10 papers
Multilevel-in-Layer Training for Deep Neural Network Regression
Colin Ponce, Ruipeng Li, Christina Mao +1
A common challenge in regression is that for many problems, the degrees of freedom required for a high-quality solution also allows for overfitting. Regularization is a class of st…
An Aggregation-based Nonlinear Multigrid Solver for Two-phase Flow and Transport in Porous Media
Chak Shing Lee, François P. Hamon, Nicola Castelletto +2
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 framew…
Multilevel Hierarchical Decomposition of Finite Element White Noise with Application to Multilevel Markov Chain Monte Carlo
Hillary R. Fairbanks, Umberto Villa, Panayot S. Vassilevski
In this work we develop a new hierarchical multilevel approach to generate Gaussian random field realizations in an algorithmically scalable manner that is well-suited to incorpora…
Nonlinear multigrid based on local spectral coarsening for heterogeneous diffusion problems
Chak Shing Lee, François Hamon, Nicola Castelletto +2
This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is…
Multilevel spectral coarsening for graph Laplacian problems with application to reservoir simulation
Andrew T. Barker, Stephan V. Gelever, Chak S. Lee +2
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 resulti…
A Condensed Constrained Nonconforming Mortar-based Approach for Preconditioning Finite Element Discretization Problems
Delyan Z. Kalchev, Panayot S. Vassilevski
This paper presents and studies an approach for constructing auxiliary space preconditioners for finite element problems using a constrained nonconforming reformulation, that is ba…