The state of art of electromagnetic integral equations has seen significant growth over the past few decades, overcoming some of the fundamental bottlenecks: computational complexity, low frequency and dense discretization breakdown, preconditioning, and so on. Likewise, the community has seen extensive investment in development of methods for higher order analysis, in both geometry and physics. Unfortunately, these standard geometric descriptors are continuous, but their normals are discontinuous at the boundary between triangular tessellations of control nodes, or patches, with a few exceptions; as a result, one needs to define additional mathematical infrastructure to define physical basis sets for vector problems. In stark contrast, the geometric representation used for design are second order differentiable almost everywhere on the surfaces. Using these description for analysis opens the door to several possibilities, and is the area we explore in this paper. Our focus is on Loop subdivision based isogeometric methods. In this paper, our goals are two fold: (i) development of computational infrastructure for isogeometric analysis of electrically large simply connected objects, and (ii) to introduce the notion of manifold harmonics transforms and its utility in computational electromagnetics. Several results highlighting the efficacy of these two methods are presented.

翻译：在过去几十年里,电磁整体方程式的先进状态有了显著的发展,克服了某些基本瓶颈:计算复杂性、低频率和密集离散性崩溃、先决条件等等。同样,社区在开发更高秩序分析方法方面,在几何学和物理方面,都看到大量投资。不幸的是,这些标准的几何描述仪是连续的,但在控制节点或补丁的三角交融点之间的界限上,它们的正常状态不连续,只有少数例外;因此,需要界定更多的数学基础设施,以界定矢量问题物理基础组。在鲜明对比之下,设计所用的几何表示法是几乎可以在所有表面都区分的第二顺序。使用这些描述进行分析打开了几种可能性的大门,是我们在本文中探讨的领域。我们的重点是基于象形测量方法的Loop亚视。在本文中,我们的目标是两个折叠合的:(一)为对简单的相连接天体进行等离测量分析开发计算基础设施,以及(二)引入数位调控器转换方法的概念及其在电磁测算中的效用是两种结果。