Keyes works at the algorithmic interface between parallel computing and the numerical analysis of partial differential equations, with a focus on implicit scalable solvers for emerging architectures and their use in the many large-scale applications in energy and environment governed by conservation laws that demand high performance because of high resolution, high dimension, high fidelity physical models, or the "multi-solve" requirements of optimization, control, sensitivity analysis, inverse problems, data assimilation, or uncertainty quantification. He has named and contributed to Newton-Krylov-Schwarz (NKS), Additive Schwarz Preconditioned Inexact Newton (ASPIN), and Algebraic Fast Multipole (AFM) methods for large sparse linear and nonlinear systems arising from PDEs. Through the ECRC, he now works on meeting the requirements of drastic reductions in communication and synchronization, increases in concurrency for cores sharing memory locally, local load redistribution, and algorithm-based fault tolerance for these and other algorithms.

Applied Mathematics and Computational Science, Computer Science, Extreme Computing