Amulya Pillutla, from Iowa, is a Junior at Pleasant Valley High School. Amulya’s research is focused on environmental engineering and more specifically sustainable agriculture. In her free time, she participates in a club rowing program, plays her clarinet, and volunteers in her community.

This work focuses on developing efficient and robust implementation methods for hybridizable discontinuous Galerkin (HDG) schemes for fluid and ocean dynamics. In the first part, we compare choices in weak formulations and their numerical consequences. We address details in making the leap from the mathematical formulation to the implementation, including the different spaces and mappings, discretization of the integral operators, boundary conditions, and assembly of the linear systems. We provide a flexible mapping procedure amenable to both quadrature-free and quadrature-based discretizations, and compare the accuracy of the two on different problem geometries. We verify the quadrature-free approach, demonstrating that optimal orders of convergence can be obtained, even on non-affine and curvilinear geometries. The second part of the work investigates the scalability of HDG schemes, identifying memory and time-to-solution bottlenecks. The form of the quadrature-free integral operators is exploited to develop a novel and efficient matrix-free approach to solving the global linear system that arises from HDG discretizations. Additional manipulations to improve numerical robustness are discussed. To mitigate the complexity of the implementation, we provide an automated and computationally efficient verification procedure for the HDG methodologies discussed, using a hierarchical approach to provide diagnostic information and isolate problems. Finally, challenges related to the effective visualization of high-order, discontinuous HDG-FEM data for fluid and ocean applications are illustrated and strategies are provided to address them.

Congratulations to Wael Hajj Ali for successfully clearing the MIT Mechanical Engineering Ph.D Qualifying Exams. Wael now begins his journey towards an outstanding Ph.D thesis. All the best!

Chinmay Kulkarni, a Ph.D candidate in the MSEAS group has won the first place in the de Florez Competition 2019. This year’s competition saw 44 entries, among which Chinmay was placed first (in a four-way tie) under the Graduate Science category, with his presentation titled “Persistent Rigid Sets in Ocean Flows Help Predict the Environmental Impact of Deep Sea Mining Activities”. The competition website is here.

Chinmay Kulkarni, Ph.D candidate in MSEAS group has been awarded a 2019 Wunsch Foundation Silent Hoist and Crane Award for Outstanding Graduate Research. Congratulations Chinmay!