论文标题
将功能连接的理论扩展到非矩形二维域，将功能连接的理论扩展到
Bijective Mapping Analysis to Extend the Theory of Functional Connections to Non-rectangular 2-dimensional Domains
论文作者
论文摘要
这项工作提出了使用射击映射将功能连接理论扩展到非矩形二维结构域的初步分析。具体而言，该手稿提出了三种不同的映射技术：a）复杂的映射，b）投影映射和c）多项式映射。在这方面，还为那些没有封闭形式倒数的映射开发了一个准确的最小二乘近似映射。强调使用这些映射的优点和缺点，并提供了一些示例。此外，本文展示了如何用单个函数的分段函数序列表示的边界约束，该函数是兼容的，并且是由矩形域已经开发的功能连接理论所要求的。
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.
