高頻方法與積分方程方法混合研究及應(yīng)用
發(fā)布時(shí)間：2019-03-30 13:17
【摘要】：混合算法均是取彼之長(zhǎng)、補(bǔ)己之短。高頻方法結(jié)合積分方程方法能克服各自局限、發(fā)揚(yáng)各自優(yōu)勢(shì),特別適合求解電大尺寸和精細(xì)結(jié)構(gòu)并存的電磁問(wèn)題。往往在電大尺寸部分使用高頻方法,而在精細(xì)結(jié)構(gòu)部分使用積分方程方法,這樣就可以揚(yáng)長(zhǎng)避短。在滿足所需精度的同時(shí),大大提高計(jì)算的速度和節(jié)省計(jì)算的內(nèi)存等。本文就是圍繞這類(lèi)電磁問(wèn)題而展開(kāi),研究主要內(nèi)容可以歸納如下:一、基于剪裁NURBS參數(shù)曲面的研究。首先介紹矩量法(MoM)和物理光學(xué)法(PO)基本理論,再針對(duì)平面幾何建模的不足,引入NURBS參數(shù)曲面建模。發(fā)現(xiàn)使用物理光學(xué)在矩形參數(shù)曲面上計(jì)算電磁散射時(shí),無(wú)法剔除冗余面元的貢獻(xiàn)而造成誤差太大,引入了剪裁NURBS參數(shù)曲面。相比未剪裁曲面,在剪裁NURBS參數(shù)曲面上散射場(chǎng)的計(jì)算具有非常高的準(zhǔn)確性,同時(shí)給出了相應(yīng)的算例來(lái)驗(yàn)證。二、基于高效迭代混合算法的研究。針對(duì)在傳統(tǒng)矩量法和物理光學(xué)混合(MoM-PO)中,物理光學(xué)區(qū)域?qū)亓糠▍^(qū)域的耦合矩陣占用了大量?jī)?nèi)存和時(shí)間,提出一種高效迭代混合算法(EI-MoM-PO),它是一種直接更新矩量法區(qū)域的電壓矩陣來(lái)進(jìn)行迭代計(jì)算,能在相同網(wǎng)格的情況下,保持良好精度的同時(shí)還能節(jié)省計(jì)算資源;為了擴(kuò)大計(jì)算能力,在原來(lái)Mo M區(qū)域引入多層快速多級(jí)子,形成EI-MLFMA-PO,進(jìn)一步節(jié)省內(nèi)存和時(shí)間,并求解電大尺寸的電磁問(wèn)題;最后首次提出一種針對(duì)具有大量近似平面結(jié)構(gòu)目標(biāo)混合算法時(shí),提出兩套剖分網(wǎng)格的形式來(lái)對(duì)PO區(qū)域進(jìn)行高效消隱,它具有簡(jiǎn)單、高效的特點(diǎn)。三、基于積分區(qū)域分解方法(IE-DDM)結(jié)合PO的研究。IE-DDM采取“分而治之”的思想,它一方面可以針對(duì)不同的子區(qū)采取更加適合的計(jì)算方法,并擁有天然并行的優(yōu)勢(shì)。在另一方面,不同子區(qū)可以采取非共性的網(wǎng)格來(lái)進(jìn)行剖分計(jì)算。本文在積分區(qū)域分解方法的框架下,針對(duì)電大尺寸和復(fù)雜精細(xì)結(jié)構(gòu)是整體還是分開(kāi)兩種情況,提出使用兩種方式加入物理光學(xué)方法。前者采用目標(biāo)整體分區(qū),后者分開(kāi)目標(biāo)采用矩量法區(qū)域內(nèi)部分區(qū)。由物理光學(xué)方法的加入極大地豐富和充實(shí)了積分區(qū)域分解方法的框架,在以后計(jì)算具有電大光滑尺寸的復(fù)合結(jié)構(gòu)時(shí)大大提高了求解速度,同時(shí)為后續(xù)加入有限元等其他求解器做鋪墊,為更進(jìn)一步求解復(fù)雜多尺度問(wèn)題提供一種可能。
[Abstract]:The hybrid algorithm is to take their strengths and make up for their own short. The high-frequency method combined with the integral equation method can overcome their limitations and carry forward their advantages. It is especially suitable for solving electromagnetic problems in which large size and fine structure coexist. The high frequency method is often used in the electrically large size part, while the integral equation method is used in the fine structure part, so that the advantages and disadvantages can be improved. While satisfying the required precision, the speed of calculation is greatly improved and the memory of calculation is saved. The main contents of this paper can be summarized as follows: first, the research based on clipped NURBS parametric surfaces. The basic theory of moment method (MoM) and physical optics method (PO) are introduced firstly. Then NURBS parametric surface modeling is introduced to solve the deficiency of plane geometry modeling. It is found that when using physical optics to calculate electromagnetic scattering on rectangular parametric surfaces, the contribution of redundant surface elements cannot be eliminated and the error is too large. A clipping NURBS parametric surface is introduced. Compared with the unclipped surface, the calculation of scattering field on the clipped NURBS parametric surface is very accurate. At the same time, an example is given to verify it. Second, the research based on efficient iterative hybrid algorithm. In the traditional method of moments (mom) and physical optics mixing (MoM-PO), an efficient iterative hybrid algorithm (EI-MoM-PO) is proposed to solve the problem that the coupling matrix in the physical optics region takes up a large amount of memory and time in the moment method region. It is a direct updating of the voltage matrix in the region of the moment method to calculate iteratively. It can keep good precision and save computing resources under the same grid condition. In order to expand the computing ability, the multi-layer fast multi-stage sub is introduced into the original Mo M region, which further saves the memory and time of the EI-MLFMA-PO, and solves the electromagnetic problem of the electrically large size. Finally, for the first time, a hybrid algorithm with a large number of approximate planar structures is proposed, and two sets of mesh forms are proposed to efficiently eliminate the hidden space in the PO region. It has the characteristics of simplicity and efficiency. Thirdly, based on the integration domain decomposition (IE-DDM) method combined with the research of PO, IE-DDM adopts the idea of "divide and conquer", on the one hand, it can adopt more suitable computing methods for different sub-regions, and it has the advantage of natural parallelism. On the other hand, different sub-regions can adopt non-common grid to calculate the partition. In this paper, under the framework of the integral domain decomposition method, two physical optics methods are proposed to solve the problem of whether the complex fine structure and the electrically large size are whole or separate. The former adopts the integral partition of the target, and the latter adopts the internal partition of the region of the moment method to separate the target. The framework of the integral domain decomposition method is greatly enriched and enriched by the addition of the physical optics method, and the solution speed is greatly improved when calculating the composite structure with electrically large smooth size in the future. At the same time, it provides a possibility for further solving complex multi-scale problems by adding other solvers such as finite element.
【學(xué)位授予單位】：電子科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：TN011
本文編號(hào)：2450113
[Abstract]:The hybrid algorithm is to take their strengths and make up for their own short. The high-frequency method combined with the integral equation method can overcome their limitations and carry forward their advantages. It is especially suitable for solving electromagnetic problems in which large size and fine structure coexist. The high frequency method is often used in the electrically large size part, while the integral equation method is used in the fine structure part, so that the advantages and disadvantages can be improved. While satisfying the required precision, the speed of calculation is greatly improved and the memory of calculation is saved. The main contents of this paper can be summarized as follows: first, the research based on clipped NURBS parametric surfaces. The basic theory of moment method (MoM) and physical optics method (PO) are introduced firstly. Then NURBS parametric surface modeling is introduced to solve the deficiency of plane geometry modeling. It is found that when using physical optics to calculate electromagnetic scattering on rectangular parametric surfaces, the contribution of redundant surface elements cannot be eliminated and the error is too large. A clipping NURBS parametric surface is introduced. Compared with the unclipped surface, the calculation of scattering field on the clipped NURBS parametric surface is very accurate. At the same time, an example is given to verify it. Second, the research based on efficient iterative hybrid algorithm. In the traditional method of moments (mom) and physical optics mixing (MoM-PO), an efficient iterative hybrid algorithm (EI-MoM-PO) is proposed to solve the problem that the coupling matrix in the physical optics region takes up a large amount of memory and time in the moment method region. It is a direct updating of the voltage matrix in the region of the moment method to calculate iteratively. It can keep good precision and save computing resources under the same grid condition. In order to expand the computing ability, the multi-layer fast multi-stage sub is introduced into the original Mo M region, which further saves the memory and time of the EI-MLFMA-PO, and solves the electromagnetic problem of the electrically large size. Finally, for the first time, a hybrid algorithm with a large number of approximate planar structures is proposed, and two sets of mesh forms are proposed to efficiently eliminate the hidden space in the PO region. It has the characteristics of simplicity and efficiency. Thirdly, based on the integration domain decomposition (IE-DDM) method combined with the research of PO, IE-DDM adopts the idea of "divide and conquer", on the one hand, it can adopt more suitable computing methods for different sub-regions, and it has the advantage of natural parallelism. On the other hand, different sub-regions can adopt non-common grid to calculate the partition. In this paper, under the framework of the integral domain decomposition method, two physical optics methods are proposed to solve the problem of whether the complex fine structure and the electrically large size are whole or separate. The former adopts the integral partition of the target, and the latter adopts the internal partition of the region of the moment method to separate the target. The framework of the integral domain decomposition method is greatly enriched and enriched by the addition of the physical optics method, and the solution speed is greatly improved when calculating the composite structure with electrically large smooth size in the future. At the same time, it provides a possibility for further solving complex multi-scale problems by adding other solvers such as finite element.
【學(xué)位授予單位】：電子科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：TN011
【參考文獻(xiàn)】
相關(guān)博士學(xué)位論文 前2條
1 黃鍇;混合方法分析電大目標(biāo)附近天線受擾方向圖[D];西安電子科技大學(xué);2012年
2 宗顯政;平臺(tái)與天線的一體化電磁建模及工程實(shí)踐研究[D];電子科技大學(xué);2008年
，本文編號(hào)：2450113
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