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Interpolation Error (interpolation + error)
Selected AbstractsEstimating the snow water equivalent on the Gatineau catchment using hierarchical Bayesian modellingHYDROLOGICAL PROCESSES, Issue 4 2006Ousmane Seidou Abstract One of the most important parameters for spring runoff forecasting is the snow water equivalent on the watershed, often estimated by kriging using in situ measurements, and in some cases by remote sensing. It is known that kriging techniques provide little information on uncertainty, aside from the kriging variance. In this paper, two approaches using Bayesian hierarchical modelling are compared with ordinary kriging; Bayesian hierarchical modelling is a flexible and general statistical approach that uses observations and prior knowledge to make inferences on both unobserved data (snow water equivalent on the watershed where there is no measurements) and on the parameters (influence of the covariables, spatial interactions between the values of the process at various sites). The first approach models snow water equivalent as a Gaussian spatial process, for which the mean varies in space, and the other uses the theory of Markov random fields. Although kriging and the Bayesian models give similar point estimates, the latter provide more information on the distribution of the snow water equivalent. Furthermore, kriging may considerably underestimate interpolation error. Copyright © 2006 Environment Canada. Published by John Wiley & Sons, Ltd. [source] Geodesic finite elements for Cosserat rodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010Oliver Sander Abstract We introduce geodesic finite elements as a new way to discretize the non-linear configuration space of a geometrically exact Cosserat rod. These geodesic finite elements naturally generalize standard one-dimensional finite elements to spaces of functions with values in a Riemannian manifold. For the special orthogonal group, our approach reproduces the interpolation formulas of Crisfield and Jeleni,. Geodesic finite elements are conforming and lead to objective and path-independent problem formulations. We introduce geodesic finite elements for general Riemannian manifolds, discuss the relationship between geodesic finite elements and coefficient vectors, and estimate the interpolation error. Then we use them to find static equilibria of hyperelastic Cosserat rods. Using the Riemannian trust-region algorithm of Absil et al. we show numerically that the discretization error depends optimally on the mesh size. Copyright © 2009 John Wiley & Sons, Ltd. [source] Adaptive mesh technique for thermal,metallurgical numerical simulation of arc welding processesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008M. Hamide Abstract A major problem arising in finite element analysis of welding is the long computer times required for a complete three-dimensional analysis. In this study, an adaptative strategy for coupled thermometallurgical analysis of welding is proposed and applied in order to provide accurate results in a minimum computer time. The anisotropic adaptation procedure is controlled by a directional error estimator based on local interpolation error and recovery of the second derivatives of different fields involved in the finite element calculation. The methodology is applied to the simulation of a gas,tungsten-arc fusion line processed on a steel plate. The temperature field and the phase distributions during the welding process are analyzed by the FEM method showing the benefits of dynamic mesh adaptation. A significant increase in accuracy is obtained with a reduced computational effort. Copyright © 2007 John Wiley & Sons, Ltd. [source] Adaptive moving mesh methods for simulating one-dimensional groundwater problems with sharp moving frontsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2002Weizhang Huang Abstract Accurate modelling of groundwater flow and transport with sharp moving fronts often involves high computational cost, when a fixed/uniform mesh is used. In this paper, we investigate the modelling of groundwater problems using a particular adaptive mesh method called the moving mesh partial differential equation approach. With this approach, the mesh is dynamically relocated through a partial differential equation to capture the evolving sharp fronts with a relatively small number of grid points. The mesh movement and physical system modelling are realized by solving the mesh movement and physical partial differential equations alternately. The method is applied to the modelling of a range of groundwater problems, including advection dominated chemical transport and reaction, non-linear infiltration in soil, and the coupling of density dependent flow and transport. Numerical results demonstrate that sharp moving fronts can be accurately and efficiently captured by the moving mesh approach. Also addressed are important implementation strategies, e.g. the construction of the monitor function based on the interpolation error, control of mesh concentration, and two-layer mesh movement. Copyright © 2002 John Wiley & Sons, Ltd. [source] Modelling long-term pan-European population change from 1870 to 2000 by using geographical information systemsJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES A (STATISTICS IN SOCIETY), Issue 1 2010Ian N. Gregory Summary., The paper presents work that creates a geographical information system database of European census data from 1870 to 2000. The database is integrated over space and time. Spatially it consists of regional level data for most of Europe; temporally it covers every decade from 1870 to 2000. Crucially the data have been interpolated onto the administrative units that were available in 2000, thus allowing contemporary population patterns to be understood in the light of the changes that have occurred since the late 19th century. The effect of interpolation error on the resulting estimates is explored. This database will provide a framework for much future analysis on long-term Europewide demographic processes over space and time. [source] The effects of interpolation error and location quality on animal track reconstructionMARINE MAMMAL SCIENCE, Issue 2 2009Mike Lonergan Abstract The Global Positioning System (GPS) gives precise estimates of location. However, the investigation of animal movement and behavior often requires interpolation to examine events between such fixes. We obtained 6,288 GPS locations from an electronic tag deployed for 170 d on an adult male gray seal (Halichoerus grypus) that ranged freely off the east coast of Scotland, and interpolated between subsamples of these data to investigate the growth of uncertainty within the intervals between observations. Average uncertainty over the path increased linearly as the interval between interpolating locations increased, reaching 12 km in longitude and 6 km in latitude at 2-d separation. The decrease in precision caused by duty-cycling, only collecting data in part of the day, was demonstrated. Adding noise to the GPS locations to simulate data from the ARGOS satellite system had little effect on the total errors for observations separated by more than 12 h. While the rate of growth in interpolation error is likely to vary between species, these results suggest that frequent, and preferably evenly spaced, location fixes are required to take full advantage of the precision of GPS data in the reconstruction of animal tracks. [source] Anisotropic mesh adaptation for numerical solution of boundary value problemsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2004Vít Dolej Abstract We present an efficient mesh adaptation algorithm that can be successfully applied to numerical solutions of a wide range of 2D problems of physics and engineering described by partial differential equations. We are interested in the numerical solution of a general boundary value problem discretized on triangular grids. We formulate a necessary condition for properties of the triangulation on which the discretization error is below the prescribed tolerance and control this necessary condition by the interpolation error. For a sufficiently smooth function, we recall the strategy how to construct the mesh on which the interpolation error is below the prescribed tolerance. Solving the boundary value problem we apply this strategy to the smoothed approximate solution. The novelty of the method lies in the smoothing procedure that, followed by the anisotropic mesh adaptation (AMA) algorithm, leads to the significant improvement of numerical results. We apply AMA to the numerical solution of an elliptic equation where the exact solution is known and demonstrate practical aspects of the adaptation procedure: how to control the ratio between the longest and the shortest edge of the triangulation and how to control the transition of the coarsest part of the mesh to the finest one if the two length scales of all the triangles are clearly different. An example of the use of AMA for the physically relevant numerical simulation of a geometrically challenging industrial problem (inviscid transonic flow around NACA0012 profile) is presented. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004. [source] | |||||||||||||