Bijective mapping analysis to extend the theory of functional connections to non-rectangular 2-dimensional domains
Author(s)Mortari, Daniele; Arnas, David
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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.
DepartmentMassachusetts Institute of Technology. Department of Aeronautics and Astronautics
Multidisciplinary Digital Publishing Institute
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)
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