Abstract
Motivated by the idea of algebraic multigrid (AMG) method, we take the transpose of bilinear interpolation operator as restriction operator, an improved geometric V-cycle multigrid (IGVMG) method is proposed. By combining the IGVMG method and Chen's extrapolation formula, a new extrapolation multiscale multigrid (EXMMG) method for a second order elliptic problem is constructed. Then the IGVMG method is used to solve the solutions for coarse grid and finest grid, respectively. Chen's extrapolation formula is applied to update the approximate solution of coarse grid, and the cubic interpolation operator is applied to provide a better initial value on fine grid from coarse grid. Some numerical experiments of the EXMMG method are presented, using fourth order compact difference scheme. It is demonstrated that the EXMMG method is effective.
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