关键词: 粗化算法, 插值算子, 代数三重网格法, 椭圆方程

Abstract: In order to realize the optimal selection of the V-cycle of the multigrid method and improve the convergence accuracy and speed under the smooth degree, a V-type algebraic triple grid method for solving elliptic equations is proposed based on the coarsening
algorithm of matrix atlas and algebraic interpolation operator. Through numerical analysis, the computational performance of V-cycle
algorithm and V-type algebraic triple grid method is compared. The results show that the number of iterations of the V-cycle algorithm
is positively correlated with the solution scale. When the number of iterations is 4 and the mesh generation step size is 1/224, the energy error of the V-type algebraic triple grid method is only 4.781 8 × 10-8, and the CPU time consumption is 284.294 s. Compared with the V-cycle algorithm, the new algorithm has less computation, higher calculation accuracy and shorter calculation time.

Key words: coarsening algorithm, interpolation operator, algebraic triple grid method, elliptic equation