Preconditioned iterative solution of the 2D Helmholtz equation

Using a finite element method to solve the Helmholtz equation leads to a sparse system of equations which in three dimensions is too large to solve directly. It is also non-Hermitian and highly indefinite and consequently difficult to solve iteratively. The approach taken in this paper is to precondition this linear system with a new preconditioner and then solve it iteratively using a Krylov subspace method. Numerical analysis shows the preconditioner to be effective on a simple 1D test problem, and results are presented showing considerable convergence acceleration for a number of different Krylov methods for more complex problems in 2D, as well as for the more general problem of harmonic disturbances to a non-stagnant steady flow

Preconditioning harmonic unsteady potential flow calculations

This paper considers finite element discretisations of the Helmholtz equation and its generalisation arising from harmonic acoustics perturbations to a non-uniform steady potential flow. A novel elliptic, positive definite preconditioner, with a multigrid implementation, is used to accelerate the iterative convergence of Krylov subspace solvers. Both theory and numerical results show that for a model 1D Helmholtz test problem the preconditioner clusters the discrete system's eigenvalues and lowers its condition number to a level independent of grid resolution. For the 2D Helmholtz equation, grid independent convergence is achieved using a QMR Krylov solver, significantly outperforming the popular SSOR preconditioner. Impressive results are also presented on more complex domains, including an axisymmetric aircraft engine inlet with non-stagnant mean flow and modal boundary conditions

Eigenmode Analysis of Boundary Conditions for the One-Dimensional Preconditioned Euler Equations

The effect of local preconditioning on boundary conditions is analyzed for the subsonic, one-dimensional Euler equations. Decay rates for the eigenmodes of the initial boundary value problem are determined for different boundary conditions and different preconditioners whose intent is to accelerate low Mach number computations. Riemann invariant boundary conditions based on the unpreconditioned Euler equations are shown to be reflective when used with preconditioning, and asymptotically, at low Mach numbers, initial disturbances do not decay. Other boundary conditions are shown to be perfectly non-reflective in conjunction with preconditioning. Two-dimensional numerical results confirm the trends predicted by the one-dimensional analysis

A Deep Relevance Matching Model for Ad-hoc Retrieval

In recent years, deep neural networks have led to exciting breakthroughs in speech recognition, computer vision, and natural language processing (NLP) tasks. However, there have been few positive results of deep models on ad-hoc retrieval tasks. This is partially due to the fact that many important characteristics of the ad-hoc retrieval task have not been well addressed in deep models yet. Typically, the ad-hoc retrieval task is formalized as a matching problem between two pieces of text in existing work using deep models, and treated equivalent to many NLP tasks such as paraphrase identification, question answering and automatic conversation. However, we argue that the ad-hoc retrieval task is mainly about relevance matching while most NLP matching tasks concern semantic matching, and there are some fundamental differences between these two matching tasks. Successful relevance matching requires proper handling of the exact matching signals, query term importance, and diverse matching requirements. In this paper, we propose a novel deep relevance matching model (DRMM) for ad-hoc retrieval. Specifically, our model employs a joint deep architecture at the query term level for relevance matching. By using matching histogram mapping, a feed forward matching network, and a term gating network, we can effectively deal with the three relevance matching factors mentioned above. Experimental results on two representative benchmark collections show that our model can significantly outperform some well-known retrieval models as well as state-of-the-art deep matching models.Comment: CIKM 2016, long pape

Effectiveness of Lasalocid with Solar-Dried Acid Treated and Ensiled Shelled Corn Finishing Rations

Three shelled corn storage forms (solar-dried, propionic acid-treated and ensiled) were also investigated in this trial because of the intensive interest in minimizing the energy costs required for drying or preserving high-moisture corn and to examine the relative feeding value of corn stored in these three ways. A horizontal plastic Silopress bag was used to store the ensiled shelled corn in order to gain experience with this ensiling systems

Mechanism of Reconnection on Kinetic Scales Based on Magnetospheric Multiscale Mission Observations

We examine the role that ions and electrons play in reconnection using observations from the Magnetospheric Multiscale (MMS) mission on kinetic ion and electron scales, which are much shorter than magnetohydrodynamic scales. This study reports observations with unprecedented high resolution that MMS provides for magnetic eld (7.8 ms) and plasma (30 ms for electrons and 150 ms for ions). We analyze and compare approaches to the magnetopause in 2016 November, to the electron diffusion region in the magnetotail in 2017 July followed by a current sheet crossing in 2018 July. Besides magnetic eld reversals, changes in the direction of the ow velocity, and ion and electron heating, MMS observed large uctuations in the electron ow speeds in the magnetotail. As expected from numerical simulations, we have veried that when the eld lines and plasma become decoupled a large reconnecting electric eld related to the Hall current (110 mV/m) is responsible for fast reconnection in the ion diffusion region. Although inertial accelerating forces remain moderate (12 mV/m), the electric elds resulting from the divergence of the full electron pressure tensor provide the main contribution to the generalized Ohms law at the neutral sheet (as large as 200 mV/m). In our view, this illustrates that when ions decouple electron physics dominates. The results obtained on kinetic scales may be useful for better understanding the physical mechanisms governing reconnection processes in various magnetized laboratory and space plasmas

Variability in broods of the seastar \u3ci\u3eLeptasterias aequalis\u3c/i\u3e

Enormous variation exists in the reproductive output of marine invertebrates (e.g., in the numbers of em¬bryos produced, the volumes of embryos, and the energy that they contain). It is not clear why there is such great variability or what the population-level consequences are. We sampled a population of the brooding seastar Leptasterias aequalis (Stimpson, 1862) to collect basic information on brood sizes, embryo volume, and embryo energy content with a goal to better understand the reproductive ecology of this species. We collected brooding females in February and again in April. We measured the size of their broods and sampled the broods to estimate volume and energy con¬tent of the embryos. There was great variability in the volume and energy content of embryos produced by individual females and among the embryos in a single female\u27s brood. Larger adults produced larger embryos, which generally had greater energy content and may be of a higher quality. The average energy content of embryos appeared to in¬crease during the brooding period. Larger females produced larger broods but lost a greater proportion of the embryos. The net result is that larger individuals may not produce any more juveniles than smaller individuals, but those that they do produce may be of a higher quality. Originally published in Canadian Journal of Zoologyand used with permission

Conventionally-Dried, Solar-Dried and Acid-Treated Corn for Finishing Beef Cattle

An experiment was initiated at the James Valley Research and Extension Center, Redfield, during the summer of 1976 to determine the value of corn grain dried or preserved by different methods. A portion of the trial dealt with methods of administering vitamin A and these results will be reported at a later time

Effects of Method of Supplementing Vitamin A on Feedlot Performance and Blood and Liver Vitamin A Levels in Feedlot Cattle

The objective of this experiment was to study the effects of method of administering vitamin A on the performance of feedlot cattle. The vitamin A status in terms of blood plasma level and liver storage was determined along with weight gain and feed efficiency in a trial conducted at the James Valley Research and Extension Center near Redfield during the summer and fall of 1975

String Bit Models for Superstring

We extend the model of string as a polymer of string bits to the case of superstring. We mainly concentrate on type II-B superstring, with some discussion of the obstacles presented by not II-B superstring, together with possible strategies for surmounting them. As with previous work on bosonic string we work within the light-cone gauge. The bit model possesses a good deal less symmetry than the continuous string theory. For one thing, the bit model is formulated as a Galilei invariant theory in $(D-2)+1$ dimensional space-time. This means that Poincar\'e invariance is reduced to the Galilei subgroup in $D-2$ space dimensions. Naturally the supersymmetry present in the bit model is likewise dramatically reduced. Continuous string can arise in the bit models with the formation of infinitely long polymers of string bits. Under the right circumstances (at the critical dimension) these polymers can behave as string moving in $D$ dimensional space-time enjoying the full $N=2$ Poincar\'e supersymmetric dynamics of type II-B superstring.Comment: 43 pages, phyzzx require