An ADMM-AHM integrated approach for problems with rapidly oscillating coefficients

The Advection-Diffusion Multilayer Method (ADMM) emerged to address the solution of advection-diffusion equations with variable coefficients in the context of pollutant dispersion modeling. The ADMM is based on the piecewise-constant approximation of the variable coefficients and the application of the Laplace transform. Applications of ADMM in other areas are potentially relevant for modeling the behavior of heterogeneous media. However, if such heterogeneity is characterized by rapidly oscillating coefficients, the direct application of the ADMM would increase the computational effort needed, as it would require a very fine discretization of the domain. In order to overcome such a drawback, in this contribution, an alternative approach combining the ADMM with the Asymptotic Homogenization Method (AHM) is presented. The ADMM-AHM integrated approach is compared to the direct application of the ADMM in order to assess the accuracy of the estimations of the solution of the original problem, and the computational efficiency. © 2019 Trans Tech Publications Ltd, Switzerland.