A duality-based optimization approach for model adaptivity in heterogeneous multiscale problems
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...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2018
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| In: |
Multiscale modeling & simulation
Year: 2018, Volume: 16, Issue: 1, Pages: 412-428 |
| ISSN: | 1540-3467 |
| DOI: | 10.1137/16M1105670 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1137/16M1105670 Verlag, Volltext: https://epubs.siam.org/doi/abs/10.1137/16M1105670 
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| Author Notes: | Matthias Maier and Rolf Rannacher |
MARC
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| 520 | |a 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. | ||
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