Adaptive Algorithm For Choosing Iterative Parameters With The Best Cost-effective In ECMG Method

Cascadic multigrid method (CMG) has been studied much after it was proposed by Bornemann for its simple calculation format. Economical cascadic multigrid (ECMG) was proposed recently by Shi Zhongci et al.. Economical cascadic multigrid greatly reduces complexity and remains the same accuracy compared with CMG. The main ingredient of the ECMG method is a new criteria for choosing the smoothing steps on each level as following.The ECMG method is convergent and accurate in theory whatever the parameters m_and m₀ are. But in actual calculation neither the complexity nor the accuracy of the ECMG method is not good if parameters are selected not well. In order to solve this problem, we make some study about the parameters in this paper.In this paper adaptive choosing iterative parameters algorithm for ECMG is proposed based on ECMG method. We first collect information of the parameters m_, m₀ and energy norm anorm and error accuracy by numerical experiments. Secondly, we discover the function about parameters m_, m₀ and the levels L. At last, we propose the adaptive algorithm for choosing iterative parameters with the best-effective in ECMG method.