A multiresolution approach to homogenization and effective modal analysis of complex boundary value problems

We apply multiresolution techniques to study the effective properties of bo undary value problems. Conditions under which boundary values are preserved in the effective (homogenized) formulation are developed and discussed. Re lations between the eigenfunctions and eigenvalues of the generic formulati on and those of the effective formulation are explored and their dependence on the micro-scale is studied. Applications to the construction of effecti ve Green functions in a complex lamination are discussed. The analytic resu lts are demonstrated via numerical computations.