基于样条函数的静电场部分单元等效电路法
A Spline-based Partial Element Equivalent Circuit Method for Electrostatics
摘要：
本文研究了等几何分析（IgA）和部分单元等效电路（PEEC）方法之间的联系。我们证明，使用基于样条的几何概念，从IgA允许提取电路元件，而无需网格化步骤。此外，所提出的IgA-PEEC方法收敛复杂的几何形状比传统的PEEC方法快三倍，反过来，它需要一个显着较低的数量的自由度，以解决具有可比精度的问题。所得的方法是密切相关的等几何边界元法。然而，它使用最低阶的基函数，以允许直接的物理和电路解释。通过一个具有复杂几何形状的分析实例验证了研究结果，显著的曲率，并通过电涌放电器的真实模型。
英文摘要：
This contribution investigates the connection between Isogeometric Analysis (IgA) and the Partial Element Equivalent Circuit (PEEC) method for electrostatic problems. We demonstrate that using the spline-based geometry concepts from IgA allows for extracting circuit elements without a meshing step. Moreover, the proposed IgA-PEEC method converges for complex geometries up to three times faster than the conventional PEEC approach and, in turn, it requires a significantly lower number of degrees of freedom to solve a problem with comparable accuracy. The resulting method is closely related to the isogeometric boundary element method. However, it uses lowest-order basis functions to allow for straightforward physical and circuit interpretations. The findings are validated by an analytical example with complex geometry, i.e., significant curvature, and by a realistic model of a surge arrester.
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