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Integration Methods (integration + methods)
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] Accuracy and precision of different sampling strategies and flux integration methods for runoff water: comparisons based on measurements of the electrical conductivityHYDROLOGICAL PROCESSES, Issue 2 2006Patrick Schleppi Abstract Because of their fast response to hydrological events, small catchments show strong quantitative and qualitative variations in their water runoff. Fluxes of solutes or suspended material can be estimated from water samples only if an appropriate sampling scheme is used. We used continuous in-stream measurements of the electrical conductivity of the runoff in a small subalpine catchment (64 ha) in central Switzerland and in a very small (0·16 ha) subcatchment. Different sampling and flux integration methods were simulated for weekly water analyses. Fluxes calculated directly from grab samples are strongly biased towards high conductivities observed at low discharges. Several regressions and weighted averages have been proposed to correct for this bias. Their accuracy and precision are better, but none of these integration methods gives a consistently low bias and a low residual error. Different methods of peak sampling were also tested. Like regressions, they produce important residual errors and their bias is variable. This variability (both between methods and between catchments) does not allow one to tell a priori which sampling scheme and integration method would be more accurate. Only discharge-proportional sampling methods were found to give essentially unbiased flux estimates. Programmed samplers with a fraction collector allow for a proportional pooling and are appropriate for short-term studies. For long-term monitoring or experiments, sampling at a frequency proportional to the discharge appears to be the best way to obtain accurate and precise flux estimates. Copyright © 2006 John Wiley & Sons, Ltd. [source] Iterative solution techniques for unsteady flow computations using higher order time integration schemesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8-9 2005H. Bijl Abstract In this paper iterative techniques for unsteady flow computations with implicit higher order time integration methods at large time steps are investigated. It is shown that with a minimal coding effort the standard non-linear multigrid method can be combined with a Newton,Krylov method leading to speed-ups in the order of 30%. Copyright © 2005 John Wiley & Sons, Ltd. [source] ,-Dynamics free energy simulation methodsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 11 2009Jennifer L. Knight Abstract Free energy calculations are fundamental to obtaining accurate theoretical estimates of many important biological phenomena including hydration energies, protein-ligand binding affinities and energetics of conformational changes. Unlike traditional free energy perturbation and thermodynamic integration methods, ,-dynamics treats the conventional "," as a dynamic variable in free energy simulations and simultaneously evaluates thermodynamic properties for multiple states in a single simulation. In the present article, we provide an overview of the theory of ,-dynamics, including the use of biasing and restraining potentials to facilitate conformational sampling. We review how ,-dynamics has been used to rapidly and reliably compute relative hydration free energies and binding affinities for series of ligands, to accurately identify crystallographically observed binding modes starting from incorrect orientations, and to model the effects of mutations upon protein stability. Finally, we suggest how ,-dynamics may be extended to facilitate modeling efforts in structure-based drug design. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009 [source] Comparison of ODE methods for laminar reacting gas flow simulationsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2008S. van Veldhuizen Abstract Two-dimensional transient simulations are presented of the transport phenomena and multispecies, multireaction chemistry in chemical vapor deposition (CVD). The transient simulations are run until steady state, such that the steady state can be validated against the steady state solutions from literature. We compare various time integration methods in terms of efficiency and robustness. Besides stability, which is important due to the stiffness of the problem, preservation of non-negativity is crucial. It appears that this latter condition on a time integration method is much more restrictive toward the time step size than stability. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 [source] Measuring producer welfare under output price uncertainty and risk non-neutralityAUSTRALIAN JOURNAL OF AGRICULTURAL & RESOURCE ECONOMICS, Issue 1 2005David S. Bullock Procedures to measure the producer welfare effects of changes in an output price distribution under uncertainty are reviewed. Theory and numerical integration methods are combined to show how for any form of Marshallian risk-responsive supply, compensating variation of a change in higher moments of an output price distribution can be derived numerically. The numerical procedure enables measurement of producer welfare effects in the many circumstances in which risk and uncertainty are important elements. The practical ease and potential usefulness of the procedure is illustrated by measuring the producer welfare effects of USA rice policy. [source] | ||||||||||