RT Journal Article
ID 6f301c5b11484f8f
A1 Chung, Eric T.
A1 Efendiev, Yalchin
A1 Leung, Wing Tat
A1 Vasilyeva, Maria
T1 REITERATED MULTISCALE MODEL REDUCTION USING THE GENERALIZED MULTISCALE FINITE ELEMENT METHOD
JF International Journal for Multiscale Computational Engineering
JO JMC
YR 2016
FD 2016-12-01
VO 14
IS 6
SP 535
OP 554
K1 multiscale
K1 flow
K1 adaptive
K1 reiterated
K1 multiscale finite element method
AB Numerical homogenization and multiscale finite element methods construct effective properties on a coarse grid by solving local problems and extracting the average effective properties from these local solutions. In some cases, the
solutions of local problems can be expensive to compute due to scale disparity. In this setting, one can basically apply a homogenization or multiscale method reiteratively to solve for the local problems. This process is known as reiterated homogenization and has many variations in the numerical context. Though the process seems to be a straightforward extension of two-level process, it requires some careful implementation and the concept development for problems without scale separation and high contrast. In this paper, we consider the generalized multiscale finite element method (GMsFEM) and apply it iteratively to construct its multiscale basis functions. The main idea of the GMsFEM is to construct snapshot functions and then extract multiscale basis functions (called offline space) using local spectral decompositions in the snapshot spaces. The extension of this construction to several levels uses snapshots and offline spaces interchangeably to achieve this goal. At each coarse-grid scale, we assume that the offline space is a good approximation of the solution and use all possible offline functions or randomization as boundary conditions and solve the local problems in the offline space at the previous (finer) level, to construct snapshot space. We present an adaptivity strategy and show numerical results for flows in heterogeneous media and in perforated domains.
PB Begell House
LK http://dl.begellhouse.com/journals/61fd1b191cf7e96f,4c6ececa3b8eb842,6f301c5b11484f8f.html