基于二维泊松方程六阶紧致格式的多重网格方法

Sixth-order compact multigrid method for the 2D Poisson equation

利用六阶紧致差分格式、结合多重网格V循环算法求解了二维泊松方程的Dirichlet边值问题,并用不同的松弛算子与四阶精度格式的多重网格方法进行了比较. 计算结果表明,该方法在不明显增加计算量的前提下较四阶精度格式的多重网格方法具有更好的精确度和收敛阶,且ZLGS迭代不论对四阶精度还是对六阶精度格式的多重网格算法,都是一种较其他松弛算子更加有效的“光滑剂”.

A sixth-order compact difference scheme and multigrid V-cycle algorithm are employed to solve the two-dimensional Poisson equation with Dirichlet boundary conditions. This scheme, along with several different relaxation operators, is compared with the fourth-order formula to show the dramatic improvement in both computed accuracy and convergence rate without distinctly increasing computational cost. Further more, Zebra Line Gauss-Seidel (ZLGS) relaxation is a more efficient smoother than other relaxation operators for no matter fourth-order or sixth-orer formula with multigrid method.