Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
An Aggregation-Based Nonlinear Multigrid Solver For Two-Phase Flow And Transport In Porous Media, Chak Shing Lee, Francois Hamon, Nicola Castelletto, Panayot S. Vassilevski, Joshua A. White
An Aggregation-Based Nonlinear Multigrid Solver For Two-Phase Flow And Transport In Porous Media, Chak Shing Lee, Francois Hamon, Nicola Castelletto, Panayot S. Vassilevski, Joshua A. White
Mathematics and Statistics Faculty Publications and Presentations
A nonlinear multigrid solver for two-phase flow and transport in a mixed fractional-flow velocity-pressure-saturation formulation is proposed. The solver, which is under the framework of the full approximation scheme (FAS), extends our previous work on nonlinear multigrid for heterogeneous diffusion problems. The coarse spaces in the multigrid hierarchy are constructed by first aggregating degrees of freedom, and then solving some local flow problems. The mixed formulation and the choice of coarse spaces allow us to assemble the coarse problems without visiting finer levels during the solving phase, which is crucial for the scalability of multigrid methods. Specifically, a …
An Algorithm For Identifying Eigenvectors Exhibiting Strong Spatial Localization, Jeffrey S. Ovall, Robyn Reid
An Algorithm For Identifying Eigenvectors Exhibiting Strong Spatial Localization, Jeffrey S. Ovall, Robyn Reid
Mathematics and Statistics Faculty Publications and Presentations
We introduce an approach for exploring eigenvector localization phenomena for a class of (unbounded) selfadjoint operators. More specifically, given a target region and a tolerance, the algorithm identifies candidate eigenpairs for which the eigenvector is expected to be localized in the target region to within that tolerance. Theoretical results, together with detailed numerical illustrations of them, are provided that support our algorithm. A partial realization of the algorithm is described and tested, providing a proof of concept for the approach.