双射映射分析将函数联络理论推广到非矩形二维区域
Bijective Mapping Analysis to Extend the Theory of Functional Connections to Non-rectangular 2-dimensional Domains
摘要：
本文对利用双射映射将函数联系理论推广到非矩形二维域进行了初步分析。具体来说，这篇手稿提出了三种不同的映射技术：a）复映射，b）投影映射，和c）多项式映射。在这方面，一个精确的最小二乘近似的逆映射也开发了那些没有封闭形式的逆映射。使用这些映射的优点和缺点是突出的，并提供了几个例子。此外，本文展示了如何取代边界约束表示的一个分段序列的功能与一个单一的功能，这是兼容的，并要求理论的功能连接已经开发的矩形域。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
