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Research:

Applied Mathematics pertaining to Scientific Computation (large scale parallel, multi-physics, nonlinear, PDE systems) and Numerical Analysis (multirate time integration, iterative linear and nonlinear solvers). Application areas include climate, plasma physics, cosmology, and materials science.

In recent decades computation has rapidly assumed its role alongside theory and experiment as the third pillar of the scientific method.  During this time, the complexity of scientific simulations has evolved from relatively simplistic calculations involving only a handful of basic equations, to massive models that combine vast arrays of physical processes.  While early simulation approaches could be well-understood using standard mathematical techniques, applied mathematics has unfortunately not kept up with the fast pace of scientific simulation development.  The result of these differing paths is that many numerical analysts spend their effort constructing elegant solvers for simple models of little practical use, while computational scientists study highly-realistic systems but "solve"' them using ad hoc methods with questionable accuracy and stability. 

Professor Reynolds' research aims to bridge this gap between mathematical theory and scientific computing practice, through the creation, application, and dissemination of flexible algorithms that may be tuned for modern, multiphysics problems, while still providing mathematical assurances such as accuracy, stability and parallel scalability. 

Professor Reynolds collaborates with a wide range of scientists on applications that include fusion energy, climate modeling, numerical weather prediction, cosmology, and additive manufacturing, with research funding from the U.S. Department of Energy, the U.S. National Science Foundation, and the U.S. Department of Defense.  His published work has appeared in SIAM Journal of Scientific Computing, Journal of Computational Physics, ACM Transactions on Mathematical Software, Computer Physics Communications, Journal of Advances in Modeling Earth Systems, Geoscientific Model Development, Modelling and Simulation in Materials Science and Engineering, The Astrophysical Journal, International Journal of High Performance Computing, and elsewhere.