Bijective Mapping Analysis to Extend the Theory of Functional Connections to Non-Rectangular 2-Dimensional Domains

Daniele Mortari and David Arnas
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Daniele Mortari: Aerospace Engineering, Texas A&M University, College Station, TX 77845-3141, USA
David Arnas: Aeronautics and Astronautics, Massachussetts Institute of Technology, Cambridge, MA 02139, USA

Mathematics, 2020, vol. 8, issue 9, 1-21

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.

Keywords: Theory of Functional Connections; domain mappings; least-squares; functional interpolation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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