2024 Keynote Talks

Dr. Christian Glusa at Sandia National Laboratory

Title: Scalable methods for nonlocal models

Abstract: The naive discretization of nonlocal operators leads to matrices with significant density, as compared to classical PDEs. This makes the efficient solution of nonlocal models a challenging task. In this presentation, we will discuss ongoing research into efficient hierarchical matrix assembly and geometric and algebraic multigrid preconditioners that are suitable for nonlocal models.

Dr. Duygu Vargun at Oak Ridge National Laboratory

Title: Utilizing Iterative and Observational Data to Accelerate Nonlinear Solvers in Fluid Flow Simulations

Abstract:.  This talk explores two distinct approaches to accelerate nonlinear solvers for fluid flow simulations by incorporating iterative and observational data: Anderson acceleration (AA) and continuous data assimilation (CDA). AA enhances the convergence of fixed-point iterations by utilizing data from previous iterations for extrapolation. CDA, on the other hand, incorporates observational data from true steady-state solutions to guide the iterative process. We apply AA to fixed-point iterations for Newtonian and non-Newtonian fluid models, significantly improving robustness and reducing the number of iterations. Additionally, CDA enables data integration through multiple mechanisms, leading to improved performance and enhanced convergence properties compared to conventional iterative nonlinear solvers.