Abstract: Multigrid algorithms based on the finite difference method of three dimensional（3D） convection diffusion equation are studied.The second order central difference and the fourth order compact difference schemes in general meth-size are presented.A partial semi-coarsening multigrid strategy is designed to solve the resulting sparse linear systems and the corresponding restriction and interpolation operators are also constructed.Finally，the computational results are compared with those computed by traditional multigrid method under full-coarsening strategy in equal mesh-size.The numerical experiments verify that the present partial semicoarsening multigrid method with general mesh-size is more accurate and efficient than the traditional multigrid method with equal mesh-size discretization for anisotropic problems.

摘要： 研究了三维对流扩散方程基于有限差分法的多重网格算法。差分格式采用一般网格步长下的二阶中心差分格式和四阶紧致差分格式，建立了与两种格式相适应的部分半粗化的多重网格算法，构造了相应的限制算子和插值算子，并与传统的等距网格下的完全粗化的多重网格算法进行了比较。数值研究结果表明，对于各向异性问题，一般网格步长下的部分半粗化多重网格算法比等距网格下的完全粗化多重网格算法具有个更高的精度和更好的收敛效率。