BDDC Algorithms for Advection-diffusion problems with HDG Discretizations

Abstract: In this talk, I will talk about the balancing domain decomposition by constraints  (BDDC)  methods for the non-symmetric positive definite system arising from the hybridizable discontinuous Galerkin (HDG) discretization of advection-diffusion equations. Since the degrees of freedom are only defined on the mesh element boundaries, appropriate extensions to the element interiors are needed. Additional edge/face constraints are used to improve the convergence. I will analyze the convergence rate of the GMRES solver and present the numerical results under different viscosities and polynomial degrees of the HDG basis functions.