Andrew Giuliani (PhD ’18) was one of six students who won the 2019 Huawei Prize for Best Research Paper by a Mathematics Graduate Student. This award recognizes the impact of his paper, A moment limiter for the discontinuous Galerkin method on unstructured triangular meshes, with a prize of $4,000.
Along with Professor Lilia Krivodonova, Giuliani wrote about a novel approach to limiting on unstructured meshes. Specifically, this new limiter works directly on solution moments.
Classifying information prior to his paper, the result of the Gibbs phenomenon developed numerical solutions oscillate near discontinuities or regions with very steep gradients. In addition to introducing noise, the oscillations lead to unstable growth which cause the numerical solution values exceed machine bounds. Because of this, fluid dynamics problems with shocks require robust and efficient limiters.
The research led to the development of a theory on how limiting in these directions can be done in one-dimensional fashion. This paper’s approach has already been extended to computations in three-dimensions on tetrahedral meshes.
“I think this is a fantastic result,” said Krivodonova. “Not only because of its novelty, theoretical rigor and computational advantages, but also because it opens a way to designing higher order limiters and limiters on nonconforming meshes, which are two big unresolved problems in numerical methods for fluid dynamics.”
The research was accepted for publication to the SIAM Journal on Scientific Computing. Giuliani received multiple offers from top universities in recognition of his extensive research. As of August 2018, he works as a Courant Instructor at the Courant Institute, New York University.
The 2019 Huawei Prize for Best Research Paper by a Mathematics Graduate Student would not be possible without the generous support from Huawei.