本文選題：時(shí)域有限差分方法 + FCC網(wǎng)格�。� 參考：《江蘇大學(xué)》2017年碩士論文

【摘要】：自從時(shí)域有限差分(FDTD)方法提出以來,由于其具有表述簡單、易于理解,在時(shí)域中能直觀描述電磁特性等特點(diǎn),該方法的應(yīng)用范圍越來越廣。而且,隨著計(jì)算機(jī)技術(shù)的快速發(fā)展和算法本身計(jì)算效率和計(jì)算精度的不斷提高,FDTD方法已逐漸發(fā)展為一種成熟、高效的電磁計(jì)算方法。然而,傳統(tǒng)基于Yee元胞的FDTD方法,易造成各向異性效應(yīng),從而導(dǎo)致計(jì)算精度的降低。本文針對這一問題,重點(diǎn)研究了一種新的計(jì)算網(wǎng)格(面中心立方體網(wǎng)格,FCC網(wǎng)格)FDTD方法;其相比于Yee元胞的FDTD方法,具有良好的各向同性效果,較寬松的穩(wěn)定性條件,且計(jì)算精度較高。論文研究了基于FCC網(wǎng)格的FDTD(FCC-FDTD)方法,并應(yīng)用該方法分別對填充有空氣和等離子體的兩個(gè)矩形諧振腔進(jìn)行仿真計(jì)算,得出相關(guān)結(jié)論。同時(shí),分析研究了FCC-FDTD方法的連接邊界條件,并給出算例驗(yàn)證。首先,本文詳細(xì)地介紹了FCC網(wǎng)格中場的空間分布,并在此基礎(chǔ)上,重點(diǎn)分析推導(dǎo)了FCC-FDTD方法在一般介質(zhì)情況下的電場、磁場分量的離散迭代式。同時(shí),給出了此方法的穩(wěn)定性條件,并與基于Yee元胞的FDTD方法的穩(wěn)定性進(jìn)行了比較。隨后,利用了FCC-FDTD方法仿真計(jì)算了普通諧振腔的111TM模的諧振頻率,并將其與基于Yee元胞的FDTD方法的計(jì)算結(jié)果進(jìn)行比對,結(jié)果驗(yàn)證了FCC-FDTD方法的正確性和準(zhǔn)確性。其次,又將FCC網(wǎng)格應(yīng)用到等離子體中,推導(dǎo)出電場分量、磁場分量和電流密度的離散迭代關(guān)系式;并通過卷積算法和拉普拉斯變換方法離散本構(gòu)方程得出電流密度的計(jì)算迭代式。同時(shí),為了驗(yàn)證應(yīng)用FCC網(wǎng)格處理等離子體方法的正確性,本文計(jì)算了一個(gè)填充非時(shí)變等離子體的諧振腔的電磁諧振特性,與模式匹配原理結(jié)果相符。結(jié)果驗(yàn)證了此方法的正確性,同時(shí)表明了此方法具有計(jì)算等離子體目標(biāo)電磁問題的能力。最后,為了將FCC-FDTD方法應(yīng)用到電磁散射問題的計(jì)算中,論文還對此方法的連接邊界條件進(jìn)行研究分析,并給出了連接邊界處的電場、磁場分量的離散迭代式;并通過仿真計(jì)算正弦場在整個(gè)計(jì)算區(qū)域內(nèi)的幅值分布圖,驗(yàn)證FCC-FDTD方法的連接邊界條件的可行性及正確性。綜上所述,本文所研究的FCC-FDTD方法為以后計(jì)算復(fù)雜目標(biāo)提供了一種新的可行性方法。
[Abstract]:Since the finite-difference time-domain (FDTD) method was proposed, it has been widely used because of its simple expression, easy to understand and intuitive description of electromagnetic characteristics in time domain. Moreover, with the rapid development of computer technology and the continuous improvement of computational efficiency and accuracy of the algorithm itself, FDTD method has gradually developed into a mature and efficient electromagnetic calculation method. However, the traditional FDTD method based on Yee cell is easy to cause anisotropic effect, which leads to the decrease of calculation accuracy. In order to solve this problem, this paper focuses on a new computational grid (FCC mesh FDTD method), which has better isotropic effect and looser stability condition than that of Yee cell FDTD method. And the calculation accuracy is high. The FCC-FDTD method based on FCC grid is studied in this paper, and the simulation results of two rectangular resonators filled with air and plasma are obtained by using this method. At the same time, the connection boundary conditions of FCC-FDTD method are analyzed and verified by an example. Firstly, the spatial distribution of FCC meshes is introduced in detail, and on this basis, the discrete iterations of the electric and magnetic field components of the FCC-FDTD method in general media are analyzed and deduced. At the same time, the stability conditions of the method are given and compared with the FDTD method based on Yee cell. Then, the resonance frequency of 111TM mode of the common resonator is simulated by using FCC-FDTD method, and compared with the calculation results of the FDTD method based on Yee cell. The results verify the correctness and accuracy of the FCC-FDTD method. Secondly, the FCC grid is applied to plasma, and the discrete iterative equations of electric field component, magnetic field component and current density are derived. By convolution algorithm and Laplace transform method, the iterative formula of current density is obtained by discretization of constitutive equation. At the same time, in order to verify the correctness of the FCC grid plasma treatment method, the electromagnetic resonance characteristics of a cavity filled with time-invariant plasma are calculated, which is consistent with the results of mode matching principle. The results verify the correctness of the method and show that the method has the ability to calculate the electromagnetic problems of plasma targets. Finally, in order to apply the FCC-FDTD method to the calculation of electromagnetic scattering problem, the connection boundary conditions of this method are studied and analyzed, and the discrete iterative formulas of the electric field and magnetic field components at the connecting boundary are given. The feasibility and correctness of the FCC-FDTD method are verified by simulating the amplitude distribution of the sinusoidal field in the whole calculation region. To sum up, the FCC-FDTD method studied in this paper provides a new feasible method for the computation of complex targets in the future.
【學(xué)位授予單位】：江蘇大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TN011

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