A general meshsize fourth-order compact difference discretization scheme for 3D Poisson equation
A general meshsize fourth-order compact difference discretization scheme for 3D Poisson equation
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DOI：
10.1016/j.amc.2006.06.028
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发表时间：
2006-12
期刊：
影响因子：
--
通讯作者：
Jie Wang;Weijun Zhong;Jun Zhang
中科院分区：
文献类型：
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作者：
Jie Wang;Weijun Zhong;Jun Zhang
在正则三次区域上，对三维Poisson方程建立了一个四阶紧致差分格式，该格式在不同坐标方向上具有无约束的一般网格。差分格式的推导过程利用了有限差分格式的符号表示，在这种复杂的三维操作中更容易理解。我们使用一个预条件共轭梯度法来解决由此产生的稀疏线性方程组，并验证了所推导的四阶有限差分格式的形式收敛阶。
A fourth-order compact difference scheme with unrestricted general meshsizes in different coordinate directions is derived to discretize three-dimensional Poisson equation on a regular cubic domain. The difference scheme derivation procedure makes use of the symbolic representation of the finite difference schemes and is easier to understand in such complex three-dimensional manipulations. We use a preconditioned conjugate gradient method to solve the resulting sparse linear systems and verify the formal order of convergence of the derived fourth-order finite difference scheme.