On comparison of multigrid cycles for poisson solver in polar plane coordinates

Abstract

Fast Multigrid Poisson solvers have been considered essential for developing efficient numerical method solutions in diverse fields. In this paper, we compare fast and simple multigrid methods: V-Cycle, W-Cycle, and F-Cycle to solve Poisson Equation (PE) in polar plane coordinates. The solver is analysed toward different 2n + 1 grid sizes to evaluate its convergence properties, i.e. precision and accuracy, as compared to reference problem of cylindrical annulus. Each multigrid cycle is evaluated based on computation time, convergence error, and relative error. The results show that W-Cycle (γ = 4) gives more optimized solution as Poisson solver in comparison with the other multigrid methods.