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

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.

authors

• Mortari, Daniele

published proceedings

• Mathematics (Basel)

author list (cited authors)

• Mortari, D., & Arnas, D.

citation count

• 5

complete list of authors

• Mortari, Daniele||Arnas, David

publication date

• January 2020

publisher

• MDPI  Publisher

published in

• MATHEMATICS  Journal

keywords

• Domain Mappings
• Functional Interpolation
• Least-squares
• Theory Of Functional Connections

PubMed Central ID

• 33062599

Digital Object Identifier (DOI)

• 10.3390/math8091593

start page

• 1593

end page

• 1593

volume

• 8

issue

• 9

URL

• http://dx.doi.org/10.3390/math8091593