Optimizations of Fuzzy Controller for Solving Poisson Equations with Fast Convergence

Abstract

Fuzzy control was applied to speed up the convergence of a Poisson equation solver for the numerical calculations of incompressible fluid. The optimizations of the control rule were carried out by means of a hybrid method of the conjugate gradient method and the improved random walk method. The residual of the equation and the relaxation parameter are employed as input for the controller. It is found that this method is effective in obtaining fast convergence. Moreover, it is clarified that this control does not affect the bifurcation characteristics of the solution. The changes in optimized relaxation parameter are similar to Bang-Bang control.