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A Fast Poisson Solver of Arbitrary Order Accuracy in Rectangular Regions

Summary: A Fast Poisson Solver of Arbitrary Order Accuracy in
Rectangular Regions
Appeared in SIAM J. Scientific Computing, Vol. 19(3), pp. 933­952, May 1998
A. Averbuch y M. Israeli z L. Vozovoi z
y School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
z Faculty of Computer Science, Technion, Haifa 32000, Israel
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 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 inhomogeneous terms.
The solution of a boundary value problem is obtained in the series form in O(N log N)
floating point operations, where N 2 is the number of grid nodes. Evaluating the solu­
tion at all N 2 interior points requires O(N 2 log N) operations.
1 Introduction


Source: Averbuch, Amir - School of Computer Science, Tel Aviv University


Collections: Computer Technologies and Information Sciences