A multi-grid method for a periodic heterogeneous medium in 1-D is presented. Based on the homogenization theory special intergrid connection operators have been developed to imitate 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 < q < 1 depends on the microstructure. This estimate reveals that the rate of convergence increases as q to 0, which corresponds to the increasing material heterogeneity.

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