A simple compact fourth-order Poisson solver on polar geometry

  • Authors:

  • Ming-Chih Lai

  • Affiliations:

  • Department of Applied Mathematics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 30050, Taiwan, Republic of China

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2002

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Abstract

We present a simple and efficient compact fourth-order Poisson solver in polar coordinates. This solver relies on the truncated Fourier series expansion, where the differential equations of the Fourier coefficients are solved by the compact fourth-order finite difference scheme. By shifting a grid a half mesh away from the origin and incorporating the symmetry constraint of Fourier coefficients, we can easily handle coordinate singularities without pole conditions. The numerical evidence confirms fourth-order accuracy for the problem on an annulus and third-order accuracy for the problem on a disk. In addition, a simple and comparably accurate approximation for the derivatives of the solution is also presented.