Summary: A Fast Poisson Solver of Arbitrary Order Accuracy in
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.