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arXiv · 2008.07310

Bijective Mapping Analysis to Extend the Theory of Functional Connections to Non-rectangular 2-dimensional Domains

Daniele Mortari·David Anas
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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) projection mapping, and c) polynomial mapping. In that respect, an accurate least-squares approximated inverse mapping is also developed for those mappings having no closed-form inverse. The 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 piecewise sequence of functions with a single function, that is compatible and required by the Theory of Functional Connections already developed by rectangular domains.

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BibTeXRIS

Daniele Mortari, David Anas. 2020-07-28. Bijective Mapping Analysis to Extend the Theory of Functional Connections to Non-rectangular 2-dimensional Domains. https://arxiv.org/abs/2008.07310

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