Affiliation and Research Interests
I am a postdoctoral researcher in the Center for Computational Sciences and Engineering (CCSE) in the Computational Research Division of the Computing Sciences Directorate at the Lawrence Berkeley National Laboratory. I am interested in improving efficiency for simulations involving time integration methods.
I am interested in improving the efficiency of simulations involving time integration methods. My current focus is on the Nyx N-body hydro code for computational cosmology.
Cosmological simulations allow us to investigate physical parameters which are not directly observable. Specifically, I am improving the numerical coupling between the hydrodynamic solver and the integration of the heating and cooling source terms as well as improving the overall algorithm efficiency. More efficient numerical methods and improved parallelism allow for more highly refined and complex models.
I have implemented a spectral deferred correction coupling strategy (which accounts for the comoving frame) in order to improve Nyx's heating-cooling integration efficiency and robustness. New improvements include updates to Nyx's use of the CVODE integration C-Fortran2003 interface, including an option to better use the most advanced version of CVODE by focusing solely on the C implementation.
I am currently working on porting these new implementations to hybrid CPU/GPU architectures by using CUDA to offload work to the GPU. This GPU implementation has been tested in standalone drivers to focus on the heating-cooling integration process, and is currently being added to the general use Nyx code.
I received my doctorate in Computational and Applied Mathematics from Southern Methodist University in late 2017. My dissertation research fits broadly in the applied mathematics fields of scientific computing and numerical analysis. Specifically, I focused on the development of numerical methods for the time integration of problems with multiple characteristic time scales. These methods are motivated by multiphysics, multiscale real-world application problems which are constructed by coupling physical processes with potential disparate length and time scales together. I developed a family of efficient, fully coupled fourth-order multirate method with comparable stability properties to leading existing third-order multirate methods. These methods were based on existing Recursive Flux-Splitting Multirate methods using Generalized Additive Runge-Kutta theory to analyze order conditions.
J. M. Sexton, D. R. Reynolds. "Relaxed Multirate Infinitesimal Step Methods: an extension of Multirate Infinitesimal Step Methods and Recursive Flux-Splitting Multirate Methods." (Submitted) [arxiv]
D. R. Reynolds, D. J. Gardner,C. S. Woodward, A. C. Hindmarsh,J. M. Sexton. "ARKode--a solver for stiff, nonstiff, and mixed systems of ODEs." (In Preparation)
W. Thompson, S. McGinnis, D. McDaniel, J.M. Sexton, R. Pettit, S. Anderson, M. C. Jackson, K. Sellers. "A Geographical and Statistical Analysis of Childhood Leukemia Deaths Relating to the Locations of Nuclear Power Plants." Advances and Applications in Statistical Sciences 6.5 pp 313-328, 2011. [link]
J. M. Sexton, D. R. Reynolds. Efficient Multirate Methods from High Order. Minisymposium talk at the SIAM Conference on Computational Science and Engineering 2019..
J. M. Sexton. A Deferred Correction Coupling Strategy for Cosmological Simulations. Lightning talk at the Women in HPC Workshop at Supercomputing 2018.
J. M. Sexton. A Deferred Correction Coupling Strategy for Cosmological Simulations. Contributed talk at the IEEE WIE International Leadership Summit 2018.
J. M. Sexton, D. R. Reynolds. "High-order Relaxed Multirate Infinitesimal Step Methods for Multiphysics Applications." Contributed talk at the Texas Applied Mathematics and Engineering Symposium 2017.
D. R. Reynolds, C. S. Woodward, D. J. Gardner, J. M. Sexton. "Flexible and Accurate Multiphysics Time Integration with ARKode." Presentation at the SIAM Conference on Computational Science and Engineering 2017.
J. M. Sexton,D. R. Reynolds. "An Optimal Multirate Method for Climate Applications." Poster Presentation at the SIAM Conference on Mathematics of Planet Earth 2016