A High Convergence Rate Solution Method, the Residual Cutting Algorithm, in Iterative Solution of Poisson’s Equation

In most numerical approaches, the boundary value problems of elliptic partial differential equations are discretized and reduced to finite difference equations; then the huge matrix is solved using the appropriate numerical procedure. However, the numerical methods available, such as SOR, CG [1], ADI [2], and the multigrid method [3,4], are not accurate enough, and the rate of convergence is low for three-dimensional actual engineering applications, especially in Neumann type boundary value problems [5].