Fast spectral solver for Poisson equation in an annular domain

A simple and efficient spectral method is formulated to solve Poisson equation in an annular domain. The solver relies on the Fourier expansion, where the differential equations for the Fourier coefficients are solved using an ultraspherical spectral method. For a domain with N grid points in the polar direction and M grid points in the radial direction, the solver only requires O(NM log(2) N) arithmetic operations.