Sixth order compact scheme combined with multigrid method and extrapolation technique for 2D poisson equation
Sixth order compact scheme combined with multigrid method and extrapolation technique for 2D poisson equation
复制标题
DOI：
10.1016/j.jcp.2008.09.002
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Yin Wang;Jun Zhang
中科院分区：
文献类型：
--
作者：
Yin Wang;Jun Zhang
我们开发了六阶有限差分离散化策略来求解二维泊松方程，该策略基于四阶紧凑离散化、多重网格方法、Richardson 外推技术和基于算子的插值方案。我们使用多重网格 V-Cycle 过程来构建多尺度多重网格算法，该算法类似于完整多重网格方法 (FMG)。多重网格计算在细网格和粗网格上产生四阶精确解。使用理查森外推技术计算六阶精确粗网格解。然后我们应用基于算子的插值方案来计算精细网格上的六阶精确解。数值实验显示了我们的新方法的求解精度和计算效率，与孙张使用交替方向隐式（ADI）方法的六阶理查森外推紧凑（REC）离散化策略和使用多重网格方法的标准四阶紧凑差分（FOC）方案进行了比较。
We develop a sixth order finite difference discretization strategy to solve the two dimensional Poisson equation, which is based on the fourth order compact discretization, multigrid method, Richardson extrapolation technique, and an operator based interpolation scheme. We use multigrid V-Cycle procedure to build our multiscale multigrid algorithm, which is similar to the full multigrid method (FMG). The multigrid computation yields fourth order accurate solution on both the fine grid and the coarse grid. A sixth order accurate coarse grid solution is computed by using the Richardson extrapolation technique. Then we apply our operator based interpolation scheme to compute sixth order accurate solution on the fine grid. Numerical experiments are conducted to show the solution accuracy and the computational efficiency of our new method, compared to Sun–Zhang’s sixth order Richardson extrapolation compact (REC) discretization strategy using Alternating Direction Implicit (ADI) method and the standard fourth order compact difference (FOC) scheme using a multigrid method.