浸入边界- conformal isogeometric 方法用于磁静学
Immersed boundary-conformal isogeometric methods for magnetostatics
AI总结：
本文提出三种非共形离散化策略用于磁静学问题，通过减少几何预处理工作量和所需网格数量，提高复杂电磁设备模拟效率。
摘要：
Isogeometric 分析被提出以弥合计算机辅助设计与数值离散化的差距。然而，标准多补丁 isogeometric 分析要求在补丁界面处进行共形离散化，这对多材料域问题提出了挑战。在电动机领域，这种要求在表示由多个域和材料组成的电机时需要大量的补丁。本文采用、扩展和评估了三种非共形离散化策略：完全浸入方法、非共形补丁的联合方法以及带有共形层的联合方法。在所有三种方法中，使用边界-共形的高阶四次规则进行修剪边界和界面元素的积分。在两种联合方法中，材料区域尽可能由独立的非共形样条补丁表示，这些补丁嵌入在背景补丁中并通过 Nitsche 方法弱耦合。在后者框架中，关键界面还被共形层包围，这使得边界条件的强施加和界面行为的改进解析成为可能。所提出的方法通过多个磁静学基准问题和工业应用进行了评估。数值结果表明，联合方法实现了高度准确的解，而完全浸入方法在材料界面处的场梯度不连续性方面表现不佳。然而，这些方法相比传统共形多补丁分析显著减少了几何预处理工作量，并且所需补丁数量大幅减少。总体而言，这证明了我们提出的浸入边界-共形 isogeometric 框架在高效模拟复杂电磁设备方面具有巨大潜力。
英文摘要：
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.
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