Graduate Student Organization Seminar

Date: October 2, 2019

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Jun Sur Richard Park

Title: Hierarchical multiscale finite element method for multi-continuum media

Abstract: Computing the effective coefficients of the homogenized equations can be expensive because one needs to solve local cell problems for a large number of macroscopic points. We develop a hierarchical approach for solving cell problems at a dense network of macro-scopic points with an essentially optimal computation cost. The method employs the fact that neighboring representative volume elements (RVEs) share similar features; and effective properties of the neighboring RVEs are close to each other. The hierarchical approach reduces computation cost by using different levels of resolution for cell problems at different macroscopic points. We prove rigorously that this hierarchical method achieves the same level of accuracy as that of the full solve where cell problems at every macroscopic point are solved using the FE spaces with the highest level of resolution, but at the essentially optimal computation cost. We present some numerical results that computes effective permeabilities of a two scale multi-continuum system via the numerical solutions of the cell problems. We prove the homogenization convergence for our multiscale multi-continuum system.