發(fā)布時(shí)間：2018-08-24 07:36

【摘要】：近幾十年來(lái),隨著不斷提高的工程電磁場(chǎng)應(yīng)用需求,追求高效且精確的數(shù)值分析方法成為計(jì)算電磁學(xué)領(lǐng)域一直以來(lái)的重點(diǎn)研究工作。時(shí)域有限元法由于其能夠?qū)Ψ蔷鶆蚪橘|(zhì)和復(fù)雜幾何結(jié)構(gòu)進(jìn)行精確模擬的優(yōu)勢(shì),越來(lái)越受到計(jì)算電磁學(xué)研究者們的關(guān)注。面對(duì)電磁工程分析越來(lái)越高的精度要求,本文研究的高階疊層矢量基函數(shù)是一個(gè)有效的方法。通過(guò)算例計(jì)算結(jié)果表明,在同樣的精度要求下,應(yīng)用高階基可以使網(wǎng)格的剖分尺寸更大,從而使未知量數(shù)目降低,計(jì)算效率能夠得到有效提高。傳統(tǒng)的時(shí)域有限元法在計(jì)算電大尺寸問(wèn)題的時(shí)候,大型矩陣的求逆便會(huì)嚴(yán)重影響求解時(shí)間,甚至因?yàn)橛?jì)算資源的影響無(wú)法求解。本文使用不連續(xù)伽遼金時(shí)域有限元法,通過(guò)在時(shí)間步進(jìn)前對(duì)每個(gè)子域系統(tǒng)矩陣的分別處理,大大縮短了求逆時(shí)間。不連續(xù)伽遼金時(shí)域有限元法中,整個(gè)計(jì)算區(qū)域被分為多個(gè)互不重疊的子區(qū)域,每個(gè)子域中的電場(chǎng)和磁場(chǎng)單獨(dú)求解,且只與相鄰子域交界面相關(guān)。然而基函數(shù)在區(qū)域分界面處是不連續(xù)的,因此本文引入了中心數(shù)值通量,強(qiáng)加電磁場(chǎng)切向連續(xù)性。除此之外,本文還研究了另一種解決大型稀疏矩陣求解問(wèn)題的方法——基于H-矩陣的高效有限元直接求解技術(shù)。在基于H-矩陣直接解法的研究中,首先介紹了H-矩陣的基本概念和運(yùn)算法則,詳細(xì)討論了H-LU分解算法,最后仔細(xì)分析了該方法的計(jì)算復(fù)雜度和內(nèi)存消耗。
[Abstract]:In recent decades, with the increasing demand for engineering electromagnetic applications, the pursuit of efficient and accurate numerical analysis methods has been the focus of research in the field of computational electromagnetics. Time domain finite element method (TFEM) has attracted more and more attention of computational electromagnetics because of its advantages of accurate simulation of inhomogeneous media and complex geometric structures. In the face of the higher and higher precision requirement of electromagnetic engineering analysis, the high order laminated vector basis function is an effective method studied in this paper. The numerical results show that the application of higher order basis can make the mesh size larger and reduce the number of unknowns under the same precision requirement. The computational efficiency can be improved effectively. When the traditional time domain finite element method is used to solve electrically large size problems, the inverse of large matrices will seriously affect the solution time, even because of the influence of computational resources can not be solved. In this paper, the discontinuous Galerkin time domain finite element method is used to deal with each subdomain system matrix separately before the time step, and the inverse time is greatly shortened. In the discontinuous Galerkin time domain finite element method, the whole computational region is divided into several non-overlapping subregions. The electric and magnetic fields in each subdomain are solved separately and are only related to the interface between adjacent subdomains. However, the basis function is discontinuous at the regional interface, so the central numerical flux is introduced and the tangential continuity of the electromagnetic field is imposed. In addition, another method to solve the problem of large sparse matrix is studied in this paper, which is an efficient finite element method based on H-matrix. In the research of direct solution based on H- matrix, the basic concepts and algorithms of H- matrix are introduced, and the H-LU decomposition algorithm is discussed in detail. Finally, the computational complexity and memory consumption of this method are analyzed in detail.
【學(xué)位授予單位】：南京郵電大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O441;O241.82

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本文編號(hào)：2200087