Krylov.jl: Empowering Performance and Portability in High-Performance Computing

Abstract: Explore the capabilities of Krylov methods through Krylov.jl, an advanced Julia-based software crafted for the efficient resolution of linear systems. In this presentation, we delve into the intricacies of Krylov methods, highlighting their distinct advantages over direct methods, particularly in dealing with large, sparse matrices. With a primary focus on portability, we demonstrate Krylov.jl’s seamless adaptability across diverse computing environments, including supercomputers like Frontier and Aurora. The software boasts thirty-five optimized solvers, ensuring high performance and memory efficiency, in-place functionality, GPU compatibility, and support for various floating-point systems (real and complex numbers).

Bio: Dr. Alexis Montoison is an engineer with a background in high-performance computing, having earned his engineering degree from ENSEEIHT in Toulouse, France. Subsequently, he pursued a Ph.D. in applied mathematics at Polytechnique Montréal, focusing on ​“Krylov Methods for Linear Algebra and Polymorphic Implementation”. His main interests are in the theoretical and numerical study of algorithms for continuous nonlinear optimization and linear algebra. His current work is focused on iterative methods working in multiple precisions and different architectures (CPU – GPU).