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

【摘要】：自從時域有限差分(FDTD)方法提出以來,由于其具有表述簡單、易于理解,在時域中能直觀描述電磁特性等特點,該方法的應用范圍越來越廣。而且,隨著計算機技術的快速發(fā)展和算法本身計算效率和計算精度的不斷提高,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,從而導致計算精度的降低。本文針對這一問題,重點研究了一種新的計算網(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,且計算精度較高。論文研究了基于FCC網(wǎng)格的FDTD(FCC-FDTD)方法,并應用該方法分別對填充有空氣和等離子體的兩個矩形諧振腔進行仿真計算,得出相關結論。同時,分析研究了FCC-FDTD方法的連接邊界條件,并給出算例驗證。首先,本文詳細地介紹了FCC網(wǎng)格中場的空間分布,并在此基礎上,重點分析推導了FCC-FDTD方法在一般介質情況下的電場、磁場分量的離散迭代式。同時,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)定性進行了比較。隨后,利用了FCC-FDTD方法仿真計算了普通諧振腔的111TM模的諧振頻率,并將其與基于Yee元胞的FDTD方法的計算結果進行比對,結果驗證了FCC-FDTD方法的正確性和準確性。其次,又將FCC網(wǎng)格應用到等離子體中,推導出電場分量、磁場分量和電流密度的離散迭代關系式;并通過卷積算法和拉普拉斯變換方法離散本構方程得出電流密度的計算迭代式。同時,為了驗證應用FCC網(wǎng)格處理等離子體方法的正確性,本文計算了一個填充非時變等離子體的諧振腔的電磁諧振特性,與模式匹配原理結果相符。結果驗證了此方法的正確性,同時表明了此方法具有計算等離子體目標電磁問題的能力。最后,為了將FCC-FDTD方法應用到電磁散射問題的計算中,論文還對此方法的連接邊界條件進行研究分析,并給出了連接邊界處的電場、磁場分量的離散迭代式;并通過仿真計算正弦場在整個計算區(qū)域內的幅值分布圖,驗證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方法為以后計算復雜目標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.
【學位授予單位】：江蘇大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN011

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本文編號：2014852