The Frenet apparatus is a new framework for constructing high order geometry-conforming immersed finite element functions for interface problems. In this report, we present a procedure for constructing the local IFE bases in some detail as well as a new approach for constructing orthonormal bases using the singular value decomposition of the local generalized Vandermonde matrix. A sample implementation in MATLAB is provided to showcase the simplicity and extensionability of the framework.

翻译：Frenet 框架是一种为界面问题构造高阶几何相容浸入有限元函数的新框架。本报告中，我们详细阐述了构造局部浸入有限元基函数的过程，并提出了一种利用局部广义范德蒙矩阵的奇异值分解来构造正交基的新方法。文中提供了一个MATLAB示例实现，以展示该框架的简洁性和可扩展性。