| Author | Jacob Fish and Vladimir Belsky |
|---|---|
| Title | Multi-Grid Method for Periodic Heterogeneous Media. Part 1: Convergence Studies for One-Dimensional Case |
| Year | 1994 |
| Journal | Computer Methods in Applied Mechanical Engineering |
| Volume | 126 |
| Pages | 1-16 |
| Abstract | A multi-grid method for a periodic heterogeneous medium in 1-D is presented. Based on the homogenization theory special intergrid transfer operators have been developed to simulate a low frequency response of the differential equations with oscillatory coefficients. The proposed multi-grid method have been proved to have a fast rate of convergence governed by the ratio , where depends on the microstructure. This estimate reveals that the rate of convergence increases as , which corresponds to the increasing material heterogeneity. Numerical results have been found to be in good agreement with the theoretical estimate. |