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Minimising the Calculation Time of the Cluster Program by Choosing the Minimum Convergent Cluster Size and the Best Relaxation Factor

Minimising the Calculation Time of the Cluster Program by Choosing the Minimum Convergent Cluster Size and the Best Relaxation Factor


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About the Book

This dissertation, "Minimising the Calculation Time of the Cluster Program by Choosing the Minimum Convergent Cluster Size and the Best Relaxation Factor" by Wai-ping, Lau, 劉偉平, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled MINIMISING THE CALCULATION TIME OF THE CLUSTER PROGRAM BY CHOOSING THE MINIMUM CONVERGENT CLUSTER SIZE AND THE BEST RELAXATION FACTOR submitted by Lau Wai Ping for the Degree of Master of Philosophy at The University of Hong Kong in July 1999 The formulation of accurate multiple scattering theories of structural determination is a major accomplishment in surface science. Unfortunately, conventional slab approach to multiple scattering calculation of angle-resolved photoelectron diffraction cannot be applied to systems without long-range order. Recently, Rehr and Albers have introduced a separable propagator perturbation cluster approach which can deal with disorder systems. In this approach, the multiple scattering is divided into scattering paths in a perturbation expansion. Based on the achievements of Rehr and Albers, Wu et al. introduced a backward summing method that casts the cluster approach into solving a set of linear equations. The computation time of this method depends linearly on the multiple scattering order. To solve the set of linear equations, a relaxation-iterative method is used rather than conventional Gaussian elimination method. This iteration method reduces the computation time 3 1.5 2 from the scale of N to N where N = 6n and n is the number of atoms in a cluster. In this thesis, results obtained by this backward summing relaxation-iterative method show that it is convergent for different materials. By comparing the photoelectron spectra of different cluster sizes, minimum convergent cluster size of different elements have been found. Moreover, the best relaxation factor of the iteration equation, which minimises the multiple scattering order, has been found too. By choosing the minimum convergent cluster size and the best relaxation factor, the computation time of this backward summing relaxation-iterative method is thus significantly reduced. DOI: 10.5353/th_b2976039 Subjects: Electrons - Diffraction Surfaces (Physics) - Mathematical models


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Product Details
  • ISBN-13: 9781374712058
  • Publisher: Open Dissertation Press
  • Publisher Imprint: Open Dissertation Press
  • Height: 279 mm
  • No of Pages: 48
  • Weight: 413 gr
  • ISBN-10: 1374712051
  • Publisher Date: 27 Jan 2017
  • Binding: Hardback
  • Language: English
  • Spine Width: 6 mm
  • Width: 216 mm

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Minimising the Calculation Time of the Cluster Program by Choosing the Minimum Convergent Cluster Size and the Best Relaxation Factor
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