| Summary: | A high-order Galerkin Least-Squares (GLS) finite element discretization is combined
with massively parallel implicit solvers. The stabilization parameter of the GLS
discretization is modified to improve the resolution characteristics and the condition
number for the high-order interpolation. The Balancing Domain Decomposition
by Constraints (BDDC) algorithm is applied to the linear systems arising from
the two-dimensional, high-order discretization of the Poisson equation, the advectiondiffusion
equation, and the Euler equation. The Robin-Robin interface condition
is extended to the Euler equation using the entropy-symmetrized variables. The
BDDC method maintains scalability for the high-order discretization for the diffusiondominated
flows. The Robin-Robin interface condition improves the performance of
the method significantly for the advection-diffusion equation and the Euler equation.
The BDDC method based on the inexact local solvers with incomplete factorization
maintains the scalability of the exact counterpart with a proper reordering.
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