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Fine Grid (fine + grid)
Selected AbstractsSpace,time modeling of 20 years of daily air temperature in the Chicago metropolitan regionENVIRONMETRICS, Issue 5 2009Hae-Kyung Im Abstract We analyze 20 years of daily minimum and maximum air temperature data in the Chicago metropolitan region and propose a parsimonious model that describes their mean function and the space,time covariance structure. The mean function contains a long-term trend, annual and semiannual harmonics, and physical covariates such as latitude, distance to the Lake Michigan, and winds, each interacted with the harmonic terms, thus allowing the effects of physical covariates to vary smoothly over time. The temporal correlation at a given location is described using an ARMA(1,2) model. The residuals (innovations) from this models are treated as independent replications of a spatial process with covariance structure in the Matérn class. The space,time covariance structure parameters are allowed to vary seasonally. Using the estimated covariance structure, we interpolate the temperature to a fine grid in the Chicago metropolitan region. This procedure borrows information from temporally and spatially adjacent data. The methods presented in this paper should be useful to approach other environmental problems where the data are discrete and regular in time but irregular in space. Copyright © 2008 John Wiley & Sons, Ltd. [source] A two-grid method for expanded mixed finite-element solution of semilinear reaction,diffusion equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003Yanping Chen Abstract We present a scheme for solving two-dimensional semilinear reaction,diffusion equations using an expanded mixed finite element method. To linearize the mixed-method equations, we use a two-grid algorithm based on the Newton iteration method. The solution of a non-linear system on the fine space is reduced to the solution of two small (one linear and one non-linear) systems on the coarse space and a linear system on the fine space. It is shown that the coarse grid can be much coarser than the fine grid and achieve asymptotically optimal approximation as long as the mesh sizes satisfy H=O(h1/3). As a result, solving such a large class of non-linear equation will not be much more difficult than solving one single linearized equation. Copyright © 2003 John Wiley & Sons, Ltd. [source] A simple spatio-temporal procedure for the prediction of air pollution levelsJOURNAL OF CHEMOMETRICS, Issue 12 2002Jorge M. Mendes Abstract In this paper we study the spatio-temporal behaviour of air pollutants measured daily over the city of Lisbon, Portugal. Our specific aim is to predict air pollutant levels in time and space over a fine grid of locations based on observations from a small number of monitoring sites. Our suggested prediction procedure is based on the simple and intuitive idea of first making predictions in time at the monitoring sites and then extending these predictions in space to locations other than the monitoring sites using kriging methods. Copyright © 2002 John Wiley & Sons, Ltd. [source] Wavelet-based functional mixed modelsJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2006Jeffrey S. Morris Summary., Increasingly, scientific studies yield functional data, in which the ideal units of observation are curves and the observed data consist of sets of curves that are sampled on a fine grid. We present new methodology that generalizes the linear mixed model to the functional mixed model framework, with model fitting done by using a Bayesian wavelet-based approach. This method is flexible, allowing functions of arbitrary form and the full range of fixed effects structures and between-curve covariance structures that are available in the mixed model framework. It yields nonparametric estimates of the fixed and random-effects functions as well as the various between-curve and within-curve covariance matrices. The functional fixed effects are adaptively regularized as a result of the non-linear shrinkage prior that is imposed on the fixed effects' wavelet coefficients, and the random-effect functions experience a form of adaptive regularization because of the separately estimated variance components for each wavelet coefficient. Because we have posterior samples for all model quantities, we can perform pointwise or joint Bayesian inference or prediction on the quantities of the model. The adaptiveness of the method makes it especially appropriate for modelling irregular functional data that are characterized by numerous local features like peaks. [source] A time-independent approach for computing wave functions of the Schrödinger,Poisson systemNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2008C.-S. Chien Abstract We describe a two-grid finite element discretization scheme for computing wave functions of the Schrödinger,Poisson (SP) system. To begin with, we compute the first k eigenpairs of the Schrödinger,Poisson eigenvalue (ESP) problem on the coarse grid using a continuation algorithm, where the nonlinear Poisson equation is solved iteratively. We use the k eigenpairs obtained on the coarse grid as initial guesses for computing their counterparts of the ESP on the fine grid. The wave functions of the SP system can be easily obtained using the formula of separation of variables. The proposed algorithm has the following advantages. (i) The initial approximate eigenpairs used in the fine grid can be obtained with low computational cost. (ii) It is unnecessary to discretize the partial derivative of the wave function with respect to the time variable in the SP system. (iii) The major computational difficulties such as closely clustered eigenvalues that occur in the SP system can be effectively computed. Numerical results on the ESP and the SP system are reported. In particular, the rate of convergence of the proposed algorithm is O(h4). Copyright © 2007 John Wiley & Sons, Ltd. [source] Analysis of local defect correction and high-order compact finite differencesNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2006M. Sizov Abstract We study the possibility of combining the LDC technique with high-order compact schemes. An algorithm is shown first for the 1D stationary convection-diffusion equation, and then it is extended to 2D. The results of testing show that we get the same accuracy of the solution as on the reference fine grid with much less points in the domain (up to 50% fewer points for the examples presented here). © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006 [source] Comparing mass-consistent atmospheric moisture budgets on an irregular grid: An Arctic exampleTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 592 2003M. Göber Abstract We present a method to minimize the effects of different resolution and mass imbalance when comparing atmospheric energy and water budgets from different datasets. Sizeable differences between re-analysis- and radiosonde-based atmospheric budgets had been found in earlier studies and it had been suspected that the different resolutions of the datasets strongly contributes to these discrepancies. Furthermore, most studies so far had used mass-imbalanced wind fields, which can lead to serious errors. We balance the wind field by using a variational modification algorithm combined with a finite-element discretization which allows the use of data on a grid defined by the radiosonde network. This method permits the computation of flux divergences in integral form and gives a consistent numerical method to get a mass-balanced wind field with minimum modifications. Applying this method to Arctic radiosonde and re-analysis data on the same grid leads to a better agreement with respect to the horizontal distribution and the mean annual cycle of the moisture flux convergence. The constraint of mass balance on the wind field leads to a greatly reduced and more realistic variability in space and time. However, a systematic difference of about 20% remains between the estimate based on a re-analysis dataset sampled only on the coarse grid of the radiosonde network and an estimate based on the use of the full, fine grid of the re-analysis. These systematic differences can be significantly reduced by creating a simulated radiosonde dataset from the re-analysis with doubled resolution. We undertake an extensive analysis of the uncertainty of the estimates originating from the choices made in the specification of the algorithm. Based solely on radiosonde data, which are likely to result in a low bias, we estimate the net water gain of the Arctic atmosphere as 164 ± 10 mm yr,1 (0.45 ± 0.03 mm d,1) for 1979,93. Copyright © 2003 Royal Meteorological Society. [source] A Stable and Efficient Numerical Algorithm for Unconfined Aquifer AnalysisGROUND WATER, Issue 4 2009Elizabeth Keating The nonlinearity of equations governing flow in unconfined aquifers poses challenges for numerical models, particularly in field-scale applications. Existing methods are often unstable, do not converge, or require extremely fine grids and small time steps. Standard modeling procedures such as automated model calibration and Monte Carlo uncertainty analysis typically require thousands of model runs. Stable and efficient model performance is essential to these analyses. We propose a new method that offers improvements in stability and efficiency and is relatively tolerant of coarse grids. It applies a strategy similar to that in the MODFLOW code to the solution of Richard's equation with a grid-dependent pressure/saturation relationship. The method imposes a contrast between horizontal and vertical permeability in gridblocks containing the water table, does not require "dry" cells to convert to inactive cells, and allows recharge to flow through relatively dry cells to the water table. We establish the accuracy of the method by comparison to an analytical solution for radial flow to a well in an unconfined aquifer with delayed yield. Using a suite of test problems, we demonstrate the efficiencies gained in speed and accuracy over two-phase simulations, and improved stability when compared to MODFLOW. The advantages for applications to transient unconfined aquifer analysis are clearly demonstrated by our examples. We also demonstrate applicability to mixed vadose zone/saturated zone applications, including transport, and find that the method shows great promise for these types of problem as well. [source] Coupled ghost fluid/two-phase level set method for curvilinear body-fitted gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2007Juntao Huang Abstract A coupled ghost fluid/two-phase level set method to simulate air/water turbulent flow for complex geometries using curvilinear body-fitted grids is presented. The proposed method is intended to treat ship hydrodynamics problems. The original level set method for moving interface flows was based on Heaviside functions to smooth all fluid properties across the interface. We call this the Heaviside function method (HFM). The HFM requires fine grids across the interface. The ghost fluid method (GFM) has been designed to explicitly enforce the interfacial jump conditions, but the implementation of the jump conditions in curvilinear grids is intricate. To overcome these difficulties a coupled GFM/HFM method was developed in which approximate jump conditions are derived for piezometric pressure and velocity and pressure gradients based on exact continuous velocity and stress and jump in momentum conditions with the jump in density maintained but continuity of the molecular and turbulent viscosities imposed. The implementation of the ghost points is such that no duplication of memory storage is necessary. The level set method is adopted to locate the air/water interface, and a fast marching method was implemented in curvilinear grids to reinitialize the level set function. Validations are performed for three tests: super- and sub-critical flow without wave breaking and an impulsive plunging wave breaking over 2D submerged bumps, and the flow around surface combatant model DTMB 5512. Comparisons are made against experimental data, HFM and single-phase level set computations. The proposed method performed very well and shows great potential to treat complicated turbulent flows related to ship flows. Copyright © 2007 John Wiley & Sons, Ltd. [source] | |||||||||||||