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

2020/07/28 by Daniele Mortari, Mortari, Daniele, David Anas +1 · 2 citations
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Optimization Algorithms Research #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2008.07310

openalex publication_date 2020/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work presents an initial analysis of using bijective mappings to extend\nthe Theory of Functional Connections to non-rectangular two-dimensional\ndomains. Specifically, this manuscript proposes three different mappings\ntechniques: a) complex mapping, b) projection mapping, and c) polynomial\nmapping. In that respect, an accurate least-squares approximated inverse\nmapping is also developed for those mappings having no closed-form inverse. The\nadvantages and disadvantages of using these mappings are highlighted and a few\nexamples are provided. Additionally, the paper shows how to replace boundary\nconstraints expressed in terms of a piecewise sequence of functions with a\nsingle function, that is compatible and required by the Theory of Functional\nConnections already developed by rectangular domains.\n

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