A duality-based optimization approach for model adaptivity in heterogeneous multiscale problems
This work provides a systematic, goal-oriented method for model adaptivity in multiscale problems, benefiting researchers and practitioners in computational science and engineering who need to balance accuracy and efficiency.
The paper introduces a novel framework for model adaptivity in heterogeneous multiscale problems, using a duality-based optimization approach to minimize local error indicators derived from the Dual Weighted Residual method. Numerical tests on elliptic diffusion and advection-diffusion problems demonstrate the framework's ability to systematically tune effective models without requiring strict a priori knowledge.
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.