A DUALITY-BASED OPTIMIZATION APPROACH FOR MODEL ADAPTIVITY IN HETEROGENEOUS MULTISCALE PROBLEMS Academic Article

abstract

• 2018 Society for Industrial and Applied Mathematics. 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.

authors

• Maier, Matthias Sebastian

published proceedings

• MULTISCALE MODELING & SIMULATION

author list (cited authors)

• Maier, M., & Rannacher, R.

citation count

• 5

complete list of authors

• Maier, Matthias||Rannacher, Rolf

publication date

• January 2018

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM: Multiscale Modeling and Simulation  Journal

keywords

• Dwr Method
• Finite Element Method
• Goal-oriented Adaptivity
• Mesh Adaptation
• Model Adaptation
• Model Optimization

Digital Object Identifier (DOI)

• 10.1137/16M1105670

start page

• 412

end page

• 428

volume

• 16

issue

• 1

URL

• http://dx.doi.org/10.1137/16m1105670