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Deformation and Smoothing of Cusp Singularities

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submitted on 2024-09-16, 09:31 and posted on 2024-09-17, 06:11 authored by F Mumtaz, F H Alharbi

A cusp singularity (CS), is a point at which the slope of a continuous curve changes abruptly in sign and magnitude. A particular type of CS, which is the focus of this paper, is where only the sign of the slope is altered while the magnitude of the slope is unchanged. This type of CSs occur in many natural phenomena such as Kato's cusp and particular plasmonics. Solving such problems numerically can be challenging because of the discontinuity in the derivatives. In this paper, we present an efficient spectral method incorporated with transformation (mapping) to handle the cusp problem. The transformation is based on functions that are locally odd around all the cusp points. The idea is to transform functions from C0 continuity to CN continuity (N < 1), and then implement a spectral method to solve the mapped problem without any domain decomposition. The final solution is obtained with inverse mapping.

Other Information

Published in: Journal of Physics: Conference Series
License: https://creativecommons.org/licenses/by/3.0/
See article on publisher's website: https://dx.doi.org/10.1088/1742-6596/1391/1/012021

Conference information: 8th International Conference on Mathematical Modeling in Physical Science 26–29 August 2019, Bratislava, Slovakia

History

Language

  • English

Publisher

IOP Publishing

Publication Year

  • 2019

License statement

This Item is licensed under the Creative Commons Attribution 3.0 Unported License.

Institution affiliated with

  • Hamad Bin Khalifa University
  • College of Science and Engineering - HBKU
  • Qatar Environment and Energy Research Institute - HBKU