A state-defect constraint pairing graph coarsening method is described for improving computational efficiency during the numerical factorization of large sparse Karush–Kuhn–Tucker matrices that arise from the discretization of optimal control problems via an Legendre–Gauss–Radau orthogonal collocation method. The method takes advantage of the particular sparse structure of the Karush–Kuhn–Tucke...

This paper describes the application of a new three-dimensional adaptive finite element scheme to the simulation of shock interaction with complex geometry bodies such as tanks, trucks, etc. The classic h-enrichment/coarsening is employed in this scheme in conjunction with a tetrahedal finite element discretization in three dimensions. In order to simplify the refinement/coarsening logic and to...

The eeects of ow induced by a random acceleration eld (g-jitter) are considered in two related situations that are of interest for microgravity uid experiments: the random motion of isolated buoyant particles, and diiusion driven coarsening of a solid-liquid mixture. We start by analyzing in detail actual accelerometer data gathered during a recent microgravity mission, and obtain the values of...

Shallow-water equations with bottom drag and viscosity are used to study the dynamics of roll waves. First, we explore the effect of bottom topography on linear stability of turbulent flow over uneven surfaces. Low-amplitude topography is found to destabilize turbulent roll waves and lower the critical Froude number required for instability. At higher amplitude, the trend reverses and topograph...

In this paper we report on bubble growth rates and on the statistics of bubble topology for the coarsening of a dry foam contained in the narrow gap between two hemispheres. By contrast with coarsening in flat space, where six-sided bubbles neither grow nor shrink, we observe that six-sided bubbles grow with time at a rate that depends on their size. This result agrees with the modification to ...

Presented in this paper is a new sparse linear solver methodology motivated by multigrid principles and based around general local transformations that diagonalize a matrix while maintaining its sparsity. These transformations are approximate, but the error they introduce can be systematically reduced. The cost of each transformation is independent of matrix size but dependent on the desired ac...

We report on experimental measurements of the growth of regular domains evolving from an irregular pattern in electroconvection. The late-time growth of the domains is consistent with the size of the domains scaling as t(n). We use two isotropic measurements of the domain size: the structure factor and the domain wall length. Measurements using the structure factor are consistent with t(1/5) gr...

We study the driven dynamics of quantum coarsening. We analyze models of M-component rotors coupled to two electronic reservoirs at different chemical potential that generate a current threading through the system. In the large M limit, we derive the dynamical phase diagram as a function of temperature, strength of quantum fluctuations, voltage, and coupling to the leads. We show that the slow ...