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Eddy Current Modeling in Multiply Connected Regions via a Full-Wave Solver Based on the Quasi-Helmholtz Projectors
IEEE Open Journal of Antennas and Propagation Pub Date : 2020-09-29 , DOI: 10.1109/ojap.2020.3027186
Tiffany L. Chhim , Adrien Merlini , Lyes Rahmouni , John Erick Ortiz Guzman , Francesco P. Andriulli

Eddy currents are central to several industrial applications and there is a strong need for their efficient modeling. Existing eddy current solution strategies are based on a quasi-static approximation of Maxwell’s equations for lossy conducting objects and thus their applicability is restricted to low frequencies. On the other hand, available full-wave solvers such as the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) equation become highly ill-conditioned and inaccurate in eddy current settings. This work presents a new well-conditioned and stable full-wave formulation which encompasses the simulation of eddy currents. Our method is built upon the PMCHWT equation and thus remains valid over the entire frequency range. Moreover, our scheme is also compatible with structures containing holes and handles (multiply connected geometries). The effectiveness of quasi-Helmholtz projectors is leveraged to obtain a versatile solver, which is computationally efficient and allows for a seamless transition between low and high frequencies. The stability and accuracy of the new method are demonstrated both theoretically and through numerical experiments on canonical and realistic structures.

中文翻译:

基于准亥姆霍兹投影仪的全波解算器在多个连通区域中的涡流建模

涡流对于几种工业应用至关重要,因此对其高效建模非常有需求。现有的涡流解决方案策略基于有损传导物体的麦克斯韦方程组的准静态逼近,因此它们的适用性仅限于低频。另一方面,可用的全波求解器,例如Poggio-Miller-Chang-Harrington-Wu-Tsai(PMCHWT)方程,在涡流设置中变得病态严重且不准确。这项工作提出了一种新的条件良好且稳定的全波公式,其中包括对涡流的仿真。我们的方法基于PMCHWT公式,因此在整个频率范围内仍然有效。此外,我们的方案还与包含孔和手柄(多重连接的几何体)的结构兼容。利用准亥姆霍兹投影机的有效性来获得通用的求解器,该求解器的计算效率很高,并允许在低频和高频之间无缝过渡。从理论上以及通过对规范结构和实际结构的数值实验证明了该方法的稳定性和准确性。
更新日期:2020-10-26
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