新外推完全多重网格法

New Extrapolation Full Multigrid Method

使用新外推公式和高阶插值算子,为相邻细层提供好的初值,对初值使用磨光算子磨光几次后,再调用V型多重网格法求得该层数值解,构造了基于四阶紧致差分格式的新外推完全多重网格法.数值实验表明,与对比算法相比,新算法迭代次数少、计算时间短、稳健性强.

Based on a fourth order compact different scheme, the new extrapolation full multigrid （EXFMG） method is proposed. The new extrapolation formula and high order in- terpolation operator are applied to interpolate a initial value on fine grid. Then the smoothing operator and V-Cycle multigrid method are applied to compute the approximate solution on the grid. Numerical experiments illustrated the new method can solve the examples with highly accurate solution and keep the low cpu cost and high robust, compared with the other methods we tested.