I am currently a Postdoctoral Researcher at the Center for Applied and Scientific Computing (CASC) at Lawrence Livermore National Laboratory.
I defended my Ph.D. in Applied Mathematics at Tufts University in July 2015, under the supervision of Professors James Adler and Scott MacLachlan.
Research Interests and Current Projects
My research interests are in the areas of computational applied mathematics and scientific computing. Specifically, I am interested in numerical linear algebra and the numerical solution of partial differential equations. My current research focuses on developing AMGe-based preconditioning strategies for systems of partial differential equations. I also work on a project involving inverse problems and the power grid. During graduate school, I worked on extending methods that were developed for incompressible fluid dynamics to complex fluid systems, as well as their implementation for HPC platforms. Part of that project investigated the use of monolithic multigrid methods as preconditioners for certain formulations of magnetohydrodynamics (MHD) models. I have also studied the applicability of several preconditioners for BDM1-P0 finite-element discretizations of the Stokes equations.
- Preconditioning a mass-conserving discontinuous Galerkin discretization of the Stokes Equations. J.H. Adler, T. R. Benson, S. P. MacLachlan. Numer. Linear Alg. Appl. (NLAA), 2016
- Monolithic Multigrid Methods for Two-Dimensional Resistive Magnetohydrodynamics. J. H. Adler, T. R. Benson, E. C. Cyr, S. P. MacLachlan, R. S. Tuminaro. SIAM J. Sci. Comput. (SISC), 38(1):B1-B24, 2016.
- Secure distributed membership tests via secret sharing: How to hide your hostile hosts: Harnessing shamir secret sharing. D. J. Zage, H. Xu, T. M. Kroeger, B. Hahn, N.P. Donoghue, and T. R. Benson. ICNC, 2016.
- Energy Minimization for Liquid Crystal Equilibrium with Electric and Flexoelectric Effects. J. H. Adler, T. J. Atherton, T. R. Benson, D. B. Emerson, and S. P. MacLachlan. SIAM J. Sci. Comput. (SISC), 37(5):S157-S176, 2015.