Bijective mapping analysis to extend the theory of functional connections to non-rectangular 2-dimensional domains
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) polynomia...
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| Format: | Article |
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Multidisciplinary Digital Publishing Institute
2020
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| Online Access: | https://hdl.handle.net/1721.1/127824 |
| _version_ | 1811068726601056256 |
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| author | Mortari, Daniele Arnas, David |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Mortari, Daniele Arnas, David |
| author_sort | Mortari, Daniele |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T08:00:24Z |
| format | Article |
| id | mit-1721.1/127824 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T08:00:24Z |
| publishDate | 2020 |
| publisher | Multidisciplinary Digital Publishing Institute |
| record_format | dspace |
| spelling | mit-1721.1/1278242022-09-30T01:39:11Z Bijective mapping analysis to extend the theory of functional connections to non-rectangular 2-dimensional domains Mortari, Daniele Arnas, David Massachusetts Institute of Technology. Department of Aeronautics and Astronautics 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. NASA (grant 80NSSC19K1149) 2020-10-07T14:56:56Z 2020-10-07T14:56:56Z 2020-09 2020-07 2020-09-25T13:26:25Z Article http://purl.org/eprint/type/JournalArticle 2227-7390 https://hdl.handle.net/1721.1/127824 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) 10.3390/math8091593 Mathematics Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ application/pdf Multidisciplinary Digital Publishing Institute Multidisciplinary Digital Publishing Institute |
| spellingShingle | Mortari, Daniele Arnas, David Bijective mapping analysis to extend the theory of functional connections to non-rectangular 2-dimensional domains |
| title | Bijective mapping analysis to extend the theory of functional connections to non-rectangular 2-dimensional domains |
| title_full | Bijective mapping analysis to extend the theory of functional connections to non-rectangular 2-dimensional domains |
| title_fullStr | Bijective mapping analysis to extend the theory of functional connections to non-rectangular 2-dimensional domains |
| title_full_unstemmed | Bijective mapping analysis to extend the theory of functional connections to non-rectangular 2-dimensional domains |
| title_short | Bijective mapping analysis to extend the theory of functional connections to non-rectangular 2-dimensional domains |
| title_sort | bijective mapping analysis to extend the theory of functional connections to non rectangular 2 dimensional domains |
| url | https://hdl.handle.net/1721.1/127824 |
| work_keys_str_mv | AT mortaridaniele bijectivemappinganalysistoextendthetheoryoffunctionalconnectionstononrectangular2dimensionaldomains AT arnasdavid bijectivemappinganalysistoextendthetheoryoffunctionalconnectionstononrectangular2dimensionaldomains |