A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems

Handle URI:
http://hdl.handle.net/10754/566068
Title:
A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems
Authors:
Efendiev, Yalchin R. ( 0000-0001-9626-303X ) ; Lazarov, Raytcho D.; Moon, Minam; Shi, Ke
Abstract:
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.
KAUST Department:
Numerical Porous Media SRI Center (NumPor)
Publisher:
Elsevier BV
Journal:
Computer Methods in Applied Mechanics and Engineering
Issue Date:
Aug-2015
DOI:
10.1016/j.cma.2014.09.036
Type:
Article
ISSN:
00457825
Sponsors:
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).
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorEfendiev, Yalchin R.en
dc.contributor.authorLazarov, Raytcho D.en
dc.contributor.authorMoon, Minamen
dc.contributor.authorShi, Keen
dc.date.accessioned2015-08-12T09:26:53Zen
dc.date.available2015-08-12T09:26:53Zen
dc.date.issued2015-08en
dc.identifier.issn00457825en
dc.identifier.doi10.1016/j.cma.2014.09.036en
dc.identifier.urihttp://hdl.handle.net/10754/566068en
dc.description.abstractWe 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.en
dc.description.sponsorshipYE'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).en
dc.publisherElsevier BVen
dc.subjectHybridizable discontinuous Galerkinen
dc.subjectMultiscale finite element methoden
dc.subjectSpectral basis functionen
dc.titleA spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problemsen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.identifier.journalComputer Methods in Applied Mechanics and Engineeringen
dc.contributor.institutionDepartment of Mathematics, Texas A and M University, College Station, TX 77843, USAen
kaust.authorEfendiev, Yalchin R.en
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