## Abstract

In this paper we propose a direct method for the solution of the Poisson equation in rectangular regions. It has an arbitrary order accuracy and low CPU requirements which makes it practical for treating large-scale problems. The method is based on a pseudospectral Fourier approximation and a polynomial subtraction technique. Fast convergence of the Fourier series is achieved by removing the discontinuities at the corner points using polynomial subtraction functions. These functions have the same discontinuities at the corner points as the sought solution. In addition to this, they satisfy the Laplace equation so that the subtraction procedure does not generate nonperiodic, nonhomogeneous terms. The solution of a boundary value problem is obtained in a series form in O(N log N) floating point operations, where N^{2} is the number of grid nodes. Evaluating the solution at all N^{2} interior points requires O(N^{2} log N) operations.

Original language | English |
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Pages (from-to) | 933-952 |

Number of pages | 20 |

Journal | SIAM Journal on Scientific Computing |

Volume | 19 |

Issue number | 3 |

DOIs | |

State | Published - May 1998 |

Externally published | Yes |

## Keywords

- Boundary value problem
- Corner discontinuities
- Poisson equation
- Polynomial subtraction
- Rectangular region
- Spectral method