Events for 03/29/2021 from all calendars

Industrial and Applied Math

Time: 6:30PM - 7:30PM

Location: Zoom

Speaker: Dr. Chak Shing Lee, Lawrence Livermore National Lab

Title: A multilevel coarsening method for graph Laplacians in mixed form and its applications

Abstract: In this talk, we will discuss a multilevel coarsening method for weighted graph Laplacians formulated in a mixed saddle-point form. In this formulation, there are two sets of degrees of freedom (dofs), which are respectively associated with the vertices and edges of the underlying graph. We construct coarse spaces for both sets of dofs based on aggregation of vertices exploiting local spectral decompositions. The coarse spaces have provable approximation property, and are constructed such that the inf-sup stability on coarse levels is maintained. The coarsening procedure is local with high computation-to-communication ratio, the benefit of which is illustrated in a parallel scaling test. An efficient linear solver for the coarse problems is also developed based on the hybridization technique. For applications of the coarsening method, we focus on graph Laplacians coming from the finite volume discretization problems in oil reservoir simulations. Numerical examples demonstrating its applications in constructing eigensolvers for graph Laplacians, multilevel samplers, multilevel Monte Carlo simulations, and nonlinear multigrid solvers will be presented.