Please use this identifier to cite or link to this item: http://ir.lib.seu.ac.lk/handle/123456789/1452
Title: An application of Fourier series expansion of a function in a non-polar spherical coordinate system
Authors: Faham, M. A. A. Mohamed
Keywords: Cubed sphere
Pole problems
Non-polar coordinates
Spherical harmonics
Fourier series
Issue Date: 2-Aug-2014
Publisher: South Eastern University of Sri Lanka, University Park, Oluvil #32360, Sri Lanka
Citation: Proceedings of 4th International Symposium 2015 on " Emerging Trends and Challenges on Sustainable Development”, p. 64
Abstract: Cubed sphere is one of the main tools used to avoid pole problems those arise in the selection of spherical polar coordinates. In this respect, earlier we considered a recently developed cubed sphere based on coordinate mapping over the cubed surface. The function on the sphere was treated as an ordered set of six-tuples. In that work, we established weakly orthogonal and completely orthogonal spherical harmonics of the system and developed corresponding symmetric and linear relations. Also, we found the norm of the orthogonal spherical harmonics. In this work, we explore the Fourier representation of a spherical function on this coordinate system in terms of weakly orthogonal spherical harmonics. The advantages of the linear relation between the two sets of spherical harmonics and diagonal property of the norm of the fully orthogonal spherical harmonics were in cooperated for this work. We also strength our work by giving an example to demonstrate how Fourier coefficients can be computed to represent a given spherical function in terms of the spherical harmonics of the coordinate system.
URI: http://ir.lib.seu.ac.lk/handle/123456789/1452
ISBN: 978-955-627-053-2
Appears in Collections:4th International Symposium - 2014

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