Multigrid method and fourth-order compact difference discretization scheme with unequal meshsizes for 3D poisson equation

作者：Ge, Yongbin^*

来源：Journal of Computational Physics, 2010, 229(18): 6381-6391.

DOI：10.1016/j.jcp.2010.04.048

• 3D Poisson equation
• Compact difference scheme
• Unequal meshsizes
• Multigrid method
• Partial semi-coarsening

A fourth-order compact difference discretization scheme with unequal meshsizes in different coordinate directions is employed to solve a three-dimensional (3D) Poisson equation on a cubic domain. Two multgrid methods are developed to solve the resulting sparse linear systems. One is to use the full-coarsening multigrid method with plane Gauss-Seidel relaxation, which uses line Gauss-Seidel relaxation to compute each planewise solution. The other is to construct a partial semi-coarsening multigrid method with the traditional point or plane Gauss-Seidel relaxations. Numerical experiments are conducted to test the computed accuracy of the fourth-order compact difference scheme and the computational efficiency of the multigrid methods with the fourth-order compact difference scheme.

• 出版日期2010-9-1
• 单位宁夏大学