Computational Mathematics and Scientific Computing Seminar

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An upwind hybridized discontinuous Galerkin methods: theory and application to atmospheric flows and magnetohydrodynamics

Speaker: Tan Bui, University of Texas, Austin

Location: Warren Weaver Hall 1302

Date: March 6, 2020, 10 a.m.

Synopsis:

We will present several new developments on the emerging Hybridized Discontinuous Galerkin

(HDG) method. First, starting either from the Godunov upwind idea or from the Rankine-
Hugoniot condition we derive a unified HDG framework for linear PDEs that allows one to

uncover new HDG methods and recover most of the existing ones for a large class of PDE
including the Friedrichs' systems. Analysis and numerical results for the unified framework will
be presented. Second, we will present an IMEX scheme for the HDG method that: 1) facilitates
high-order solutions both in time and space; 2) avoids overly small time-step sizes; 3) requires
only one linear system solve per time stage. Third, we will present our recent developments on
multilevel and multigrid as scalable solvers and preconditioners for HDG trace systems. Various
numerical results in atmospheric flows and magnetohydrodynamics will be presented to validate
the developments.