Abstract:
This talk focuses on recent developments in hypre, a high-performance library for solving large, sparse linear systems, widely used in computational science and engineering. We highlight advances in the Multigrid Reduction (MGR) framework, a general-purpose preconditioner designed to solve complex multiphysics problems, such as subsurface fluid flow and poromechanics. These problems are often tightly coupled, leading to non-symmetric and ill-conditioned linear systems that are challenging to solve efficiently.
Fully implicit methods are typically the most effective approach for such systems, but their performance depends heavily on the availability of robust preconditioners that can accelerate convergence. MGR can be viewed as a Schur-complement based framework that is designed to be highly flexible, allowing it to accommodate information about different types of physical interactions in a multilevel preconditioner.
We will discuss how recent developments in hypre have enhanced the scalability and effectiveness of the MGR framework, enabling it to take better advantage of modern high-performance computing architectures, including Lassen, Lawrence Livermore National Laboratory (LLNL)) and Frontier, Oak Ridge National Laboratory(ORNL). We will demonstrate its application in real-world subsurface flow simulations, showcasing its ability to efficiently solve coupled multiphysics problems on Frontier containing up to billions of degrees of freedom.
Speaker’s Bio:
Victor A. P. Magri is a computational mathematician at the Center for Applied Scientific Computing at LLNL, contributing to several high-impact scientific computing projects. He plays a key role in the development of hypre, a widely used library of high-performance solvers and preconditioners for large sparse linear systems, focusing on multigrid solvers such as SSAMG, MGR, and BoomerAMG across hypre’s structured, semi-structured, and linear-algebraic system interfaces. Victor also contributes with linear solver support to GEOS, a multiphysics simulation platform for modeling underground carbon storage and other subsurface processes. Recently, he expanded his work to include supporting linear solvers for liquid-metal magnetohydrodynamics simulations in Vertex, a multiphysics code developed at ORNL, as part of a SciDAC project focused on plasma simulation and fusion energy research. Victor earned his Ph.D. in Civil Engineering, specializing in numerical analysis, from the University of Padua, Italy, in 2019, and holds both an M.S. and B.S. in Mechanical Engineering from the Federal University of Santa Catarina, Brazil. His research interests include multigrid methods, preconditioning techniques, multiphysics simulations, scientific data compression, and high-performance computing.
