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Vasilyeva, Maria

Publications and source records attributed to Vasilyeva, Maria.

3 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Scalable Multilevel Uncertainty Quantification Concepts for Extreme-Scale Multiscale Problems

Our work in this project is aimed at making fundamental advances in multilevel and multiscale methods for problems with uncertainties related to flows in porous media. The main thrust of this research is to develop a systematic multiscale, multilevel parallel approaches for problems with uncertainties and use them in the uncertainty quantification. A key emphasis is on problems without an apparent scale separation in space, time, and uncertainty spaces. Multiscale solution methods are currently under active investigation. However, the develop- ment of multiscale methods for problems with uncertainties where the scales and uncertainties are tightly coupled is a research area that is less explored. During this project, we have made some significant contributions to the developments of multiscale methods, the uncertainty quantification for multiscale methods, multiscale model learning, uncertainty quantification in inverse problems, and applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Generalized Multiscale Inversion for Heterogeneous Problems

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.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗