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Rectangular Grid (rectangular + grid)
Selected AbstractsComparison of methods to model the gravitational gradients from topographic data basesGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2006Christopher Jekeli SUMMARY A number of methods have been developed over the last few decades to model the gravitational gradients using digital elevation data. All methods are based on second-order derivatives of the Newtonian mass integral for the gravitational potential. Foremost are algorithms that divide the topographic masses into prisms or more general polyhedra and sum the corresponding gradient contributions. Other methods are designed for computational speed and make use of the fast Fourier transform (FFT), require a regular rectangular grid of data, and yield gradients on the entire grid, but only at constant altitude. We add to these the ordinary numerical integration (in horizontal coordinates) of the gradient integrals. In total we compare two prism, two FFT and two ordinary numerical integration methods using 1, elevation data in two topographic regimes (rough and moderate terrain). Prism methods depend on the type of finite elements that are generated with the elevation data; in particular, alternative triangulations can yield significant differences in the gradients (up to tens of Eötvös). The FFT methods depend on a series development of the topographic heights, requiring terms up to 14th order in rough terrain; and, one popular method has significant bias errors (e.g. 13 Eötvös in the vertical,vertical gradient) embedded in its practical realization. The straightforward numerical integrations, whether on a rectangular or triangulated grid, yield sub-Eötvös differences in the gradients when compared to the other methods (except near the edges of the integration area) and they are as efficient computationally as the finite element methods. [source] Traveltime computation by wavefront-orientated ray tracingGEOPHYSICAL PROSPECTING, Issue 1 2005Radu Coman ABSTRACT For multivalued traveltime computation on dense grids, we propose a wavefront-orientated ray-tracing (WRT) technique. At the source, we start with a few rays which are propagated stepwise through a smooth two-dimensional (2D) velocity model. The ray field is examined at wavefronts and a new ray might be inserted between two adjacent rays if one of the following criteria is satisfied: (1) the distance between the two rays is larger than a predefined threshold; (2) the difference in wavefront curvature between the rays is larger than a predefined threshold; (3) the adjacent rays intersect. The last two criteria may lead to oversampling by rays in caustic regions. To avoid this oversampling, we do not insert a ray if the distance between adjacent rays is smaller than a predefined threshold. We insert the new ray by tracing it from the source. This approach leads to an improved accuracy compared with the insertion of a new ray by interpolation, which is the method usually applied in wavefront construction. The traveltimes computed along the rays are used for the estimation of traveltimes on a rectangular grid. This estimation is carried out within a region bounded by adjacent wavefronts and rays. As for the insertion criterion, we consider the wavefront curvature and extrapolate the traveltimes, up to the second order, from the intersection points between rays and wavefronts to a gridpoint. The extrapolated values are weighted with respect to the distances to wavefronts and rays. Because dynamic ray tracing is not applied, we approximate the wavefront curvature at a given point using the slowness vector at this point and an adjacent point on the same wavefront. The efficiency of the WRT technique is strongly dependent on the input parameters which control the wavefront and ray densities. On the basis of traveltimes computed in a smoothed Marmousi model, we analyse these dependences and suggest some rules for a correct choice of input parameters. With suitable input parameters, the WRT technique allows an accurate traveltime computation using a small number of rays and wavefronts. [source] The development of a new set of long-term climate averages for the UKINTERNATIONAL JOURNAL OF CLIMATOLOGY, Issue 8 2005Matthew Perry Abstract Monthly and annual long-term average datasets of 13 climate variables are generated for the periods 1961,90 and 1971,2000 using a consistent analysis method. Values are produced for each station in the Met Office's observing network and for a rectangular grid of points covering the UK at a horizontal spacing of 1 km. The variables covered are mean, maximum, minimum, grass minimum and soil temperature, days of air and ground frost, precipitation, days with rain exceeding 0.2 and 1 mm, sunshine, and days with thunder and snow cover. Gaps in the monthly station data are filled with estimates obtained via regression relationships with a number of well-correlated neighbours, and long-term averages are then calculated for each site. Gridded datasets are created by inverse-distance-weighted interpolation of regression residuals obtained from the station averages. This method does not work well for days of frost, thunder and snow, so an alternative approach is used. This involves first producing a grid of values for each month from the available station data. The gridded long-term average datasets are then obtained by averaging the monthly grids. The errors associated with each stage in the process are assessed, including verification of the gridding stage by leaving out a set of stations. The estimation of missing values allows a dense network of stations to be used, and this, along with the range of independent variables used in the regression, allows detailed and accurate climate datasets and maps to be produced. The datasets have a range of applications, and the maps are freely available through the Met Office Website. © Crown Copyright 2005. Reproduced with the permission of Her Majesty's Stationery Office. Published by John Wiley & Sons, Ltd. [source] Adaptive integral method combined with the loose GMRES algorithm for planar structures analysisINTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 1 2009W. Zhuang Abstract In this article, the adaptive integral method (AIM) is used to analyze large-scale planar structures. Discretization of the corresponding integral equations by method of moment (MoM) with Rao-Wilton-Glisson (RWG) basis functions can model arbitrarily shaped planar structures, but usually leads to a fully populated matrix. AIM could map these basis functions onto a rectangular grid, where the Toeplitz property of the Green's function would be utilized, which enables the calculation of the matrix-vector multiplication by use of the fast Fourier transform (FFT) technique. It reduces the memory requirement from O(N2) to O(N) and the operation complexity from O(N2) to O(N log N), where N is the number of unknowns. The resultant equations are then solved by the loose generalized minimal residual method (LGMRES) to accelerate iteration, which converges much faster than the conventional conjugate gradient method (CG). Furthermore, several preconditioning techniques are employed to enhance the computational efficiency of the LGMRES. Some typical microstrip circuits and microstrip antenna array are analyzed and numerical results show that the preconditioned LGMRES can converge much faster than conventional LGMRES. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009. [source] Environmental determinants of vascular plant species richness in the Austrian AlpsJOURNAL OF BIOGEOGRAPHY, Issue 7 2005Dietmar Moser Abstract Aim, To test predictions of different large-scale biodiversity hypotheses by analysing species richness patterns of vascular plants in the Austrian Alps. Location, The Austrian part of the Alps (c. 53,500 km2). Methods, Within the floristic inventory of Central Europe the Austrian part of the Alps were systematically mapped for vascular plants. Data collection was based on a rectangular grid of 5 × 3 arc minutes (34,35 km2). Emerging species richness patterns were correlated with several environmental factors using generalized linear models. Primary environmental variables like temperature, precipitation and evapotranspiration were used to test climate-related hypotheses of species richness. Additionally, spatial and temporal variations in climatic conditions were considered. Bedrock geology, particularly the amount of calcareous substrates, the proximity to rivers and lakes and secondary variables like topographic, edaphic and land-use heterogeneity were used as additional predictors. Model results were evaluated by correlating modelled and observed species numbers. Results, Our final multiple regression model explains c. 50% of the variance in species richness patterns. Model evaluation results in a correlation coefficient of 0.64 between modelled and observed species numbers in an independent test data set. Climatic variables like temperature and potential evapotranspiration (PET) proved to be by far the most important predictors. In general, variables indicating climatic favourableness like the maxima of temperature and PET performed better than those indicating stress, like the respective minima. Bedrock mineralogy, especially the amount of calcareous substrate, had some additional explanatory power but was less influential than suggested by comparable studies. The amount of precipitation does not have any effect on species richness regionally. Among the descriptors of heterogeneity, edaphic and land-use heterogeneity are more closely correlated with species numbers than topographic heterogeneity. Main conclusions, The results support energy-driven processes as primary determinants of vascular plant species richness in temperate mountains. Stressful conditions obviously decrease species numbers, but presence of favourable habitats has higher predictive power in the context of species richness modelling. The importance of precipitation for driving global species diversity patterns is not necessarily reflected regionally. Annual range of temperature, an indicator of short-term climatic stability, proved to be of minor importance for the determination of regional species richness patterns. In general, our study suggests environmental heterogeneity to be of rather low predictive value for species richness patterns regionally. However, it may gain importance at more local scales. [source] A Comparison of the Mixing Characteristics in Single- and Two-Phase Grid-Generated Turbulent Flow SystemsCHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 6 2004J.S. Moghaddas Abstract The mixing process is studied in grid-generated turbulent flow for single- and bubbly two-phase flow systems. Concentration and mixing characteristics in the liquid phase are measured with the aid of a PLIF/PLIF arrangement. A nearly isotropic turbulent flow field is generated at the center of the vertical pipe by using a honeycomb, three grids and a contraction. In two-phase flow experiments, air bubbles were injected into the flow from a rectangular grid, with mesh size M = 6 mm, which is placed midway between two circular grids each with a mesh size of M = 2 mm. For single-phase flow, the normalized mean concentration cross-stream profiles have rather similar Gaussian shapes, and the cross-stream profiles of the normalized root-mean-square (RMS) values of concentration were found to be quite similar. Cross-stream profiles of the mean concentration, for bubbly two-phase flow, were also found to be quite similar, but they did not have the Gaussian shape of the profiles for single-phase flow. Almost self-similar behavior was also found for the RMS values of the concentration in two-phase systems. The turbulent diffusion coefficient in the liquid phase was also calculated. At the center of the plume, the flow was found to have a periodic coherent structure, probably of vortex shedding character. Observations showed that the period of oscillation is higher in the case of two-phase flow than in single-phase flow. [source] A parallel adaptive projection method for low Mach number flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1-2 2002J. B. Bell We describe an adaptive projection method for numerically simulating low Mach number flows. The projection method formulation enforces the velocity divergence constraint resulting from the low Mach number approximation. It is implemented on an adaptive hierarchy of logically rectangular grids, where each finer level is refined in space and in time. The adaptive algorithm has been shown in previous papers to be robust and second-order accurate, and to satisfy the principles of conservation and free-stream preservation as applicable. Here, the parallelization is described in some detail, and the methodology is demonstrated on two examples from premixed, low Mach number combustion. Published in 2002 by John Wiley & Sons, Ltd. [source] A cell boundary element method for elliptic problems,NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2005Youngmok Jeon Abstract An elementary analysis on the cell boundary element (CBEM) was given by Jeon and Sheen. In this article we improve the previous results in various aspects. First of all, stability and convergence analysis on the rectangular grids are established. Moreover, error estimates are improved. Our improved analysis was possible by recasting of the CBEM in a Petrov-Galerkin setting. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 [source] | |||||||||||||