Comparison of preconditioning techniques for solving linear systems arising from the fourth order approximation of the three-dimensional elliptic equation

In this article, we introduce a suitable preconditioner for the class of fourth order approximations employed for solving the elliptic partial differential equations Auxx + Buyy + Cuzz = f(x, y, z, u, ux, uy, uz), where A, B and C are constants. Numerical results are given to show the efficiency of the presented approach.