Abstract: A new approach for producing the MG interpolatory formula is proposed on the basis of the defect equation. This new interpolatory formula makes full use of information of coarser grids, and thus has higher accuracy. Numerical experiments for Poisson equation, anisotropic equation, biharmonic equation, and even 3D problem show that the new interpolatory formula improves the asymptotic convergence rate, and reduces the storage capacity and computational time for the AMG method.

Key words: multigrid, defect equation, interpolatory formula, asymptotic convergence rate