The embedded finite difference method for the Poisson equation in a domain with an irregular boundary and Dirichlet boundary conditions
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Publication:703776
DOI10.1016/j.jcp.2004.07.011zbMath1061.65107OpenAlexW2049254953MaRDI QIDQ703776
Publication date: 11 January 2005
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2004.07.011
Error bounds for boundary value problems involving PDEs (65N15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06)
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Cites Work
- Unnamed Item
- The rapid evaluation of volume integrals of potential theory on general regions
- Improved volume conservation in the computation of flows with immersed elastic boundaries
- Numerical analysis of blood flow in the heart
- A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
- The embedded curved boundary method for orthogonal simulation meshes
- The CASL algorithm for quasi-geostrophic flow in a cylinder.
- Superconvergence of the Shortley-Weller approximation for Dirichlet problems
- A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
- Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids
- A fast Poisson solver for complex geometries
- A boundary condition capturing method for Poisson's equation on irregular domains
- On the formulation of finite difference analogues of the Dirichlet problem for Poisson's equation
- Einige abstrakte Begriffe in der numerischen Mathematik (Anwendungen der Halbordnung).(Some abstract notions in the numerical mathematic. (Applications et semiorder))
- Discrete approximations to elliptic differential equations
- Fast Parallel Iterative Solution of Poisson’s and the Biharmonic Equations on Irregular Regions
- High Order Fast Laplace Solvers for the Dirichlet Problem on General Regions
- The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
- Superconvergence of finite difference approximations for convection-diffusion problems
- The Fast Solution of Poisson’s and the Biharmonic Equations on Irregular Regions
- The Numerical Solution of Laplace's Equation