Computational fluid models often require the solution of Poisson's equation in models based on a stream function, velocity potential, vorticity, or the pressure of an incompressible fluid. In time-dependent models, Poisson's equation is solved at each time step and contributes substantially to the overall computing time. Prior to the advent of Fourier and cyclic reduction methods, the solution of Poisson's equation could take 70-80% of the total computer time. However, using these methods, the solution of Poisson's equation takes about 10% of the computing time. In addition, the solution is accurate to roundoff error and a convergence test is not required. Solutions can be obtained for several boundary conditions including the specification of the solution, its normal derivative or periodic boundary conditions. Solutions can be computed on a rectangle in various coordinate systems including Cartesian, cylindrical, spherical or any separable coordinate system. A least squares solution can be obtained when a solution does not exist in the traditional sense. Here we provide an introduction to the methods and their use for solving Poisson's equation. We also discuss the availability of software and the implementation of the methods on multiprocessor computers.

• Download a PostScript version of the original manuscript, 84K
• Download the PDF version, 36K
• Back to Publications
• Swarztrauber's Home Page