Multi-grid Method for Periodic Heterogeneous Media. Part 2: Multiscale Modeling and Quality Control in Multidimensional Case

A multi-grid method for a periodic heterogeneous medium in multidimensions is developed. Based on the homogenization theory special intergrid transfer operators have been developed to simulate a low frequency response of the boundary value problem with oscillatory coefficients. An adaptive strategy is developed to form a nearly optimal two-scale computational model consisting of the finite element mesh entirely constructed on the microscale in the regions identified by the idealization error indicators, while elsewhere, the modeling level is only sufficient to capture the response of homogenized medium. Numerical experiments show the usefulness of the proposed adaptive multi-level procedure for predicting a detailed response of composite specimens.