Multigrid method for periodic heterogeneous media Part 1: Convergence studies for one-dimensional case

Abstract A multi-grid method for a periodic heterogeneous medium in 1-D is presented. Based on the homogenization theory, special integrid transfer operators have been developed to simulate a low frequency response of the differential equations with oscillatory coefficients. The proposed multi-grid method has been proved to have a fast rate of convergence governed by the ratio q (4− q ) , where 0