Analysis of a parallelized nonlinear elliptic boundary value problem solver with application to reacting flows

A parallelized finite difference code based on the Newton method for systems of nonlinear elliptic boundary value problems in two dimensions is analyzed in terms of computational complexity and parallel efficiency. An approximate cost function depending on 15 dimensionless parameters is derived for algorithms based on stripwise and boxwise decompositions of the domain and a one-to-one assignment of the strip or box subdomains to processors. The sensitivity of the cost functions to the parameters is explored in regions of parameter space corresponding to model small-order systems with inexpensive function evaluations and also a coupled system of nineteen equations with very expensive function evaluations. The algorithm was implemented on the Intel Hypercube, and some experimental results for the model problems with stripwise decompositions are presented and compared with the theory. In the context of computational combustion problems, multiprocessors of either message-passing or shared-memory type may be employed with stripwise decompositions to realize speedup of O(n), where n is mesh resolution in one direction, for reasonable n

Domain-decomposed preconditionings for transport operators

The performance was tested of five different interface preconditionings for domain decomposed convection diffusion problems, including a novel one known as the spectral probe, while varying mesh parameters, Reynolds number, ratio of subdomain diffusion coefficients, and domain aspect ratio. The preconditioners are representative of the range of practically computable possibilities that have appeared in the domain decomposition literature for the treatment of nonoverlapping subdomains. It is shown that through a large number of numerical examples that no single preconditioner can be considered uniformly superior or uniformly inferior to the rest, but that knowledge of particulars, including the shape and strength of the convection, is important in selecting among them in a given problem

Potential energy landscape-based extended van der Waals equation

The inherent structures ({\it IS}) are the local minima of the potential energy surface or landscape, $U({\bf r})$, of an {\it N} atom system. Stillinger has given an exact {\it IS} formulation of thermodynamics. Here the implications for the equation of state are investigated. It is shown that the van der Waals ({\it vdW}) equation, with density-dependent $a$ and $b$ coefficients, holds on the high-temperature plateau of the averaged {\it IS} energy. However, an additional ``landscape'' contribution to the pressure is found at lower $T$. The resulting extended {\it vdW} equation, unlike the original, is capable of yielding a water-like density anomaly, flat isotherms in the coexistence region {\it vs} {\it vdW} loops, and several other desirable features. The plateau energy, the width of the distribution of {\it IS}, and the ``top of the landscape'' temperature are simulated over a broad reduced density range, $2.0 \ge \rho \ge 0.20$, in the Lennard-Jones fluid. Fits to the data yield an explicit equation of state, which is argued to be useful at high density; it nevertheless reproduces the known values of $a$ and $b$ at the critical point

The Potential Energy Landscape and Mechanisms of Diffusion in Liquids

The mechanism of diffusion in supercooled liquids is investigated from the potential energy landscape point of view, with emphasis on the crossover from high- to low-T dynamics. Molecular dynamics simulations with a time dependent mapping to the associated local mininum or inherent structure (IS) are performed on unit-density Lennard-Jones (LJ). New dynamical quantities introduced include r2_{is}(t), the mean-square displacement (MSD) within a basin of attraction of an IS, R2(t), the MSD of the IS itself, and g_{loc}(t) the mean waiting time in a cooperative region. At intermediate T, r2_{is}(t) posesses an interval of linear t-dependence allowing calculation of an intrabasin diffusion constant D_{is}. Near T_{c} diffusion is intrabasin dominated with D = D_{is}. Below T_{c} the local waiting time tau_{loc} exceeds the time, tau_{pl}, needed for the system to explore the basin, indicating the action of barriers. The distinction between motion among the IS below T_{c} and saddle, or border dynamics above T_{c} is discussed.Comment: submitted to pr

Inherent-Structure Dynamics and Diffusion in Liquids

The self-diffusion constant D is expressed in terms of transitions among the local minima of the potential (inherent structure, IS) and their correlations. The formulae are evaluated and tested against simulation in the supercooled, unit-density Lennard-Jones liquid. The approximation of uncorrelated IS-transition (IST) vectors, D_{0}, greatly exceeds D in the upper temperature range, but merges with simulation at reduced T ~ 0.50. Since uncorrelated IST are associated with a hopping mechanism, the condition D ~ D_{0} provides a new way to identify the crossover to hopping. The results suggest that theories of diffusion in deeply supercooled liquids may be based on weakly correlated IST.Comment: submitted to PR

Age, period and cohort effects in frequent cannabis use among US students: 1991–2018

Background and AimsAs the legal status of cannabis changes across the United States and modes of administration expand, it is important to examine the potential impact on adolescent cannabis use. This study aimed to assess changes in prevalence of frequent cannabis use in adolescents in the United States and how far this varies by age and cohort.DesignAnalysis of Monitoring the Future, a nationally representative annual survey of 8th‐, 10th‐ and 12th‐grade students in the United States conducted from 1991 to 2018.SettingIn‐school surveys completed by US adolescents.ParticipantsA total of 1 236 159 8th‐, 10th‐ and 12th‐graders; 51.5% female, 59.6% non‐Hispanic white, 12.3% non‐Hispanic black, 13.4% Hispanic and 14.7% other race/ethnicity.MeasurementsFrequent cannabis use (FCU), defined as six or more occasions in the past 30 days, stratified by sex, race/ethnicity and parental education.FindingsFCU among US adolescents increased over the study period; the peak in 2010–18 was 11.4% among 18‐year‐old students. This increase was best explained by both period and cohort effects. Compared with respondents in 2005, adolescents surveyed in 2018 had period effects in FCU that were 1.6 times greater. Adolescents in younger birth cohorts (those born > 1988) had a lower increase in FCU than those born prior to 1988. Results were consistent across sex, parent education and race/ethnicity, with period effects indicating increasing FCU after 2005 and cohort effects indicating a lower magnitude of increase in more recent birth cohorts. Age and parental education disparities in FCU have increased over time, whereas race/ethnicity differences have converged over time; black students were 0.67 [95% confidence interval (CI) = 0.64–0.70] times as likely to use cannabis frequently as white students from 1991 to 2000, and 1.03 (95% CI = 0.98–1.09) times as likely from 2011 to 2018 (P‐value for time interaction < 0.001).ConclusionsThe prevalence of frequent cannabis use (FCU) increased from 1991 to 2018 among older adolescents in the United States. Racial/ethnic differences in FCU converged, whereas parental education differences have diverged.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151314/1/add14665_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151314/2/add14665.pd

Implicit solvers for large-scale nonlinear problems

Abstract. Computational scientists are grappling with increasingly complex, multi-rate applications that couple such physical phenomena as fluid dynamics, electromagnetics, radiation transport, chemical and nuclear reactions, and wave and material propagation in inhomogeneous media. Parallel computers with large storage capacities are paving the way for high-resolution simulations of coupled problems; however, hardware improvements alone will not prove enough to enable simulations based on brute-force algorithmic approaches. To accurately capture nonlinear couplings between dynamically relevant phenomena, often while stepping over rapid adjustments to quasi-equilibria, simulation scientists are increasingly turning to implicit formulations that require a discrete nonlinear system to be solved for each time step or steady state solution. Recent advances in iterative methods have made fully implicit formulations a viable option for solution of these large-scale problems. In this paper, we overview one of the most effective iterative methods, Newton-Krylov, for nonlinear systems and point to software packages with its implementation. We illustrate the method with an example from magnetically confined plasma fusion and briefly survey other areas in which implicit methods have bestowed important advantages, such as allowing high-order temporal integration and providing a pathway to sensitivity analyses and optimization. Lastly, we overview algorithm extensions under development motivated by current SciDAC applications

Mean-atom-trajectory model for the velocity autocorrelation function of monatomic liquids

We present a model for the motion of an average atom in a liquid or supercooled liquid state and apply it to calculations of the velocity autocorrelation function $Z(t)$ and diffusion coefficient $D$. The model trajectory consists of oscillations at a distribution of frequencies characteristic of the normal modes of a single potential valley, interspersed with position- and velocity-conserving transits to similar adjacent valleys. The resulting predictions for $Z(t)$ and $D$ agree remarkably well with MD simulations of Na at up to almost three times its melting temperature. Two independent processes in the model relax velocity autocorrelations: (a) dephasing due to the presence of many frequency components, which operates at all temperatures but which produces no diffusion, and (b) the transit process, which increases with increasing temperature and which produces diffusion. Because the model provides a single-atom trajectory in real space and time, including transits, it may be used to calculate all single-atom correlation functions.Comment: LaTeX, 8 figs. This is an updated version of cond-mat/0002057 and cond-mat/0002058 combined Minor changes made to coincide with published versio