本文選題：不連續(xù)伽遼金 + 非共形網(wǎng)格　； 參考：《南京理工大學》2016年碩士論文

【摘要】：在工程實踐中,由于時域積分方程方法在分析目標的電磁散射特性時,可以一次性地求解出多個頻點,因此在處理寬頻帶問題時,時域積分方程方法得到了廣泛地應用。然而基于伽遼金測試的普通時域積分方程方法為了滿足物理上的連續(xù)性,目標模型剖分之后的網(wǎng)格必須保證共形。但是在現(xiàn)實世界里,目標一般都比較復雜,產(chǎn)生一套符合目標參數(shù)的共形網(wǎng)格因此也比較困難,所以研究能夠處理非共形網(wǎng)格的算法是很有必要的。根據(jù)上述問題,本文提出了不連續(xù)伽遼金的時域體面積分方程方法。該方法通過將不連續(xù)伽遼金思想引入到時域體面積分方程中,從而實現(xiàn)了算法對非共形網(wǎng)格地處理。此方法在求解目標的電磁參數(shù)時不需要相鄰單元之間隱含的連續(xù)性條件,所以對于不同的單元網(wǎng)格可以采用不同的基函數(shù),從而在確保結(jié)果精確的前提下減少計算所消耗的內(nèi)存與時間�；谝陨蟽�(yōu)勢,在求解復雜目標的寬頻帶電磁參數(shù)時,不連續(xù)伽遼金的時域體面積分方程方法具有比較大的通用性。本文首先介紹了時域積分方程的推導過程和不連續(xù)伽遼金方法的基本原理。然后詳細推導了不連續(xù)伽遼金的時域體積分方程和改進之后的連續(xù)-不連續(xù)伽遼金的時域體積分方程,并對形成的矩陣進行分析和求解,然后又推導出了連續(xù)-不連續(xù)伽遼金的時域體面積分方程。最后為了分析電大尺寸目標,在體面積分方程方法的基礎上又引入了時域平面波技術,極大地拓展了前者在求解實際電磁問題時的能力。
[Abstract]:In engineering practice, the time-domain integral equation method has been widely used in dealing with wide-band problems because it can solve multiple frequency points at one time when analyzing the electromagnetic scattering characteristics of the target.However, in order to satisfy the physical continuity of the ordinary time-domain integral equation method based on Galerkin test, the mesh of the target model must be conformal.However, in the real world, the target is generally more complex, so it is difficult to produce a set of conformal mesh which accords with the target parameters. Therefore, it is necessary to study the algorithm to deal with the non-conformal mesh.Based on the above problems, a method of discrete Galerkin time domain decent integral equation is presented.In this method, the discontinuous Galerkin idea is introduced into the time domain decent integral equation, and the algorithm is used to deal with non-conformal grids.In order to solve the electromagnetic parameters of the target, this method does not need the implicit continuity condition between adjacent elements, so different basis functions can be used for different element meshes.Thus reducing the memory and time consumed by the calculation while ensuring the accuracy of the results.Based on the above advantages, the discontinuous Galerkin's time domain decent integral equation method is of great generality in solving the broadband electromagnetic parameters of complex targets.In this paper, the derivation process of time domain integral equation and the basic principle of discontinuous Galerkin method are introduced.Then the time domain volume fraction equation of discontinuous Galerkin and the modified continuous discontinuous Galerkin time domain volume fraction equation are derived in detail, and the resulting matrix is analyzed and solved.Then the time-domain decent integral equation of continuous-discontinuous Galerkin is derived.Finally, in order to analyze the electrically large size target, the time domain plane wave technique is introduced on the basis of the decent integral equation method, which greatly expands the former's ability to solve the actual electromagnetic problem.
【學位授予單位】：南京理工大學
【學位級別】：碩士
【學位授予年份】：2016
【分類號】：TN011
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本文編號：1737823