A duality-based optimization approach for model adaptivity in heterogeneous multiscale problems

• Verfasst von: Maier, Matthias [VerfasserIn]
• Verfasst von: Rannacher, Rolf [VerfasserIn]
• Titel: A duality-based optimization approach for model adaptivity in heterogeneous multiscale problems
• Verf.angabe: Matthias Maier and Rolf Rannacher
• Umfang: 17 S.
• Fussnoten: Gesehen am 28.05.2018
• Titel Quelle: Enthalten in: Multiscale modeling & simulation
• Jahr Quelle: 2018
• Band/Heft Quelle: 16(2018), 1, S. 412-428
• ISSN Quelle: 1540-3467
• DOI: doi:10.1137/16M1105670
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1575771780

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 postprocessing 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 a strong microscopic, random advection field.