We design a multiscale model reduction framework within the hybridizable discontinuous Galerkin finite element method. Our approach uses local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We propose several multiscale finite element spaces on the coarse edges that provide a reduced dimensional approximation for numerical traces within the HDG framework. We provide a general framework for systematic construction of multiscale trace spaces. Using local snapshots, we avoid high dimensional representation of trace spaces and use some local features of the solution space in constructing a low dimensional trace space. We investigate the solvability and numerically study the performance of the proposed method on a representative number of numerical examples.
|Original language||English (US)|
|Number of pages||14|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|State||Published - Oct 22 2014|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: YE's work is partially supported by the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-FG02-13ER26165, and the DoD Army ARO Project. R. Lazarov's research was supported in part by the National Science Foundation (DMS-1016525).
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Mechanics of Materials
- Mechanical Engineering
- Computational Mechanics
- Computer Science Applications