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Topology optimization for cross-section designs of electromagnetic waveguides targeting guiding characteristics

机译：针对导向特性的电磁波导横截面设计的拓扑优化

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摘要

Electromagnetic waveguides effectively conduct electromagnetic microwaves using resonance phenomena in RF-ranges, and are widely used in high-frequency electronic devices and equipment. The waveguide guiding characteristics related to eigen-frequencies and eigen-modes are critical factors determining the design performances pertaining to the bandwidth of appropriate response frequencies, and high performance electromagnetic waveguides can be obtained by designing cross-sections of waveguides that appropriately control such guiding characteristics at the conceptual design phase. This paper proposes a new application of a topology optimization method for the design of inhomogeneous electromagnetic waveguide cross-sections composed of dielectric material and air, with the resulting configurations performing according to specified guiding characteristics. First, the concept of topology optimization and a way to apply it to electromagnetic wave problems are explained. Next, design requirements for the design of waveguide cross-sections are clarified and corresponding objective functions and the optimization problem are formulated. A new multi-objective function is formulated to reduce grayscales since using a penalization parameter for physical property interpolation is ineffective in electromagnetic problems. The optimization algorithm is constructed based on these formulations, Sequential Linear Programming and the finite element method, where hybrid edgeodal elements are used. Finally, several design examples of waveguide cross-sections are presented to confirm the usefulness of the proposed method.
机译：电磁波导利用RF范围内的共振现象有效地传导电磁微波，并被广泛用于高频电子设备和设备中。与本征频率和本征模有关的波导导引特性是决定与适当响应频率的带宽有关的设计性能的关键因素，可以通过设计适当控制这种导引特性的波导截面来获得高性能电磁波导。在概念设计阶段。本文提出了一种拓扑优化方法的新应用，该方法可用于设计由介电材料和空气组成的非均匀电磁波导管截面，并根据指定的导向特性执行最终的配置。首先，说明拓扑优化的概念以及将其应用于电磁波问题的方法。接下来，阐明了波导截面设计的设计要求，并提出了相应的目标函数和优化问题。制定了一种新的多目标函数来减少灰度，因为将惩罚参数用于物理属性插值对于电磁问题无效。基于这些公式，顺序线性规划和有限元方法构造了优化算法，其中使用了混合边缘/节点元素。最后，给出了波导横截面的几个设计实例，以确认所提出方法的有效性。

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