  An efficient algorithm for solving Poisson's equation in two and three
spatial dimensions is discussed. The algorithm, which is described in detail,
is based on the integral form of Poisson's equation and utilizes spherical
coordinates and an expansion into spherical harmonics. The solver can be
applied to and works well for all problems for which the use of spherical
coordinates is appropriate. We also briefly discuss the implementation of the
algorithm into hydrodynamic codes which are based on a conservative
finite--difference scheme.
