A FAST POISSON SOLVER OF ARBITRARY ORDER ACCURACY IN RECTANGULAR REGIONS

In this paper we propose a direct method for the solution of the Poiss on 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 approx imation and a polynomial subtraction technique. Fast convergence of th e Fourier series is achieved by removing the discontinuities at the co rner points using polynomial subtraction functions. These functions ha ve the same discontinuities at the corner points as the sought solutio n. In addition to this, they satisfy the Laplace equation so that the subtraction procedure does not generate nonperiodic, nonhomogeneous te rms. 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 requ ires O(N-2 log N) operations.