LAUSR

Abstract Because of its local property, cellular automaton method has been widely applied in different subjects, but the main problem is that the cellular updating is time-consuming. In order to improve its calculation efficiency, a fast successive relaxation updating method is proposed in this paper. Firstly, an accelerating factor ω is defined, and a fast successive relaxation updating theory and its corresponding convergence conditions are developed. In each updating step, the displacement increment is enlarged ω times as a new increment to replace the old one, similarly, the nodal forces for its neighbors caused by this displacement increment are also enlarged by the same accelerating factor, and do those updating operations until the convergence is achieved. By this method, the convergence rate is greatly improved, by a suitable accelerating factor, 90 to 98% of iteration steps are decreased compared to that of the traditional method. Besides, the influence factors for the accelerating factor are studied, and numerical studies show that the suitable accelerating factor is 1.85