An adaptive cellular updating scheme for the continuous-discontinuous cellular automaton method

The updating scheme is very important for cellular automata, which costs the vast majority of CPU time of the whole calculating process and dramatically influences the convergence rate, and the traditional node sequence scheme is often ineffective. Aimed at this issue, based on the unbalanced nodal force, an adaptive updating scheme for continuous-discontinuous cellular automaton method is proposed in this paper. The cell whose unbalanced force is maximum is the first updating cell, and the next one is its neighbors whose unbalanced force is also maximum in all remain neighbors, and do the updating operation according to this scheme until the updating for all cells is finished. Theory and convergence of the present scheme is studied, then we can get the maximum calculating efficiency, and the computational expanse can be greatly improved. Some examples by different iteration schemes are shown to demonstrate that the present scheme is efficient and time saving.