TY - JOUR
T1 - A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems
AU - Efendiev, Yalchin R.
AU - Lazarov, Raytcho D.
AU - Moon, Minam
AU - Shi, Ke
N1 - KAUST 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).
PY - 2014/10/22
Y1 - 2014/10/22
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/566068
UR - https://manuscript.elsevier.com/S0045782514003594/pdf/S0045782514003594.pdf
UR - http://www.scopus.com/inward/record.url?scp=84939995475&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2014.09.036
DO - 10.1016/j.cma.2014.09.036
M3 - Article
SN - 0045-7825
VL - 292
SP - 243
EP - 256
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -