Thumbnail Image
Publication

Fourth-order finite difference scheme for Poisson's equation in polar coordinates on the unit disc, A

Wright, Lyndsey
Citations
Altmetric:
Advisor
Bialecki, Bernard
Editor
Date
Date Issued
2013
Date Submitted
Keywords
Poisson's equation
 polar coordinates
 fourth-order
 Poisson's equation
 Finite differences
 Coordinates, Polar
 Matrices
 Linear systems
 Fourier transformations
Collections
2010-2019 - Mines Theses & Dissertations
Show all metadata
Files
Thumbnail Image
A fourth-order finite difference scheme for Poisson's equation in polar coordinates on the unit disc
Adobe PDF, 267.63 KB
Research Projects
Organizational Units
Journal Issue
URI
https://hdl.handle.net/11124/12196
Embargo Expires
2014-12-01
Abstract
We solve Poisson's Equation on the unit disc in polar coordinates using a fourth-order finite difference method. We use a half-point shift in the r direction, in order to avoid approximating the solution at r = 0. We derive a new fourth-order accurate finite difference method from analysis of the truncation error of the well-known second-order scheme. The resulting linear system is solved very efficiently (with cost almost proportional to the number of unknowns) using a combination of a Matrix Diagonalization Algorithm and Fast Fourier Transforms.
Associated Publications
Rights
Copyright of the original work is retained by the author.
Embedded videos