A duality-based optimization approach for model adaptivity in heterogeneous multiscale problems
Abstract
This paper introduces a novel framework for model adaptivity in the context of heterogeneous multiscale problems. The framework is based on the idea to interpret model adaptivity as a minimization problem of local error indicators, that are derived in the general context of the Dual Weighted Residual (DWR) method. Based on the optimization approach a post-processing strategy is formulated that lifts the requirement of strict a priori knowledge about applicability and quality of effective models. This allows for the systematic, "goal-oriented" tuning of effective models with respect to a quantity of interest. The framework is tested numerically on elliptic diffusion problems with different types of heterogeneous, random coefficients, as well as an advection-diffusion problem with strong microscopic, random advection field.
Keywords
Cite
@article{arxiv.1611.09437,
title = {A duality-based optimization approach for model adaptivity in heterogeneous multiscale problems},
author = {Matthias Maier and Rolf Rannacher},
journal= {arXiv preprint arXiv:1611.09437},
year = {2017}
}