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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Daniele Mortari & David Arnas, 2020. "Bijective Mapping Analysis to Extend the Theory of Functional Connections to Non-Rectangular 2-Dimensional Domains," Mathematics, MDPI, vol. 8(9), pages 1-21, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1593-:d:414137
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