MULTIGRID METHOD FOR PERIODIC HETEROGENEOUS MEDIA .2. MULTISCALE MODELING AND QUALITY-CONTROL IN MULTIDIMENSIONAL CASE

A multi-grid method for a periodic heterogeneous medium in multidimens ions is developed. Based on the homogenization theory, special intergr id 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 c omputational model consisting of the finite element mesh entirely cons tructed on the microscale in the regions identified by the idealizatio n error indicators, while elsewhere, the modeling level is only suffic ient to capture the response of homogenized medium. Numerical experime nts show the usefulness of the proposed adaptive multi-level procedure for predicting a detailed response of composite specimens.