Optimal Grid Size Research Articles

Information measure of location precision

The optimal grid size for specifying object location in one and two dimensions is found by maximizing the information content (entropy) of the system in which the objects reside. The information content increases logarithmically as the decreasing grid size approaches the object size, reflecting the increasing precision of object location, but thereafter the increase is not monotonic. This implies, for example, that the fidelity of a digitized image is dependent on pixel size in a nontrivial way.

Complete Hydrodynamic Border-Strip Irrigation Model

In this study, a hydrodynamic model is presented for simulating all the phases of border-strip irrigation. The explicit, second-order accurate MacCormack scheme is used for solving the governing equations of surface irrigation. In this method, the advance and recession fronts need not be considered explicitly and any infiltration equation can be coupled to the surface flow equations easily. The empirical Kostiakov equation (Model 1DKO) and the analytical Parlange equation (Model 1DPA) for infiltration are considered in this study. The implicit Parlange equation is solved using the Newton-Raphson technique. The models are validated using the experimental data available in literature. The present results are also compared with the earlier numerical results based on the characteristic method. A simple subgrid technique is introduced in order to obtain a high grid resolution near the advancing front and at the same time achieve a minimum computational cost. This is based on using two different grid sizes for computation. An equation for the optimum grid size ratio is presented and is validated using numerical experimentation.

An Estimation of Optimum Grid Size for Kashmir Valley by Spectral Method

In many of the short-range numerical weather prediction models, an accurate specification of grid size is essential in mountainous and valley regions to adequately represent terrain forcing without resorting to subgrid-scale parameterization. Since the geomorphology of the earth is quite varied, an improper specification of grid size will neither be adequate nor realistic. In this study, the spectral method is used to determine the required optimum horizontal grid size for numerical simulations enclosing Kashmir Valley and its surroundings.

Parallel complexity of domain decomposition methods and optimal coarse grid size

In this paper, we analyze the parallel complexity of domain decomposition method through estimating the arithmetic time as well as the communication time. In most domain decomposition (DD) methods, a coarse grid solve is employed to provide global coupling and obtain an optimal convergence rate. Generally, a small coarse grid size H improves the convergence rate at the cost of a larger coarse grid problem and a large number P of processors results in more costly global communication, whereas a large H and a small P have the opposite effect. Therefore, there often exists an optimal H such that the execution time on the parallel machine reaches a minimum. Our main goal here is to find this optimal coarse grid size H in the parallel environment. We assume the same solver is used for the subdomains as well as the coarse problem. By expressing the parallel complexity as a function of H and h, we can derive the analytic optimal coarse grid size H opt. When the number of processors is equal to the number of subdomains, we can prove that the choice of H opt = √ h asymptotically minimises the execution time as h tends to zero. This optimal coarse grid size is independent of the choice of subproblem solvers and the spatial dimension. However, when the number of processors is much less than the number of subdomains, the optimal coarse grid size depends on the number of processors, the subdomain solver and dimension.

Optimum size of feeder grids in relation to the welfare of broiler breeder females fed on a separate sex basis

1. The rate of eating food was studied in two experiments to assess the relationship between head width and size of feeder grids in broiler breeder females. 2. The optimum grid size for food intake was 4 mm wider than head width. 3. Physical injury should be avoided if the grid aperture is 2 mm wider than the maximum head width in the flock measured at the posterior edge of the mandibles. 4. The rate of eating was decreased in all grid sizes examined compared to feeders without grids but the importance of this observation for the welfare of broiler breeders is not clear.

ON REGIONAL OPTIMISATION OF GRID AND RELAXATION PARAMETER FOR FINITE DIFFERENCE SOLUTION OF POISSONS' EQUATION IN REVERSE BIASED PLANAR TYPE p‐n JUNCTIONS

The optimisation of grid structure and relaxation parameter is considered in this paper in connection with two‐dimensional finite difference solution of Poisson's equation for determining the field profile in a reverse biased planar type p?n junction. By dividing the planar junction into regions with rectangular and circular symmetry, regional optimisations have been carried out using small area test sites. Having obtained the optimal grid size and relaxation parameter for each region, the complete solution was obtained easily with very fast convergence. The method involved in this kind of regional optimisation is presented in detail with discussions on its comparative usefulness with other known techniques.

On the optimum grid size in field experiments without replications

In unreplicated field trials a correction for soil heterogeneity is easily achieved by ‘gridding’, i.e. by expressing the observations as deviations from a local average. This paper investigates the problem of determining the optimum size of such a neighbourhood to be used in a moving average. The optimum grid size depends on two parameters, i.e. the ‘coarseness’ of the spatial variation of the trial field and the ratio of genotypic vs. non-genotypic variance. In general these parameters are not known to the breeder. We introduce a method for estimating these parameters from the data. From these estimates the optimum grid size can be obtained using tables presented in this paper.

The effect of data grid size on certain interpolation methods for unconstrained function minimization

Interpolation methods fit a model to a given objective function by evaluating the objective function at, say, M points of a grid. If the model has, say, N independent coefficients which have to be determined, they are found by solving a set of M linear simultaneous equations in N unknowns. In this paper the effect on these methods is tested of enlarging the size of the grid ( M) to include more than N points. Numerical results show that the optimal data grid size tends to occur when M = N.