Spectral Upscaling for Graph Laplacian Problems with Application to Reservoir Simulation

Barker, Andrew T.; Lee, Chak S.; Vassilevski, Panayot S.

doi:10.1137/16M1077581

Spectral Upscaling for Graph Laplacian Problems with Application to Reservoir Simulation

Journal Article · Thu Oct 26 00:00:00 EDT 2017 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/16M1077581· OSTI ID:1438732

Barker, Andrew T. ^[1]; Lee, Chak S. ^[1]; Vassilevski, Panayot S. ^[2]

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

Here, we consider coarsening procedures for graph Laplacian problems written in a mixed saddle-point form. In that form, in addition to the original (vertex) degrees of freedom (dofs), we also have edge degrees of freedom. We extend previously developed aggregation-based coarsening procedures applied to both sets of dofs to now allow more than one coarse vertex dof per aggregate. Those dofs are selected as certain eigenvectors of local graph Laplacians associated with each aggregate. Additionally, we coarsen the edge dofs by using traces of the discrete gradients of the already constructed coarse vertex dofs. These traces are defined on the interface edges that connect any two adjacent aggregates. The overall procedure is a modification of the spectral upscaling procedure developed in for the mixed finite element discretization of diffusion type PDEs which has the important property of maintaining inf-sup stability on coarse levels and having provable approximation properties. We consider applications to partitioning a general graph and to a finite volume discretization interpreted as a graph Laplacian, developing consistent and accurate coarse-scale models of a fine-scale problem.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1438732

Report Number(s):: LLNL-JRNL--693123

Journal Information:: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 5 Vol. 39; ISSN 1064-8275

Publisher:: SIAMCopyright Statement

Country of Publication:: United States

Language:: English

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