arXiv subjects

Andrew Dougherty

Publications and source records attributed to Andrew Dougherty.

6 recordsLinked to original sources

arXiv2012

Nonsymmetric multigrid preconditioning for conjugate gradient methods

We numerically analyze the possibility of turning off post-smoothing (relaxation) in geometric multigrid when used as a preconditioner in conjugate gradient linear and eigenvalue solvers for the 3D Laplacian. The geometric Semicoarsening Multigrid (SMG) method is provided by the hypre parallel software package. We solve linear systems using two variants (standard and flexible) of the preconditioned conjugate gradient (PCG) and preconditioned steepest descent (PSD) methods. The eigenvalue problems are solved using the locally optimal block preconditioned conjugate gradient (LOBPCG) method available in hypre through BLOPEX software. We observe that turning off the post-smoothing in SMG dramatically slows down the standard PCG-SMG. For flexible PCG and LOBPCG, our numerical results show that post-smoothing can be avoided, resulting in overall acceleration, due to the high costs of smoothing and relatively insignificant decrease in convergence speed. We numerically demonstrate for linear systems that PSD-SMG and flexible PCG-SMG converge similarly if SMG post-smoothing is off. We experimentally show that the effect of acceleration is independent of memory interconnection. A theoretical justification is provided.

math.NA↗

arXiv2012

The initial growth of sidebranches in ammonium chloride dendrites

We report measurements for the initial stages of sidebranching during the dendritic growth of ammonium chloride from supersaturated aqueous solution. The earliest sidebranches are approximately periodic; they are first evident about $36 \rho$ behind the tip, where $\rho$ is the tip radius, and have an average initial spacing of about $5 \rho$, though both values show considerable variation. The initial sidebranch amplitude grows approximately exponentially, but quickly saturates as sidebranches compete and coarsening sets in. This initial sidebranch growth is reasonably consistent with what would be expected for noise-driven sidebranches, though there are some quantitative differences.

nlin.PS↗

arXiv2012

Measurement of the Capillary Length for the Dendritic Growth of Ammonium Chloride

We report the results of a new method of measuring the capillary length for the dendritic crystal growth of non-faceted materials. This method uses a nearly spherical crystal held near unstable equilibrium in an oscillating temperature field. For the growth of ammonium chloride crystals from aqueous solution, previous published estimates of the capillary length varied by over a factor of 20. With this new method, we find the product of the diffusion constant and capillary length $D d_0$ to be $0.78 \pm 0.07 \,\mathrm{\mu m^3/s}$, similar to that obtained for ammonium bromide crystals.

cond-mat.mtrl-sci↗

arXiv2006

The Transient Growth of Ammonium Chloride Dendrites

We report measurements of the initial growth and subsequent transient response of dendritic crystals of ammonium chloride grown from supersaturated aqueous solution. Starting from a small, nearly spherical seed held in unstable equilibrium, we lower the temperature to initiate growth. The growth speed and tip radius approach the same steady state values independent of initial seed size. We then explore the response of the growing dendrite to changes in temperature. The crystal adjusts quickly and smoothly to the new growth conditions, maintaining an approximately constant value of $v \rho ^2$ throughout. Dissolving dendrites, on the other hand, are not characterized by the same value of $v \rho ^2$.

cond-mat.mtrl-sci↗

arXiv2004

Shape of ammonium chloride dendrite tips at small supersaturation

We report detailed shape measurements of the tips of three-dimensional ammonium chloride dendrites grown from supersaturated aqueous solution. For growth at small supersaturation, we compare two different models: parabolic with a fourth-order correction, and power law. Neither is ideal, but the fourth-order fit appears to provide the most robust description of both the tip shape and position for this material. For that fit, the magnitude of the fourth-order coefficient is about half of the theoretically expected value.

cond-mat.mtrl-sci↗

arXiv1998

Driven interfaces in disordered media: determination of universality classes from experimental data

While there have been important theoretical advances in understanding the universality classes of interfaces moving in porous media, the developed tools cannot be directly applied to experiments. Here we introduce a method that can identify the universality class from snapshots of the interface profile. We test the method on discrete models whose universality class is well known, and use it to identify the universality class of interfaces obtained in experiments on fluid flow in porous media.

cond-mat.stat-mech↗