本文選題：拋物線方程方法　切入點(diǎn)：譜元法　出處：《南京郵電大學(xué)》2015年碩士論文

【摘要】：電磁場數(shù)值計(jì)算方法在電磁仿真領(lǐng)域中得到了廣泛應(yīng)用,例如頻域有限差分法(FDFD)、矩量法(MOM)和有限元法(FEM)等。這些方法在分析電大尺寸目標(biāo)的電磁散射問題時(shí),雖然計(jì)算精度高,但存在著消耗內(nèi)存多、對計(jì)算機(jī)配置要求高等缺點(diǎn)。物理光學(xué)等高頻方法可快速求解且消耗計(jì)算機(jī)資源少,但其計(jì)算精度卻不理想。拋物線方程(Parabolic Equation,PE)是由波動方程近似而來,它可以將三維問題降為一系列的二維問題,沿拋物線軸向方向進(jìn)行迭代求解,在降低了求解難度和計(jì)算內(nèi)存的同時(shí),仍能保證較高的計(jì)算精度。本文對電磁散射分析中的譜元拋物線方程方法進(jìn)行了研究,主要有以下幾方面的內(nèi)容:首先,詳細(xì)介紹了拋物線方程方法的基本理論,以及三維矢量拋物線方程方法分析電磁散射問題的基本原理和實(shí)施過程。其次,分析研究了標(biāo)量的譜元拋物線方程方法在電磁散射中的應(yīng)用。有限差分的拋物線方程方法采用規(guī)則網(wǎng)格來離散散射目標(biāo),足夠細(xì)密的剖分網(wǎng)格才能模擬散射體外型,而譜元拋物線方程方法采用非規(guī)則網(wǎng)格建模的方法能更好模擬散射體外型,提高計(jì)算精度。通過雙線性插值的方法獲得每個(gè)步進(jìn)面上任意點(diǎn)處的場量。在此基礎(chǔ)上,詳細(xì)推導(dǎo)了譜元拋物線方程的表達(dá)式,通過數(shù)值算例驗(yàn)證了其正確性。最后,研究了矢量的譜元拋物線方程方法在電磁散射中的應(yīng)用。我們詳細(xì)推導(dǎo)了矢量拋物線方程對應(yīng)的譜元法表達(dá)式,詳細(xì)描述了矢量邊界條件的處理以及求解過程,并通過數(shù)值算例進(jìn)行了驗(yàn)證。在網(wǎng)格剖分較粗時(shí),譜元拋物線方程方法比有限差分的拋物線方程方法具有更高的計(jì)算精度。對于拋物線方程方法的近軸限制,我們可以利用旋轉(zhuǎn)拋物線方程方法來獲得散射目標(biāo)的全向雙站雷達(dá)散射截面積(RCS);根據(jù)單/雙站RCS之間的轉(zhuǎn)換關(guān)系,可由散射目標(biāo)的雙站RCS快速插值出一定角度范圍內(nèi)的目標(biāo)單站RCS,通過算例驗(yàn)證了方法的正確性。
[Abstract]:Numerical calculation methods of electromagnetic field have been widely used in electromagnetic simulation, such as FDFDF, mom and FEMM in frequency domain, etc. These methods have high accuracy in analyzing electromagnetic scattering problem of electrically large size targets, such as finite element method (FEM), finite element method (FEM) and finite element method (FEM). However, there are many disadvantages such as high memory consumption and high demand for computer configuration. High frequency methods such as physical optics can be solved quickly and consume less computer resources, but their calculation accuracy is not ideal. The parabolic equation PE) is derived from the wave equation. It can reduce the three-dimensional problem to a series of two-dimensional problems and iteratively solve the problem along the parabola axis. It reduces the difficulty of solving the problem and computes the memory at the same time. The method of spectral parabola equation in electromagnetic scattering analysis is studied in this paper. The main contents are as follows: firstly, the basic theory of parabola equation method is introduced in detail. The basic principle and implementation process of electromagnetic scattering problem are analyzed by three-dimensional vector parabola equation method. Secondly, The application of spectral parabola equation method of scalar to electromagnetic scattering is analyzed and studied. The finite difference parabola equation method uses regular grids to discretize scattering objects. The spectral element parabola equation method using irregular mesh modeling method can better simulate the external scattering patterns and improve the calculation accuracy. The bilinear interpolation method is used to obtain the field quantities at any point on each step surface. The expression of spectral parabola equation is derived in detail, and its correctness is verified by numerical examples. Finally, The application of spectral parabola equation method of vector in electromagnetic scattering is studied. The expression of spectral element method corresponding to vector parabola equation is derived in detail, and the processing and solving process of vector boundary condition are described in detail. Numerical examples show that the spectral parabola equation method is more accurate than the finite difference parabola equation method when the mesh is coarse. We can use the method of rotating parabola equation to obtain the cross section area of omnidirectional bistatic radar for scattering target, according to the conversion relation between single and one bistatic RCS, The bistatic RCS of the scattered target can be rapidly interpolated from a certain angle range. The correctness of the method is verified by an example.
【學(xué)位授予單位】：南京郵電大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：TN011

【參考文獻(xiàn)】

相關(guān)博士學(xué)位論文 前1條

1 樊振宏;電磁散射分析中的快速方法[D];南京理工大學(xué);2007年

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本文編號：1668716