A second-order-accurate symmetric discretization of the Poisson equation on irregular domains

By Frédéric Gibou, Ronald Fedkiw, Li-Tien Cheng, Myung-joo Kang. 2002

574 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/9aa1f6e74db9b460751e958f7930dae94053e754

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Linear Algebra and its Applications (2010, unknown): “However, for Maxwell problems for which (2.7) holds stability can be concluded from the 2 × 2-model (2.11).”
Numerical construction of Green's functions in high dimensional elliptic problems with variable coefficients and analysis of renewable energy data via sparse and separable approximations (2012, methodology): “Numerous methods tailored specifically to the Poisson and PoissonBoltzmann equations, utilizing finite differences, finite elements, and finite volumes, have been and continue to be proposed [146, 40, 12, 57, 107, 34].”
A Level Set Method for Analysis of Film Boiling on an Immersed Solid Surface (2007, background): “(11), is evaluated at the interface and then extrapolated to the entire domain, as described in [17].”
A sharp interface immersed boundary method for compressible viscous flows (2007, methodology): “Keywords: Computational fluid dynamics; Immersed boundary method; Ghost-cell; Non-conformal grid”
A cartesian grid embedded boundary method for the heat equation and poisson's equation in three dimensions (2004, background): “More recently, these methods have been rediscovered and extended by a number of authors [6,5,10,11].”
A level set based sharp interface method for the multiphase incompressible Navier-Stokes equations with phase change (2007, methodology): “for the Stefan problem [12] and the work of Nguyen et al.”
USING THE PARTICLE LEVEL SET METHOD AND A SECOND ORDER ACCURATE PRESSURE BOUNDARY CONDITION FOR FREE SURFACE FLOWS (2003, methodology): “We instead use the fully second order accurate discretization proposed in [16].”
A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem (2005, methodology): “Such computations for the curvature, which do not hinder the first order accuracy of the method presented in [9], cannot be used in this present work without lowering the third order accuracy of our method.”
A sharp interface method for incompressible two-phase flows (2007, methodology): “As mentioned by [19], this specification of the pressure boundary condition is second-order accurate; as opposed to the ‘‘ghost-fluid’’ perspective, we do not have to make assumptions regarding the orientation of the interface in order to get second-order.”
A Dimension‐reduced Pressure Solver for Liquid Simulations (2015, methodology): “We use the level set method to track the liquid free surface [OF03], and we enforce the Dirichlet boundary conditions with the ghost ﬂuid method [GFCK02].”