本文關(guān)鍵詞：旋轉(zhuǎn)對(duì)稱(chēng)體寬帶電磁散射的快速算法研究　出處：《南京理工大學(xué)》2017年碩士論文　論文類(lèi)型：學(xué)位論文

  更多相關(guān)文章： 旋轉(zhuǎn)對(duì)稱(chēng)體 時(shí)域積分方程 曲線基函數(shù) 階數(shù)步進(jìn) 自適應(yīng)交叉近似 拋物線方程 傅里葉級(jí)數(shù)

【摘要】：在計(jì)算電磁學(xué)領(lǐng)域,如何高效分析電大尺寸目標(biāo)的電磁特性一直是人們研究的重要課題,而旋轉(zhuǎn)對(duì)稱(chēng)體(BoR)由于其特殊的幾何外形,也一直都是研究的熱點(diǎn)。采用時(shí)域矩量法對(duì)旋轉(zhuǎn)對(duì)稱(chēng)體目標(biāo)分析時(shí),可精確求解其全向的電磁散射特性。旋轉(zhuǎn)對(duì)稱(chēng)體空間上的離散只需要在其母線上進(jìn)行,一般采用三角基函數(shù),若采用高階基函數(shù),離散尺寸可以選取的較大,求解計(jì)算的未知量變少,在保證計(jì)算精度的同時(shí)效率就會(huì)提高。若只需求解旋轉(zhuǎn)對(duì)稱(chēng)體目標(biāo)的前向散射特性或電磁波的傳播特性時(shí),拋物線方程方法能夠以極少的計(jì)算資源完成對(duì)此類(lèi)問(wèn)題的求解。拋物線方程(PE)是波動(dòng)方程的一種近似,與矩量法(MoM)等積分方法相比,拋物線方程方法求解得到的結(jié)果精度較低,但計(jì)算資源的消耗會(huì)很少,在分析旋轉(zhuǎn)對(duì)稱(chēng)體時(shí)若結(jié)合其周?chē)膱?chǎng)分布特性簡(jiǎn)化標(biāo)準(zhǔn)的三維拋物線方程,可大幅減少計(jì)算資源的消耗。本文研究的是旋轉(zhuǎn)對(duì)稱(chēng)體寬帶電磁散射的快速算法,分別為基于階數(shù)步進(jìn)的時(shí)域積分方程方法以及拋物線方程方法。文章首先介紹了旋轉(zhuǎn)對(duì)稱(chēng)體結(jié)構(gòu)的特殊性及基于階數(shù)步進(jìn)的時(shí)域積分方法的理論基礎(chǔ),考慮到旋轉(zhuǎn)對(duì)稱(chēng)體目標(biāo)在空間上剖分是對(duì)線型結(jié)構(gòu)剖分,引入了一階、二階、三階曲線基函數(shù),詳細(xì)推導(dǎo)了基于這三類(lèi)基函數(shù)的旋轉(zhuǎn)對(duì)稱(chēng)導(dǎo)體時(shí)域積分方程和旋轉(zhuǎn)對(duì)稱(chēng)介質(zhì)體時(shí)域積分方程,實(shí)現(xiàn)對(duì)旋轉(zhuǎn)對(duì)稱(chēng)導(dǎo)體及介質(zhì)體電磁特性的快速分析。同時(shí),在本文方法中加入自適應(yīng)交叉近似(ACA)方法,進(jìn)一步降低了計(jì)算機(jī)資源的消耗。最后介紹了旋轉(zhuǎn)對(duì)稱(chēng)導(dǎo)體的拋物線方程方法,拋物線方程方法的求解是利用迭代推進(jìn)的方法,根據(jù)旋轉(zhuǎn)對(duì)稱(chēng)體周?chē)鷪?chǎng)可展開(kāi)成傅里葉級(jí)數(shù)的形式,簡(jiǎn)化標(biāo)準(zhǔn)的三維拋物線方程,使需要求解的三維問(wèn)題最終簡(jiǎn)化成一系列的一維問(wèn)題,計(jì)算消耗的時(shí)間和內(nèi)存自然大幅減少。
[Abstract]:In the field of computational electromagnetics, electromagnetic characteristics, how to analyze the electrically large target has been becoming an important research topic, and the body of revolution (BoR) because of its special geometrical shape, it has always been a hot research. The analysis of rotationally symmetric targets using time domain method of moments, the exact solution of the electromagnetic scattering characteristics of omnidirectional the discrete rotational symmetry. The body space only in the bus, generally use the trigonometric function, if the higher order function, discrete size can be selected larger, unknown quantitative computing, in ensuring the accuracy and efficiency will be improved. If only needs to solve rotational symmetry target before scattering characteristics or propagation characteristics of electromagnetic waves, parabolic equation method can be completed with very little computational resources to solve the problem. The parabolic equation (PE) is a kind of approximate wave equation And with the method of moments (MoM) and integral method for solving parabolic equations method compared to results obtained with low accuracy, but the computational resource consumption will be small in three-dimensional parabolic equation in the analysis of rotationally symmetric body if combined with the field distribution around the simplified criteria, can significantly reduce the consumption of computational resources. This paper studies the body of revolution is a fast algorithm of broadband electromagnetic scattering, respectively. The order of the step time domain integral equation method and parabolic equation method. Firstly, based on the introduction of special rotational symmetry structure and theoretical basis of order step time integration method based on considering the rotational symmetry target in space section is on the linear structure partition, introduced one order, two order, three order curve function, with rotational symmetry conductors of these three types of basis functions in time domain integral equation and rotational symmetry are deduced based on media Time domain integral equation, realize the fast analysis of electromagnetic characteristics of rotational symmetric conductor and dielectric bodies. At the same time, in this method with adaptive cross approximation (ACA) method, to further reduce the computer resource consumption. Finally introduces the parabolic equation method of rotation symmetric conductor, solving parabolic equation method is a method of using iterative push. According to the rotational symmetry field can be expanded into Fu Liye Series in the form of three-dimensional parabolic equation simplified standard, the three-dimensional problem to solve the final simplified into a series of one-dimensional problems, the calculating time and significantly reduce the memory consumption.

【學(xué)位授予單位】：南京理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：TN011

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