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Generating efficient basis sets for unbounded domains

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submitted on 2024-09-16, 09:37 and posted on 2024-09-17, 06:14 authored by F Mumtaz, F H Alharbi

The treatment of the problems involving unbounded domains (UDs) with vanishing boundary conditions is always challenging. For spectral methods, in particular, very limited basis sets are commonly used for such domains, in which the ranges of the decay rates with acceptable computational efficiency, are very small. Furthermore, maintaining high level of analyticity becomes burdensome. Developing efficient mapped basis tailored for such problem is one of the main strategies to overcome these difficulties. In this work, we present a technique to generate efficient basis sets for UDs. This approach allows using basis sets defined for bounded domains (BDs) for problems in UDs, and hence, providing more freedom to choose from a variety of basis sets. To ensure computational efficiency, the designed transformations cover a wide range of decay rates and allow solving integrals analytically. The method is applied to solve many differential equations encountered frequently in many physics related problems. The results illustrate the efficiency of the developed technique and mapped basis sets.

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/10.1088/1742-6596/1391/1/012020

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

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