弧形邊界在伴隨變量法下的電磁靈敏度分析

張玉賢; 朱海鴿; 馮曉麗; 楊利霞; 黃志祥

doi:10.11999/JEIT240432

弧形邊界在伴隨變量法下的電磁靈敏度分析

doi: 10.11999/JEIT240432 cstr: 32379.14.JEIT240432

張玉賢^{1, 2},
朱海鴿¹,
馮曉麗³,
楊利霞^{1, 2, ,},
黃志祥^{1, 2, 3}

1.
安徽大學電子信息工程學院合肥 230601
2.
安徽大學信息材料與智能感知安徽省實驗室合肥 230601
3.
安徽大學集成電路先進材料與技術(shù)產(chǎn)教研融合研究院合肥 230601

基金項目: 國家自然科學基金(62101333, 62071003, U21A20457)，安徽省高校優(yōu)秀科研創(chuàng)新團隊項目(2022AH010002)

詳細信息

作者簡介:
張玉賢：男，副教授，研究方向為計算電磁學、電磁逆時偏移成像技術(shù)

朱海鴿：男，碩士生，研究方向為計算電磁學、靈敏度分析

馮曉麗：女，助理工程師，研究方向為集成電路工藝設(shè)計

楊利霞：男，教授，研究方向為等離子體物理、時域有限差分方法

黃志祥：男，教授，研究方向為計算電磁學、多物理場

通訊作者:
楊利霞　lixiayang@yeah.net

中圖分類號: TN011; O441.4
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- 文章訪問數(shù): 332
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- 被引次數(shù): 0
出版歷程
- 收稿日期: 2024-05-30
- 修回日期: 2024-09-20
- 網(wǎng)絡(luò)出版日期: 2024-09-28
- 刊出日期: 2024-12-01

Electromagnetic Sensitivity Analysis of Curved Boundaries under the Method of Accompanying Variables

ZHANG Yuxian^{1, 2},
ZHU Haige¹,
FENG Xiaoli³,
YANG Lixia^{1, 2
, ,},
HUANG Zhixiang^{1, 2, 3}

1.
School of Electronic and Information Engineering, Anhui University, Hefei 230601, China
2.
Anhui Provincial Laboratory of Information Materials and Intelligent Perception at Anhui University, Hefei 230601, China
3.
Anhui University Integrated Circuit Advanced Materials and Technology Industry Education Research Integration Research Institute, Hefei 230601, China

Funds: The National Natural Science Foundation of China (62101333, 62071003, U21A20457), The Project of Excellent Scientific Research and Innovation Team of Universities in Anhui Province (2022AH010002)

摘要

摘要: 電磁靈敏度分析是評估設(shè)計參數(shù)變化對電磁性能影響的一種方法，它通過計算靈敏度信息指導(dǎo)結(jié)構(gòu)模型分析，以滿足設(shè)計規(guī)范。商業(yè)軟件在進行電磁結(jié)構(gòu)優(yōu)化設(shè)計時，常通過調(diào)整幾何結(jié)構(gòu)并使用傳統(tǒng)算法，但這種方法計算耗時且資源占用大。為了提高模型設(shè)計的效率，該文提出一種穩(wěn)定高效的處理方案，即伴隨變量法(AVM)，利用僅有2次算法模擬條件下，實現(xiàn)在參數(shù)變換上進行1～2階靈敏度估計。當前AVM的絕大多數(shù)應(yīng)用局限在矩形邊界參數(shù)的靈敏度分析，該文首次開拓性地將AVM拓展到弧形邊界參數(shù)的靈敏度分析?；诠潭ǖ谋緲?gòu)參數(shù)、頻率依賴性目標函數(shù)以及瞬態(tài)脈沖函數(shù)的3種不同情形設(shè)計的條件，實現(xiàn)了對弧形結(jié)構(gòu)的電磁靈敏度的高效分析。與有限差分方法(FDM)相比，該方法在計算效率上得到了顯著的提高。該方法有效實施顯著拓寬了AVM在弧形邊界上的應(yīng)用范圍，可應(yīng)用于等離子體模型的電磁結(jié)構(gòu)、復(fù)雜天線模型的邊緣結(jié)構(gòu)等優(yōu)化問題上。當計算資源較少的情況下，可滿足電磁結(jié)構(gòu)優(yōu)化的可靠性和穩(wěn)定性。
- 電磁靈敏度分析 /
- 有限差分法 /
- 伴隨變量法
Abstract: Sensitivity analysis an evaluation method for the influence with variations of the design parameters on electromagnetic performance, which is utilized to calculate sensitivity information. This information guides the analysis of structural models to ensure compliance with design specifications. In the optimization design of electromagnetic structures by commercial software, traditional algorithms are often employed, involving adjustments to the geometry. However, this approach is known to be extensive in terms of computational time and resource consumption. In order to enhance the efficiency of model design, a stable and efficient processing scheme is proposed in the paper, known as the Adjoint Variable Method (AVM). This method achieves estimation of 1st～2nd order sensitivity on parameter transformations with only two algorithmic simulation conditions required. The application of AVM has predominantly been confined to the sensitivity analysis of rectangular boundary parameters, with this paper making the first extension of AVM to the sensitivity analysis of arc boundary parameters. Efficient analysis of the electromagnetic sensitivity of curved structures is accomplished based on the conditions designed for three distinct scenarios: fixed intrinsic parameters, frequency-dependent objective functions, and transient impulse functions. Compared to the Finite-Difference Method (FDM), a significant enhancement in computational efficiency is achieved by the proposed method. The effective implementation of the method substantially expands the application scope of AVM to curved boundaries, which can be utilized in optimization problems such as the electromagnetic structures of plasma models and the edge structures of complex antenna models. When computational resources are limited, the reliability and stability of electromagnetic structure optimization can be ensured by the application of the proposed method.
- Electromagnetic sensitivity analysis /
- Finite Difference Method(FDM) /
- Adjoint Variable Method(AVM)

HTML全文

圖 1 有損介質(zhì)不連續(xù)面的不同節(jié)點分類

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圖 2 2維TMz的平面波入射結(jié)構(gòu)

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圖 3 2維示例對介質(zhì)相對介電常數(shù)、電導(dǎo)率和半徑掃描的靈敏度

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圖 4 頻譜實部與虛部對所有參數(shù)的靈敏度

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圖 5 探測點場值在整個時間步中有限差分法與伴隨變量法靈敏度對比

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表 1 本構(gòu)無關(guān)目標函數(shù)下AVM和FDM之間的范數(shù)誤差

誤差類型	$ {\varepsilon _{\mathrm{r}}} $	$ {\sigma ^{\mathrm{e}}} $	$ r $
AVM和CFD	2.0255×10^–3	5.1667×10^–4	6.2553×10^–2
AVM和FFD	2.7232×10^–3	5.5774×10^–4	7.3643×10^–3
AVM和BFD	1.3269×10^–3	4.7567×10^–4	1.4296×10^–1

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表 2 頻率相關(guān)目標函數(shù)下AVM和FDM之間的范數(shù)誤差

誤差類型	$ {\varepsilon _{\mathrm{r}}} $		$ {\sigma ^{\mathrm{e}}} $		r
誤差類型	實部	虛部	實部	虛部	實部	虛部
AVM和CFD	0.0099	0.0459	0.0551	0.0101	0.1178	0.1132
AVM和FFD	0.0137	0.0594	0.0573	0.0101	0.1145	0.2525
AVM和BFD	0.0013	0.0820	0.0533	0.0104	0.1287	0.1842

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表 3 瞬態(tài)函數(shù)下AVM和FDM之間的范數(shù)誤差

誤差類型	$ {\varepsilon _{\mathrm{r}}} $ (×10^–2)	$ {\sigma ^{\mathrm{e}}} $ (×10^–3)	r (×10^–1)
AVM和CFD	0.3689	4.0714	1.1738
AVM和FFD	1.3879	4.9260	1.3187
AVM和BFD	1.9305	4.1873	1.3244

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