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

Barker, Andrew T.; Gelever, Stephan V.; Lee, Chak S.; Osborn, Sarah V.; Vassilevski, Panayot S.

doi:10.1137/19m1296343

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

Journal Article · Wed Aug 04 00:00:00 EDT 2021 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/19m1296343· OSTI ID:1824746

Barker, Andrew T. ^[1]; Gelever, Stephan V. ^[2];

^[1]; Osborn, Sarah V. ^[1]; Vassilevski, Panayot S. ^[3]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Portland State Univ., OR (United States)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Portland State Univ., OR (United States)

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.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1824746

Report Number(s):: LLNL-JRNL-795643; 996879

Journal Information:: SIAM Journal on Scientific Computing, Vol. 43, Issue 4; ISSN 1064-8275

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

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58 GEOSCIENCES
97 MATHEMATICS AND COMPUTING
graph Laplacian
algebraic multigrid
finite volume methods
numerical upscaling
multilevel Monte Carlo
full approximation scheme

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

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