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

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    A fourth-order finite difference ...
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    Author
    Wright, Lyndsey
    Advisor
    Bialecki, Bernard
    Date issued
    2013
    Keywords
    Poisson's equation
    polar coordinates
    fourth-order
    Poisson's equation
    Finite differences
    Coordinates, Polar
    Matrices
    Linear systems
    Fourier transformations
    
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    URI
    https://hdl.handle.net/11124/12196
    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.
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