@Article{CiCP-25-1213,
author = {Eric T. Chung, Yalchin Efendiev, Bangti Jin, Wing Tat Leung and Maria Vasilyeva},
title = {Generalized Multiscale Inversion for Heterogeneous Problems},
journal = {Communications in Computational Physics},
year = {2018},
volume = {25},
number = {4},
pages = {1213--1234},
abstract = {<p style="text-align: justify;">In this work, we propose a generalized multiscale inversion algorithm for
heterogeneous problems that aims at solving an inverse problem on a computational
coarse grid. Previous inversion techniques for multiscale problems seek a coarse-grid
medium properties, e.g., permeability and conductivity, and by doing so, they assume
that there exists a homogenized representation of the underlying fine-scale permeability field on a coarse grid. Generally such assumptions do not hold for highly heterogeneous fields, e.g., fracture media or channelized fields, where the width of channels
are very small compared to the scale of coarse grids. In these cases, grid refinement
can lead to many degrees of freedom, and thus numerically unattractive to apply. The
proposed algorithm is based on the Generalized Multiscale Finite Element Method
(GMsFEM), which uses local spectral problems to identify non-localized features, i.e.,
channels (high-conductivity inclusions that connect the boundaries of the coarse-grid
block). The inclusion of these features in the coarse space enables one to achieve a
good accuracy. The approach is valid under the assumption that the solution can be
well represented in a reduced-dimensional space spanned by multiscale basis functions. In practice, these basis functions are non-observable as we do not identify the
fine-scale features of the permeability field. Our inversion algorithm finds the discretization parameters of the resulting system on the coarse grid. By doing so, we&nbsp;identify the appropriate coarse-grid parameters representing the permeability field instead of fine-grid permeability field. We illustrate the potential of the approach by
numerical results for fractured media.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2017-0184},
url = {http://global-sci.org/intro/article_detail/cicp/12896.html}
}