neutral): “This class of problems arises when there is a singular force applied on the interface [1–3] and is more difﬁcult to deal with than problems with discontinuous coefﬁcients.”
An improved immersed boundary method with direct forcing for the simulation of particle laden flows (2012, background): “This is a consequence of the continuous forcing approach and is a well-known fact [3, 18].”
An Isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces (2012, methodology): “Immersed boundary methods, also known as embedded domain methods, operate on a Cartesian fixed grid, which can be arbitrarily intersected by the physical boundary [57, 85, 98, 99].”
First order second moment analysis for stochastic interface problems based on low-rank approximation (2013, background): “We refer the reader to the monograph [32] and the references therein.”
Immersed finite element methods for elliptic interface problems with non-homogeneous jump conditions (2011, positive): “The recently developed immersed finite element (IFE) methods [1, 2, 8, 11, 13, 15, 16, 24, 25, 28, 30, 31, 32, 33, 34, 38, 41] also fall into this framework.”
The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models (2015, methodology): “For a more complete overview, we recommend the book by Li and Ito [99], the reviews given in [102, 105] and the references therein.”
Numerical Methods for Fluid-Structure Interaction — A Review (2012, methodology): “…to the immersed domain method mentioned above, notable examples include the immersed interface method (Layton 2009, Leveque and Li 1997, Li 2003, Li and Ito 2006, Li and Lai 2001; Tan, Lim and Khoo 2009, Xu and Wang 2008), the direct forcing method (Fadlun et al. 2000, Guy and Hartenstine 2010,…”