Generalized Multiscale Inversion for Heterogeneous Problems

Journal Article · 30 November 2018 · Communications in Computational Physics

DOI: https://doi.org/10.4208/cicp.oa-2017-0184 · OSTI ID:1611506

Chung, Eric T. ^[1]; Efendiev, Yalchin ^[2]; Jin, Bangti ^[3]; Leung, Wing Tat ^[2]; Vasilyeva, Maria ^[2]

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1. The Chinese University of Hong Kong (China); DOE/OSTI
2. Texas A & M Univ., College Station, TX (United States)
3. Univ. College London (United Kingdom)

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 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.

• Research Organization: Texas A & M University, College Station, TX (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: SC0010713
• OSTI ID: 1611506
• Journal Information: Communications in Computational Physics, Journal Name: Communications in Computational Physics Journal Issue: 4 Vol. 25; ISSN 1815-2406
• Publisher: Global Science PressCopyright Statement
• Country of Publication: United States
• Language: English