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