|Office:||Clements Hall 139|
Ph.D. 2003, Rice University
Applied Mathematics pertaining to Scientific Computation (large scale parallel, multi-physics, nonlinear, PDE systems) and Numerical Analysis (constrained evolution systems, iterative linear and nonlinear solvers, optimization). Application areas include plasma physics, astrophysics, cosmology, and materials science.
Professor Reynolds' research focuses on numerical methods of relevance to large scale scientific computing applications involving the nonlinear interaction of multiple physical processes, typically modeled using systems of partial differential equations (PDE). Such work aims to allow mathematical insight and innovation to impact the physical, biological and engineering sciences through the incorporation of increased realism into mathematical modeling systems, the development of increasingly robust and accurate numerical methods for solving these mathematical models, and the invention of computational algorithms to implement these numerical methods on increasingly large-scale computational hardware.
Specifically, Professor Reynolds investigates three fundamental applied mathematics issues: accurate modeling of physical systems involving disparate time and space scales, the development and use of highly-accurate and efficient time evolution algorithms for stiff multi-rate problems, and the investigation of discretization and solution methods that retain constraint-preserving properties of PDE models. To this end, Professor Reynolds relies on his expertise in large scale parallel computation as well as a broad range of numerical analysis techniques, including space-time discretization approaches for PDE systems and iterative solution approaches for nonlinear and linear systems of equations.
Professor Reynolds collaborates with scientists at the University of California San Diego, Columbia University, SUNY Stony Brook, Lawrence Livermore National Laboratory, Princeton Plasma Physics Laboratory, the University of Neuchatel (Switzerland), and others. His published work has appeared in SIAM Journal of Scientific Computing, Journal of Computational Physics, Computational Methods in Applied Mechanics and Engineering, Continuum Mechanics and Thermodynamics, Systems and Control Letters, Future Generation Computer Systems, Lecture Notes in Computer Science, ACM Transactions on Mathematical Software, Journal of Physics: Conference Series, Proceedings of SPIE, andProceedings of ENUMATH.