A note on cyclic reduction poisson solvers with application to bioconvective phenomena problems

This paper examines a class of algorithms related to the cyclic odd-even reduction for solving the discrete Poisson equation with Direchlet boundary condition over a rectangle. The work motivated by a study of bioconvective phenomena simulation. Our extension of the error analysis originally due to Buzbee et al. leads to some new theoretical results useful for judicious use of these algorithms. In a typical large-scale numerical simulation a modified Buneman algorithm with appropriate choice of relevant parameters is shown to be more effective as a Poisson solver than commonly used iterative ones.