基于電磁場體積分方程的區(qū)域分解方法研究
發(fā)布時(shí)間：2018-08-11 13:37
【摘要】：現(xiàn)代信息技術(shù)的許多領(lǐng)域都涉及求解復(fù)雜的電磁場問題,這促使許多高效、實(shí)用的電磁算法發(fā)展起來。但是,對(duì)于三維電大尺寸、高媒質(zhì)參數(shù)、高對(duì)比度復(fù)雜介質(zhì)結(jié)構(gòu)電磁散射特性的快速、有效分析仍然面臨挑戰(zhàn)。為應(yīng)對(duì)這樣的挑戰(zhàn),本文研究基于電磁場體積分方程的區(qū)域分解方法,并研究在區(qū)域分解方法基礎(chǔ)上進(jìn)一步減少存儲(chǔ)需求,提高計(jì)算效率,增強(qiáng)內(nèi)迭代收斂性的方法。主要貢獻(xiàn)如下：1.提出了基于體積分方程的矩量法(VIE-MoM)矩陣的快速填充方法。該方法對(duì)剖分單元進(jìn)行統(tǒng)籌安排,消除了冗余計(jì)算,使矩陣填充時(shí)間減少了約80%。2.提出了基于體積分方程的擬合Green函數(shù)快速Fourier變換法(VIE-FG-FFT)。該方法通過擬合Green函數(shù)到均勻笛卡爾網(wǎng)格節(jié)點(diǎn)上,使得矩陣-向量積可被FFT加速,其計(jì)算復(fù)雜度為O(N log N),存儲(chǔ)復(fù)雜度為O(N),其中N是未知量個(gè)數(shù)。與先前出現(xiàn)的基于FFT的方法比較,VIE-FG-FFT具有精度高、預(yù)處理時(shí)間少的優(yōu)點(diǎn)。特別地,利用擬合Green函數(shù)步驟與媒質(zhì)參數(shù)無關(guān)的特點(diǎn),進(jìn)一步將VIE-FG-FFT的應(yīng)用范圍擴(kuò)展到了電各向異性介質(zhì)目標(biāo)。3.提出了基于體積分方程的重疊型區(qū)域分解方法(VIE-ODDM)及其嚴(yán)格的數(shù)學(xué)建模步驟。該方法將一個(gè)電大尺寸介質(zhì)目標(biāo)的VIE-MoM模型的全局求解問題方式轉(zhuǎn)化為許多子域問題進(jìn)行局部迭代求解,大幅度降低了內(nèi)存需求,能夠有效地求解那些其快速算法模型對(duì)用戶計(jì)算機(jī)太大的介質(zhì)體電磁散射問題。特別地,從理論和數(shù)值的角度研究了VIE-ODDM的外迭代格式的收斂性,證明是非常好的,并進(jìn)一步將VIE-ODDM的應(yīng)用范圍擴(kuò)展到電各向異性介質(zhì)目標(biāo)。4.提出了基于體積分方程的重疊型區(qū)域分解方法與擬合Green函數(shù)快速Fourier變換法的混合的方法(VIE-ODDM-FG-FFT)。該方法保持了VIE-ODDM的優(yōu)點(diǎn),進(jìn)一步降低了存儲(chǔ)需求,大幅度提高了計(jì)算效率,增強(qiáng)了內(nèi)迭代的收斂性。與采用多層快速多極子算法(MLFMA)加速的方法比較,這里沒有“次波長中斷”問題。此外,由于引入了嵌套均勻笛卡爾網(wǎng)格方案,即使在媒質(zhì)參數(shù)分布很不均勻的情形(如高對(duì)比度結(jié)構(gòu)),該方法的計(jì)算效率也不會(huì)受到重大影響。5.提出了基于體積分方程的非重疊型區(qū)域分解方法(VIE-NDDM)并與FG-FFT形成混合方法。與VIE-ODDM不同,VIE-NDDM采用顯式邊界條件來形成各相鄰子域之間的信息耦合,從而省去了構(gòu)造緩沖區(qū)的工作量,減少了算法的預(yù)處理時(shí)間。類似于、TE-ODDM-FG-FFT那樣,FG-FFT的引入進(jìn)一步降低了存儲(chǔ)需求,大幅度提高了計(jì)算效率。
[Abstract]:Many fields of modern information technology involve in solving complex electromagnetic problems, which promote the development of many efficient and practical electromagnetic algorithms. However, the fast and effective analysis of electromagnetic scattering characteristics of three-dimensional electrically large size, high medium parameters and high contrast complex dielectric structures still faces a challenge. In order to meet this challenge, this paper studies the domain decomposition method based on the volume fraction equation of electromagnetic field, and further reduces the storage requirement, improves the computational efficiency and enhances the convergence of the internal iteration based on the domain decomposition method. The main contributions are as follows: 1. A fast filling method for the method of moments (VIE-MoM) matrix based on the volume fraction equation is proposed. This method arranges the subdivision unit as a whole, eliminates the redundant calculation, and reduces the filling time of the matrix by about 80%. 2. A fast Fourier transform method (VIE-FG-FFT) for fitting Green function based on volume fraction equation is proposed. By fitting the Green function to the uniform Cartesian grid node, the matrix vector product can be accelerated by FFT, and its computational complexity is that the O (N log N), storage complexity is O (N), where N is the number of unknown variables. Compared with the previous methods based on FFT, VIE-FG-FFT has the advantages of high precision and less pretreatment time. In particular, by using the feature of fitting the Green function step independent of the medium parameters, the application of VIE-FG-FFT is further extended to the target of electrically anisotropic medium .3. An overlapping domain decomposition method (VIE-ODDM) based on volume fraction equation and its strict mathematical modeling steps are proposed. In this method, the global solution of a VIE-MoM model for an electrically large dielectric target is transformed into a number of subdomain problems for local iterative solution, which greatly reduces the memory requirement. It can effectively solve the electromagnetic scattering problem of dielectric bodies whose fast algorithm models are too large for user computers. In particular, the convergence of VIE-ODDM 's external iteration scheme is studied theoretically and numerically, which is proved to be very good. Furthermore, the application of VIE-ODDM is extended to the target of electrically anisotropic media .4. An overlap domain decomposition method based on volume fraction equation and a hybrid method (VIE-ODDM-FG-FFT) for fast Fourier transform of fitting Green function are proposed. This method preserves the advantages of VIE-ODDM, further reduces the storage requirements, greatly improves the computational efficiency and enhances the convergence of the inner iteration. Compared with the multilayer fast multipole algorithm (MLFMA) acceleration, there is no subwavelength interruption problem. In addition, due to the introduction of a nested uniform Cartesian mesh scheme, the computational efficiency of the method will not be significantly affected even in the case of very uneven distribution of medium parameters (such as high contrast structure). A nonoverlapping domain decomposition method (VIE-NDDM) based on volume fraction equation is proposed and mixed with FG-FFT. Unlike VIE-ODDM, VIE-NDDM uses explicit boundary conditions to form information coupling between adjacent subdomains, which saves the workload of constructing buffer zones and reduces the preprocessing time of the algorithm. The introduction of FG-FFT similar to that of TE-ODDM-FG-FFT further reduces the storage requirement and greatly improves the computational efficiency.
【學(xué)位授予單位】：東南大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O441.4
[Abstract]:Many fields of modern information technology involve in solving complex electromagnetic problems, which promote the development of many efficient and practical electromagnetic algorithms. However, the fast and effective analysis of electromagnetic scattering characteristics of three-dimensional electrically large size, high medium parameters and high contrast complex dielectric structures still faces a challenge. In order to meet this challenge, this paper studies the domain decomposition method based on the volume fraction equation of electromagnetic field, and further reduces the storage requirement, improves the computational efficiency and enhances the convergence of the internal iteration based on the domain decomposition method. The main contributions are as follows: 1. A fast filling method for the method of moments (VIE-MoM) matrix based on the volume fraction equation is proposed. This method arranges the subdivision unit as a whole, eliminates the redundant calculation, and reduces the filling time of the matrix by about 80%. 2. A fast Fourier transform method (VIE-FG-FFT) for fitting Green function based on volume fraction equation is proposed. By fitting the Green function to the uniform Cartesian grid node, the matrix vector product can be accelerated by FFT, and its computational complexity is that the O (N log N), storage complexity is O (N), where N is the number of unknown variables. Compared with the previous methods based on FFT, VIE-FG-FFT has the advantages of high precision and less pretreatment time. In particular, by using the feature of fitting the Green function step independent of the medium parameters, the application of VIE-FG-FFT is further extended to the target of electrically anisotropic medium .3. An overlapping domain decomposition method (VIE-ODDM) based on volume fraction equation and its strict mathematical modeling steps are proposed. In this method, the global solution of a VIE-MoM model for an electrically large dielectric target is transformed into a number of subdomain problems for local iterative solution, which greatly reduces the memory requirement. It can effectively solve the electromagnetic scattering problem of dielectric bodies whose fast algorithm models are too large for user computers. In particular, the convergence of VIE-ODDM 's external iteration scheme is studied theoretically and numerically, which is proved to be very good. Furthermore, the application of VIE-ODDM is extended to the target of electrically anisotropic media .4. An overlap domain decomposition method based on volume fraction equation and a hybrid method (VIE-ODDM-FG-FFT) for fast Fourier transform of fitting Green function are proposed. This method preserves the advantages of VIE-ODDM, further reduces the storage requirements, greatly improves the computational efficiency and enhances the convergence of the inner iteration. Compared with the multilayer fast multipole algorithm (MLFMA) acceleration, there is no subwavelength interruption problem. In addition, due to the introduction of a nested uniform Cartesian mesh scheme, the computational efficiency of the method will not be significantly affected even in the case of very uneven distribution of medium parameters (such as high contrast structure). A nonoverlapping domain decomposition method (VIE-NDDM) based on volume fraction equation is proposed and mixed with FG-FFT. Unlike VIE-ODDM, VIE-NDDM uses explicit boundary conditions to form information coupling between adjacent subdomains, which saves the workload of constructing buffer zones and reduces the preprocessing time of the algorithm. The introduction of FG-FFT similar to that of TE-ODDM-FG-FFT further reduces the storage requirement and greatly improves the computational efficiency.
【學(xué)位授予單位】：東南大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O441.4
【相似文獻(xiàn)】
相關(guān)期刊論文 前10條
1 _5世勛;具正墢核的zM分方程[J];數(shù)學(xué)學(xué)報(bào);1954年01期
2 李云章,黃達(dá)人;關(guān)于非齊次細(xì)分方程的一個(gè)注記(英文)[J];數(shù)學(xué)進(jìn)展;1999年03期
3 段永紅;;非線性四階差分方程的多重解[J];宜賓學(xué)院學(xué)報(bào);2011年12期
4 高載河;Qiz.非}諦詚M分方程}D的存在定理[J];數(shù)學(xué)學(xué)報(bào);1954年04期
5 彭旭麟;zM分方程固有值的一種近似求法[J];武漢水利電力學(xué)院學(xué)報(bào);1964年01期
6 王志珍;五階差分方程解的漸近性[J];曲阜師范大學(xué)學(xué)報(bào)(自然科學(xué)版);1999年02期
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