A family of sixth-order compact finite-difference schemes for the three-dimensional Poisson equation
type: Item
instance of: scholarly article
title: A family of sixth-order compact finite-difference schemes for the three-dimensional Poisson equation
zbMATH Open document ID: 1202.65139
DOI: 10.1155/2010/352174
author: Yaw Kyei
author: John Paul Roop
author: Guoqing Tang
published in: Advances in Numerical Analysis
publication date: 2010-11-17T00:00:00Z
full work available at URL: https://eudml.org/doc/229327
review text: Summary: We derive a family of sixth-order compact finite-difference schemes for the three-dimensional Poisson's equation. As opposed to other research regarding higher-order compact difference schemes, our approach includes consideration of the discretization of the source function on a compact finite-difference stencil. The schemes derived approximate the solution to Poisson's equation on a compact stencil, and thus the schemes can be easily implemented and resulting linear systems are solved in a high-performance computing environment. The resulting discretization is a one-parameter family of finite-difference schemes which may be further optimized for accuracy and stability. Computational experiments are implemented which illustrate the theoretically demonstrated truncation errors.
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 5816753
zbMATH Keywords: numerical examples
zbMATH Keywords: sixth-order compact finite-difference schemes
zbMATH Keywords: three-dimensional Poisson's equation
Wikidata QID: Q58650144
MaRDI profile type: Publication
OpenAlex ID: W2007275229
cites work: Q4663944
cites work: Symbolic computation of high order compact difference schemes for three dimensional linear elliptic partial differential equations with variable coefficients
cites work: Finite-volume compact schemes on staggered grids
cites work: High‐order compact scheme for the steady stream‐function vorticity equations
cites work: A fourth-order compact difference scheme on face centered cubic grids with multigrid method for solving 2D convection diffusion equation.
cites work: Compact finite difference schemes with spectral-like resolution
cites work: Higher-Order, Cartesian Grid Based Finite Difference Schemes for Elliptic Equations on Irregular Domains
cites work: Maximum principle preserving schemes for interface problems with discontinuous coefficients
cites work: Efficient iterative solution of the three-dimensional Helmholtz equation
cites work: On a class of preconditioners for solving the Helmholtz equation
description: scientific article; zbMATH DE number 5816753