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Comparable Accuracy (comparable + accuracy)
Selected AbstractsSelf-regular boundary integral equation formulations for Laplace's equation in 2-DINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2001A. B. Jorge Abstract The purpose of this work is to demonstrate the application of the self-regular formulation strategy using Green's identity (potential-BIE) and its gradient form (flux-BIE) for Laplace's equation. Self-regular formulations lead to highly effective BEM algorithms that utilize standard conforming boundary elements and low-order Gaussian integrations. Both formulations are discussed and implemented for two-dimensional potential problems, and numerical results are presented. Potential results show that the use of quartic interpolations is required for the flux-BIE to show comparable accuracy to the potential-BIE using quadratic interpolations. On the other hand, flux error results in the potential-BIE implementation can be dominated by the numerical integration of the logarithmic kernel of the remaining weakly singular integral. Accuracy of these flux results does not improve beyond a certain level when using standard quadrature together with a special transformation, but when an alternative logarithmic quadrature scheme is used these errors are shown to reduce abruptly, and the flux results converge monotonically to the exact answer. In the flux-BIE implementation, where all integrals are regularized, flux results accuracy improves systematically, even with some oscillations, when refining the mesh or increasing the order of the interpolating function. The flux-BIE approach presents a great numerical sensitivity to the mesh generation scheme and refinement. Accurate results for the potential and the flux were obtained for coarse-graded meshes in which the rate of change of the tangential derivative of the potential was better approximated. This numerical sensitivity and the need for graded meshes were not found in the elasticity problem for which self-regular formulations have also been developed using a similar approach. Logarithmic quadrature to evaluate the weakly singular integral is implemented in the self-regular potential-BIE, showing that the magnitude of the error is dependent only on the standard Gauss integration of the regularized integral, but not on this logarithmic quadrature of the weakly singular integral. The self-regular potential-BIE is compared with the standard (CPV) formulation, showing the equivalence between these formulations. The self-regular BIE formulations and computational algorithms are established as robust alternatives to singular BIE formulations for potential problems. Copyright © 2001 John Wiley & Sons, Ltd. [source] An approximate projection method for incompressible flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2002David E. Stevens This paper presents an approximate projection method for incompressible flows. This method is derived from Galerkin orthogonality conditions using equal-order piecewise linear elements for both velocity and pressure, hereafter Q1Q1. By combining an approximate projection for the velocities with a variational discretization of the continuum pressure Poisson equation, one eliminates the need to filter either the velocity or pressure fields as is often needed with equal-order element formulations. This variational approach extends to multiple types of elements; examples and results for triangular and quadrilateral elements are provided. This method is related to the method of Almgren et al. (SIAM J. Sci. Comput. 2000; 22: 1139,1159) and the PISO method of Issa (J. Comput. Phys. 1985; 62: 40,65). These methods use a combination of two elliptic solves, one to reduce the divergence of the velocities and another to approximate the pressure Poisson equation. Both Q1Q1 and the method of Almgren et al. solve the second Poisson equation with a weak error tolerance to achieve more computational efficiency. A Fourier analysis of Q1Q1 shows that a consistent mass matrix has a positive effect on both accuracy and mass conservation. A numerical comparison with the widely used Q1Q0 (piecewise linear velocities, piecewise constant pressures) on a periodic test case with an analytic solution verifies this analysis. Q1Q1 is shown to have comparable accuracy as Q1Q0 and good agreement with experiment for flow over an isolated cubic obstacle and dispersion of a point source in its wake. Copyright © 2002 John Wiley & Sons, Ltd. [source] Development of an Antibody Hapten-Chip System for Detecting the Residues of Multiple Antibiotic Drugs,JOURNAL OF FORENSIC SCIENCES, Issue 4 2009Ailiang Chen M.Sc. Abstract:, The abuse of antibiotic drugs during animal production remains a worldwide problem and the subsequent detection of the residues of various drugs present at low concentrations in complex biological matrices poses significant analytical challenges. The present study outlines a practical biochip assay system to identify antibiotic residues in different animal tissue extracts. The system uses a simple but efficient multiresidue sample extraction procedure to isolate the antibiotic residues which were then identified directly using high-affinity monoclonal antibodies presented in a competitive immunoassay with conjugated antibiotic hapten-chips. The hapten-chip can analyze six samples each for eight antibiotics on a single chip within 3 h. The analytical results with both artificial positive standard samples and the incurred samples show that the antibody hapten-chip system has a comparable accuracy and a similar sensitivity to a standard ultra performance liquid chromatography,mass spectrometry (MS)/MS assay. In conclusion, an effective analytical screening system based on antibody hapten-chip was developed for detecting multiple antibiotic residues from multiple samples. [source] Group contribution prediction of surface charge density profiles for COSMO-RS(Ol)AICHE JOURNAL, Issue 12 2007Tiancheng Mu Abstract A new method for predicting the surface charge density distribution (, profile) and cavity volume of molecules based on group contributions was developed. The original , profiles used for the regression were obtained using Gaussian 03 B3LYP/6-311G(d,p). In total 1363 , profiles were used for the regression of group parameters. Group definitions are identical to those used previously for boiling point estimation. Original and estimated , profiles were used to predict activity coefficients at infinite dilution and VLE data of binary systems using the COSMO-RS(Ol) model. The results were compared with the experimental data stored in the Dortmund Data Bank. In many cases the results were of comparable accuracy. However, for a few compounds, poor results were obtained, in particular for conjugated components like nitrobenzenes. The method offers a fast and reliable generation of , profiles to be used with COSMO-RS(Ol) within its range of applicability. © 2007 American Institute of Chemical Engineers AIChE J, 2007 [source] Pitfalls and advantages of different strategies for the absolute quantification of N -acetyl aspartate, creatine and choline in white and grey matter by 1H-MRSNMR IN BIOMEDICINE, Issue 10 2009E. Malucelli Abstract This study extensively investigates different strategies for the absolute quantitation of N -acetyl aspartate, creatine and choline in white and grey matter by 1H-MRS at 1.5,T. The main focus of this study was to reliably estimate metabolite concentrations while reducing the scan time, which remains as one of the main problems in clinical MRS. Absolute quantitation was based on the water-unsuppressed concentration as the internal standard. We compared strategies based on various experimental protocols and post-processing strategies. Data were obtained from 30 control subjects using a PRESS sequence at several TE to estimate the transverse relaxation time, T2, of the metabolites. Quantitation was performed with the algorithm QUEST using two different metabolite signal basis sets: a whole-metabolite basis set (WhoM) and a basis set in which the singlet signals were split from the coupled signals (MSM). The basis sets were simulated in vivo for each TE used. Metabolites' T2s were then determined by fitting the estimated signal amplitudes of the metabolites obtained at different TEs. Then the absolute concentrations (mM) of the metabolites were assessed for each subject using the estimated signal amplitudes and either the mean estimated relaxation times of all subjects (mean protocol, MP) or the T2 estimated from the spectra derived from the same subject (individual protocol, IP). Results showed that MP represents a less time-consuming alternative to IP in the quantitation of brain metabolites by 1H-MRS in both grey and white matter, with a comparable accuracy when performed by MSM. It was also shown that the acquisition time might be further reduced by using a variant of MP, although with reduced accuracy. In this variant, only one water-suppressed and one water-unsuppressed spectra were acquired, drastically reducing the duration of the entire MRS examination. However, statistical analysis highlights the reduced accuracy of MP when performed using WhoM, particularly at longer echo times. Copyright © 2009 John Wiley & Sons, Ltd. [source] A twisted factorization method for symmetric SVD of a complex symmetric tridiagonal matrixNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 10 2009Wei Xu Abstract This paper presents an O(n2) method based on the twisted factorization for computing the Takagi vectors of an n -by- n complex symmetric tridiagonal matrix with known singular values. Since the singular values can be obtained in O(n2) flops, the total cost of symmetric singular value decomposition or the Takagi factorization is O(n2) flops. An analysis shows the accuracy and orthogonality of Takagi vectors. Also, techniques for a practical implementation of our method are proposed. Our preliminary numerical experiments have verified our analysis and demonstrated that the twisted factorization method is much more efficient than the implicit QR method, divide-and-conquer method and Matlab singular value decomposition subroutine with comparable accuracy. Copyright © 2009 John Wiley & Sons, Ltd. [source] | |||||||||||||