We present a comparison between hybridized and non-hybridized discontinuous Galerkin methods in the context of target-based hp-adaptation. Using a discrete-adjoint approach, sensitivities with respect to output functionals are computed to drive the adaptation. From the error distribution given by the adjoint-based error estimator, h-or p-refinement is chosen based on the smoothness of the solution which can be quantified by properly-chosen smoothness indicators. Numerical results are shown for inviscid subsonic and transonic, and laminar viscous flow around the NACA0012 airfoil.
Network reliability algorithms which produce sums of disjoint products (SDP) are sensitive to the order in which the minimal pathsets are analyzed. The minpaths are preprocessed by choosing this order in the hope that an SDP algorithm will then provide a relatively efficient analysis. The most commonly used preprocessing strategy is to list the minpaths in order of increasing size. This paper gives examples for which this strategy is not optimal. A new preprocessing strategy which works well for SDP algorithms with single-variable inversion (SVI) is introduced. It is also observed that optimal preprocessing for SVI-SDP can be different from optimal preprocessing for SDP algorithms which use multiple-variable inversion; one reason for this is that MVI-SDP algorithms handle disjoint minpaths much more effectively than SVI-SDP algorithms do. Both kinds of SDP algorithms profit from prior reduction of elements and of subsystems which are in parallel or in series.
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