Bijective mapping analysis to extend the theory of functional connections to non-rectangular 2-dimensional domains
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mathematics-08-01593.pdf
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1.86 MB
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Adobe PDF
Checksum (MD5)
b1fd6fceb802e048763a0b7c3b0b37fa
Author(s)
Mortari, Daniele
Arnas, David
Date Issued
September 2020
Journal
Mathematics
Publisher
Multidisciplinary Digital Publishing Institute
Citation
Mortari, Daniele, and David Arnas. "Bijective mapping analysis to extend the theory of functional connections to non-rectangular 2-dimensional domains." Mathematics 8, 9 (September 2020): 1593 ©2020 Author(s)
Version
Final published version
Abstract
This work presents an initial analysis of using bijective mappings to extend the Theory of Functional Connections to non-rectangular two-dimensional domains. Specifically, this manuscript proposes three different mappings techniques: (a) complex mapping, (b) the projection mapping, and (c) polynomial mapping. In that respect, an accurate least-squares approximated inverse mapping is also developed for those mappings with no closed-form inverse. Advantages and disadvantages of using these mappings are highlighted and a few examples are provided. Additionally, the paper shows how to replace boundary constraints expressed in terms of a piece-wise sequence of functions with a single function, which is compatible and required by the Theory of Functional Connections already developed for rectangular domains.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.3390/math8091593
