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  • Copernicus  (2)
  • American Institute of Physics (AIP)  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Singular value analysis and reconstruction of photon correlation data equidistant in time (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 7374-7383 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The application of the algorithm of Zeiger and McEwen to the analysis of noisy photon correlation data is investigated. For the particular case where the data are sampled at equidistant time intervals a complete solution is given allowing reliable reconstruction of the spectrum of exponential decay rates without any a priori knowledge. A particular attractive feature of the method is that the singular value analysis of the Hankel matrix of autocorrelation functions offers a practical criterion for the decomposition of the data into a signal and a noise part. Some tests of the method are illustrated with experiments on monodisperse latices, gold sols, and binary mixtures of monodisperse latices. In the latter case comparable and even better results are obtained in significantly shorter computing time when compared to an analysis with Contin and the maximum entropy method. Since the present method does not require any a priori parameter setting, it is also complementary to these methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457260
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    Paper (German National Licenses)
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  • 2
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    Improved convergence and stability properties in a three-dimensional higher-order ice sheet model (2011)
    Copernicus
    Details
    Publication Date: 2011-12-19
    Description: We present a finite difference implementation of a three-dimensional higher-order ice sheet model. In comparison to a conventional centred difference discretisation it enhances both numerical stability and convergence. In order to achieve these benefits the discretisation of the governing force balance equation makes extensive use of information on staggered grid points. Using the same iterative solver, a centred difference discretisation that operates exclusively on the regular grid serves as a reference. The reprise of the ISMIP-HOM experiments indicates that both discretisations are capable of reproducing the higher-order model inter-comparison results. This setup allows a direct comparison of the two numerical implementations also with respect to their convergence behaviour. First and foremost, the new finite difference scheme facilitates convergence by a factor of up to 7 and 2.6 in average. In addition to this decrease in computational costs, the accuracy for the resultant velocity field can be chosen higher in the novel finite difference implementation. Changing the discretisation also prevents build-up of local field irregularites that occasionally cause divergence of the solution for the reference discretisation. The improved behaviour makes the new discretisation more reliable for extensive application to real ice geometries. Higher accuracy and robust numerics are crucial in time dependent applications since numerical oscillations in the velocity field of subsequent time steps are attenuated and divergence of the solution is prevented.
    Print ISSN: 1991-959X
    Electronic ISSN: 1991-9603
    Topics: Geosciences
    Published by Copernicus on behalf of European Geosciences Union.
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  • 3
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    Improved convergence and stability properties in a three-dimensional higher-order ice sheet model (2011)
    Copernicus
    Details
    Publication Date: 2011-07-20
    Description: We present a novel finite difference implementation of a three-dimensional higher-order ice sheet model that performs well both in terms of convergence rate and numerical stability. In order to achieve these benefits the discretisation of the governing force balance equation makes extensive use of information on staggered grid points. Using the same iterative solver, an existing discretisation that operates exclusively on the regular grid serves as a reference. Participation in the ISMIP-HOM benchmark indicates that both discretisations are capable of reproducing the higher-order model inter-comparison results. This allows a direct comparison not only of the resultant velocity fields but also of the solver's convergence behaviour which holds main differences. First and foremost, the new finite difference scheme facilitates convergence by a factor of up to 7 and 2.6 in average. In addition to this decrease in computational costs, the precision for the resultant velocity field can be chosen higher in the novel finite difference implementation. For high precisions, the old discretisation experiences difficulties to converge due to large variation in the velocity fields of consecutive Picard iterations. Finally, changing discretisation prevents build-up of local field irregularites that occasionally cause divergence of the solution for the reference discretisation. The improved behaviour makes the new discretisation more reliable for extensive application to real ice geometries. Higher precision and robust numerics are crucial in time dependent applications since numerical oscillations in the velocity field of subsequent time steps are attenuated and divergence of the solution is prevented. Transient applications also benefit from the increased computational efficiency.
    Print ISSN: 1991-9611
    Electronic ISSN: 1991-962X
    Topics: Geosciences
    Published by Copernicus on behalf of European Geosciences Union.
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