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Background
I have been an assistant professor in the department of mathematics at the University of Wisconsin-Madison since 2023. I was previously at Brown University in the Division of Applied Mathematics as Prager assistant professor and presidential postdoctoral scholar. In 2019 I received my PhD from Rice University.
My research explores numerical methods for partial differential equations, numerical linear algebra, massively parallel computational architectures, and applications to real-world phenomena. Primary areas of focus are discontinuous Galerkin finite element methods, multilevel solvers (multigrid, domain decomposition), and accelerators (GPUs, FPGAs, Xeon Phi, etc.). Example applications include long-wave phenomena (tsunamis, storm surges, ocean waves), subterranean flows (mantle and lava dynamics, groundwater recovery). By leveraging numerical methods, computational science, and computer simulations, my work aims to better understand, predict, and assess complex phenomena that would be otherwise difficult, if not impossible to examine through classical experimentation alone.
Something that is unique about my work is my non-trivial commitment to broadening participation in the mathematical sciences. My outreach work has been recognized by the Society for Industrial and Applied Mathematics through an MGB early career fellowship. For instance, I have been a research program director for the MSRI Undergraduate Program, instructor for Enhancing Diversity in Graduate Education program, and participant in Empowering a Diverse Computational Mathematics Research Community.
Interests
High-performance parallel computing. Numerical methods for partial differential equations. Computational fluid dynamics simulations. Computational science and engineering.
Sample Work
Publication
Positivity-preserving discontinuous Galerkin scheme for linear hyperbolic equations with characteristics informed augmentation
“Positivity-preserving discontinuous Galerkin scheme for linear hyperbolic equations with characteristics informed augmentation”, Results in Applied Mathematics, 2024.
Publication
Hybridization and postprocessing in finite element exterior calculus
G. Awanou, M. S. Fabien, J. Guzman, and A. Stern. “Hybridization and postprocessing in finite element exterior calculus”, Mathematics of Computation, 2024.
Publication
Fluid mechanics approach to analyzing collagen fiber organization
A. C. Salazar Coariti and M. S. Fabien, and J. Guzman and J. A. McGuire, R. De Vita and K. C. Toussaint. “Fluid mechanics approach to analyzing collagen fiber organization”, Journal of Biomedical Optics 27 (1), 016503-016503, 2023.
Publication
Numerical error analysis for an energy-stable HDG method for the Allen-Cahn equation
M. S. Fabien. “Numerical error analysis for an energy-stable HDG method for the Allen-Cahn equation”, Journal of Computational and Applied Mathematics, 2022.