Isogeometric analysis was proposed to bridge the gap between computer-aided design and numerical discretization. However, standard multi-patch isogeometric analysis mandates conformal discretizations across patch interfaces, posing challenges for multi-material domain problems. In the context of electric machines, this requirement becomes evident in a large number of patches needed to represent machines consisting of several domains and materials. In this work, we adopt, extend, and evaluate three non-conformal discretization strategies for magnetostatic problems: a fully immersed approach, the union with non-conformal patches, and the union with conformal layers. In all three methods, boundary-conformal high-order quadrature rules are employed for integration over trimmed boundary and interface elements. In the two union approaches, material regions are, as far as possible, represented by independent non-conformal spline patches that are embedded within a background patch and coupled weakly through Nitsche's method. In the latter framework, critical interfaces are additionally surrounded by conformal layers that enable the strong imposition of boundary conditions and improved resolution of interface behavior. The proposed approaches are assessed through several magnetostatic benchmark problems and an industrial application. The numerical results show that the union methods achieve highly accurate solutions, while the fully immersed approach struggles with discontinuities in field gradients across material interfaces. Nevertheless, these methods significantly reduce the geometric preprocessing effort compared to conventional, conformal multi-patch analysis and require substantially fewer patches. Overall, this demonstrates that our immersed boundary-conformal isogeometric framework possesses great potential for efficient simulation of complex electromagnetic devices.

翻译：等几何分析旨在弥合计算机辅助设计与数值离散之间的鸿沟。然而，标准的多块等几何分析要求块界面间的共形离散，这给多材料域问题带来了挑战。在电机背景下，这一要求导致表征由多个域和材料构成的电机所需块数量巨大。本文采用、扩展并评估了三种用于静磁问题的非共形离散策略：完全浸没法、非共形块联合法以及带共形层的联合法。在所有三种方法中，均采用边界共形的高阶求积规则对裁剪边界和界面单元进行积分。在两种联合法中，材料区域尽可能由独立非共形样条块表示，这些样条块嵌入背景块中，并通过尼采方法实现弱耦合。在后一种框架中，关键界面额外被共形层包围，从而能够强施加边界条件并改进界面行为的解析分辨率。所提出的方法通过多个静磁基准问题和一项工业应用进行了评估。数值结果表明，联合法能够获得高精度解，而完全浸没法在处理材料界面处场梯度不连续时存在困难。尽管如此，与传统的共形多块分析相比，这些方法显著减少了几何预处理工作量，并需要更少的块。总体而言，这证明了我们的浸没边界共形等几何框架在高效仿真复杂电磁装置方面具有巨大潜力。