Multilevel Spectral Coarsening for Graph Laplacian Problems with Application to Reservoir Simulation

We extend previously developed two-level coarsening procedures for graph Laplacian problems written in a mixed saddle point form to the fully recursive multilevel case. The resulting hierarchy of discretizations gives rise to a hierarchy of upscaled models, in the sense that they provide approximati...

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Bibliographic Details
Published in:SIAM journal on scientific computing 2021-01, Vol.43 (4), p.A2737-A2765
Main Authors: Barker, Andrew T., Gelever, Stephan V., Lee, Chak S., Osborn, Sarah V., Vassilevski, Panayot S.
Format: Article
Language:English
Subjects:
algebraic multigrid
finite volume methods
full approximation scheme
GEOSCIENCES
graph Laplacian
MATHEMATICS AND COMPUTING
multilevel Monte Carlo
numerical upscaling
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Summary:We extend previously developed two-level coarsening procedures for graph Laplacian problems written in a mixed saddle point form to the fully recursive multilevel case. The resulting hierarchy of discretizations gives rise to a hierarchy of upscaled models, in the sense that they provide approximation in the natural norms (in the mixed setting). This property enables us to utilize them in three applications: (i) as an accurate reduced model, (ii) as a tool in multilevel Monte Carlo simulations (in application to finite volume discretizations), and (iii) for providing a sequence of nonlinear operators in a full approximation scheme for solving nonlinear pressure equations discretized by the conservative two-point flux approximation. Finally, we illustrate the potential of the proposed multilevel technique in all three applications on a number of popular benchmark problems used in reservoir simulation.
ISSN:1064-8275
1095-7197
DOI:10.1137/19M1296343