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Estimated Errors (estimated + error)
Selected AbstractsA stopping criterion for the conjugate gradient algorithm in the framework of anisotropic adaptive finite elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2009M. Picasso Abstract We propose a simple stopping criterion for the conjugate gradient (CG) algorithm in the framework of anisotropic, adaptive finite elements for elliptic problems. The goal of the adaptive algorithm is to find a triangulation such that the estimated relative error is close to a given tolerance TOL. We propose to stop the CG algorithm whenever the residual vector has Euclidian norm less than a small fraction of the estimated error. This stopping criterion is based on a posteriori error estimates between the true solution u and the computed solution u (the superscript n stands for the CG iteration number, the subscript h for the typical mesh size) and on heuristics to relate the error between uh and u to the residual vector. Numerical experiments with anisotropic adaptive meshes show that the total number of CG iterations can be divided by 10 without significant discrepancy in the computed results. Copyright © 2008 John Wiley & Sons, Ltd. [source] Validation of the FACSCount AF System for Determination of Sperm Concentration in Boar SemenREPRODUCTION IN DOMESTIC ANIMALS, Issue 6 2002C Hansen Contents A flow cytometric method has been developed for rapid determination of sperm concentration in semen from various mammalian species., All cells containing DNA are stained with SYBR-14 or propidium iodide (PI) and sperm concentration is determined in relation to an internal standard of fluorescent microspheres (beads). Satisfactory staining can be achieved within 2,3 min and the following flow cytometric analysis on the FACSCount AF System rapidly provides the user with a precise and accurate assessment of the sperm concentration. In this study, the FACSCount AF System and Sperm Counting Reagent (BD Biosciences) was compared with microscopic counting using a Bürker,Türk haemocytometer. In addition, sperm concentration was determined using the Corning 254 spectrophotometer which is used routinely by Danish artificial insemination stations for boars. The results show that the agreement between flow cytometry and microscopic counting is very high. The slope for the regression line was 1.12 (SE = 0.03) with an estimated intercept with the Y-axis of 22 × 106sperm/ml (SE = 10 × 106 sperm/ml) and an estimated error of the model of 10 × 106 sperm/ml. For the spectrophotometer, the slope of the regression line was 1.09 (SE = 0.07) with an estimated intercept of 137 × 106 sperm/ml (SE = 25 × 106 sperm/ml). The average error made by the spectrophotometer was 55 × 106 sperm/ml. In addition, the results obtained using flow cytometry was highly repeatable (CV = 2.7%) in comparison with the spectrophotometric method (CV = 6.3%). These results indicate that the FACSCount AF System is a valuable tool for precise and accurate assessment of sperm concentration in boar semen and that use of this system may lead to production of more uniform insemination doses containing a specific number of sperm per dose. [source] Numerical investigation of the reliability of a posteriori error estimation for advection,diffusion equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2008A. H. ElSheikh Abstract A numerical investigation of the reliability of a posteriori error estimation for advection,diffusion equations is presented. The estimator used is based on the solution of local problems subjected to Neumann boundary conditions. The estimated errors are calculated in a weighted energy norm, a stability norm and an approximate fractional order norm in order to study the effect of the error norm on both the effectivity index of the estimated errors and the mesh adaptivity process. The reported numerical results are in general better than what is available in the literature. The results reveal that the reliability of the estimated errors depends on the relation between the mesh size and the size of local features in the solution. The stability norm is found to have some advantages over the weighted energy norm in terms of producing effectivity indices closer to the optimal unit value, especially for problems with internal sharp layers. Meshes adapted by the element residual method measured in the stability norm conform to the sharp layers and are shown to be less dependent on the wind direction. Copyright © 2007 John Wiley & Sons, Ltd. [source] Adaptive crack propagation analysis with the element-free Galerkin methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2003Gye-Hee Lee Abstract In this paper, an adaptive analysis of crack propagation based on the error estimation by the element-free Galerkin (EFG) method is presented. The adaptivity analysis in quasi-static crack propagation is achieved by adding and/or removing the nodes along the background integration cells, those are refined or recovered according to the estimated errors. These errors are obtained basically by calculating the difference between the values of the projected stresses and original EFG stresses. To evaluate the performance of the proposed adaptive procedure, the crack propagation behaviour is investigated for several examples. The results of these examples show the efficiency and accuracy of the proposed scheme in crack propagation analysis. Copyright © 2002 John Wiley & Sons, Ltd. [source] The effect of instrument exposure on marine air temperatures: an assessment using VOSClim DataINTERNATIONAL JOURNAL OF CLIMATOLOGY, Issue 7 2005David I. Berry Abstract Observations of marine air temperature (MAT) by Voluntary Observing Ships (VOS) are known to contain significant biases due to solar heating of the sensor environment. MAT and humidity observations are usually made using wet- and dry-bulb thermometers housed in Stevenson screens, or with psychrometers. These instruments are typically mounted in the bridge wings or on the wheel-house top. If not sited carefully then the instruments can be poorly exposed to the undisturbed environmental conditions and have inadequate ventilation, leading to biased observations of both MAT and humidity. In this paper we use observations collected as part of the VOS Climate (VOSClim) project to investigate the relationship between instrument exposure and heating errors. The heating errors are estimated as the difference between the observed MAT and the collocated output of a numerical weather prediction model. The instrument exposures are assessed from photographs of the instruments. Currently, photographs of the instruments and sufficient observations exist for 17 VOSClim ships. Two methods of assessing the instrument exposure using the observations are presented. The first method is based on the skewness of the distribution of estimated heating errors for individual ships. The second method is based on a correction developed to correct the heating errors and uses the ratio of the heating to cooling terms in the correction. When ships are ranked both on the skewness and on the ratio of the heating to cooling terms, there is a statistically significant correspondence between the rankings and the visual assessments of instrument exposure. The skewness of the distribution of estimated errors in MAT is proposed as a simple indicator of instrument exposure. Copyright © 2005 Royal Meteorological Society [source] | ||||||||||