【摘要】：多尺度目標(biāo)電磁分析在計算電磁學(xué)領(lǐng)域是個挑戰(zhàn)。論文針對介質(zhì)材料的多尺度問題,不均勻網(wǎng)格剖分問題,分別作了深入研究。第二章簡要介紹了傳統(tǒng)的低秩壓縮方法,自適應(yīng)交叉近似算法。主要介紹了文章中所用的低秩壓縮方法:嵌套等效源方法。第三章主要研究將嵌套等效源方法與介質(zhì)表面積分方程相結(jié)合,分析多尺度的介質(zhì)問題。嵌套等效源方法是一種精度較高的低秩壓縮類方法,本章將其與表面積分方程結(jié)合,并將方程的內(nèi)外區(qū)域部分分開壓縮,以獲得更好的壓縮效果。分析了不同介電常數(shù)下該方法的近似精度,然后通過分析了一個介質(zhì)球與冪級數(shù)對比驗證了其正確性,分析了捕食者無人機(jī)來驗證了算法的多尺度特性。為快速分析介質(zhì)問題做了進(jìn)一步的拓展。第四章主要在原來規(guī)則八叉樹分組的嵌套等效源方法上研究了一種自適應(yīng)八叉樹分組的嵌套等效源方法。該方法主要針對帶有精細(xì)結(jié)構(gòu)的目標(biāo),需要局部密剖的情況。分析了不同尺寸的組之間如何壓縮,以及分析了這樣壓縮后的精度。并通過分析一個金屬球驗證了該方法的正確性,還通過分析一個單極子天線陣列來討論該方法的效率。為了完善該方法,還引入了不連續(xù)伽遼金方法,使得剖分更加靈活。也分析了一個非共形網(wǎng)格剖分的圓柱,與商業(yè)軟件FEKO對比,驗證了其正確性,也通過分析一個單極子天線陣列來討論了它的效率。相比于原來的嵌套等效源方法更進(jìn)一步地降低內(nèi)存消耗和迭代求解時間,為分析不均勻剖分目標(biāo)的電磁輻射或散射問題做了更進(jìn)一步的改善。
[Abstract]:Multi-scale target electromagnetic analysis is a challenge in the field of computational electromagnetism. In this paper, the multi-scale problem and non-uniform mesh generation of dielectric materials are studied. In chapter 2, the traditional low rank compression method and the adaptive cross approximation algorithm are introduced briefly. This paper mainly introduces the low rank compression method used in this paper: the nested equivalent source method. In the third chapter, the nested equivalent source method is combined with the dielectric surface integral equation to analyze the multi-scale media problem. The nested equivalent source method is a kind of low rank compression method with high precision. In this chapter, we combine it with the surface integral equation, and compress the inner and outer parts of the equation separately, so as to obtain better compression effect. The approximate accuracy of the method under different dielectric constants is analyzed, and the correctness of the method is verified by comparing a dielectric sphere with power series. The multi-scale characteristic of the algorithm is verified by analyzing the predator UAV. A further development is made for the fast analysis of medium problems. In chapter 4, a nested equivalent source method of adaptive octree grouping is studied based on the nested equivalent source method of octree grouping. This method mainly aims at the target with fine structure and needs local dense profile. How to compress the groups of different sizes and the accuracy of the compression are analyzed. The correctness of the method is verified by analyzing a metal sphere, and the efficiency of the method is discussed by analyzing a monopole antenna array. In order to perfect the method, discontinuous Galerkin method is introduced, which makes the division more flexible. A non-conformal meshed cylinder is also analyzed and compared with commercial software FEKO to verify its correctness. Its efficiency is also discussed by analyzing a monopole antenna array. Compared with the original nested equivalent source method, the memory consumption and iterative solution time are further reduced, and the analysis of electromagnetic radiation or scattering problem of non-uniform subdivision targets is further improved.
【學(xué)位授予單位】：南京理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TN011

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本文編號：2184091