计算电磁学中等几何分析的最新进展
Recent Advances of Isogeometric Analysis in Computational Electromagnetics
AI总结：
本文综述了等几何分析在电磁模拟中的优缺点，讨论了基于B-样条和非均匀有理B-样条基函数的curl-和div-一致的样条函数空间，并展示了用于优化和不确定性量化的工作流程的二维和三维非学术基准示例。
摘要：
本文综述了等几何分析（IGA）在电磁模拟中的优缺点。IGA扩展了传统有限元法（FEM）常用的多项式基函数集。尽管在最低阶情况下与Nédélec基函数相同，但其基于B-样条和非均匀有理B-样条基函数。其主要优势是能够精确表示计算机辅助设计（CAD）工具中的几何形状。这简化了网格生成，因为计算网格由工程师在CAD工具中隐式创建。curl-和div-一致的样条函数空间被重新回顾，并讨论了可用的软件。最后，展示了多个用于优化和不确定性量化工作流程的二维和三维非学术基准示例。
英文摘要：
In this communication the advantages and drawbacks of the isogeometric analysis (IGA) are reviewed in the context of electromagnetic simulations. IGA extends the set of polynomial basis functions, commonly employed by the classical Finite Element Method (FEM). While identical to FEM with Nédélec's basis functions in the lowest order case, it is based on B-spline and Non-Uniform Rational B-spline basis functions. The main benefit of this is the exact representation of the geometry in the language of computer aided design (CAD) tools. This simplifies the meshing as the computational mesh is implicitly created by the engineer using the CAD tool. The curl- and div-conforming spline function spaces are recapitulated and the available software is discussed. Finally, several non-academic benchmark examples in two and three dimensions are shown which are used in optimization and uncertainty quantification workflows.
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