Iterative methods for solution of diffusion problems in r--and-thgr; geometry

Abstract

This paper compares three iteration methods for computing approximately a steady-state solution of the diffusion equation, in a pie-shaped region of the plane, using a finite mesh based on the r--and-thgr; coordinate system. The methods are successive line overrelaxation along curves of constant radius, successive line relaxation along radii, and alternating-direction-implicit iteration. It is concluded that the first-named of these three methods is superior, in that it is expected to converge faster for most problems.