發(fā)布時間：2018-06-02 11:30

  本文選題：傳輸特征值 + 非協(xié)調(diào)有限元��； 參考：《貴州師范大學(xué)》2017年碩士論文

【摘要】：傳輸特征值問題是非均勻介質(zhì)逆散射理論中的二次特征值問題.傳輸特征值能用來估計散射體材料的性質(zhì),并且在逆散射理論中唯一性和重構(gòu)性方面具有重要理論意義.本文基于Helmholtz傳輸特征值問題非協(xié)調(diào)元法和混合元法的變分格式,建立了非協(xié)調(diào)元法和混合元法二網(wǎng)格離散方案.采用該方案,在細(xì)網(wǎng)格π_H上求傳輸特征值問題的解歸結(jié)為在粗網(wǎng)格上求原特征值問題及其共軛問題的解,然后在細(xì)網(wǎng)格π_H上求兩個系數(shù)矩陣為正定稀疏Hermite的塊對角矩陣的線性代數(shù)方程組的解.對于非協(xié)調(diào)元法二網(wǎng)格離散方案,本文證明了結(jié)果解仍保持漸近最優(yōu)精度,并報道了采用修正的Zienkiewicz元在二維和三維情形的數(shù)值算例來驗(yàn)證方案的有效性.對于混合元法二網(wǎng)格離散方案,數(shù)值實(shí)驗(yàn)驗(yàn)證了該方案的有效性.
[Abstract]:The transmission eigenvalue problem is a quadratic eigenvalue problem in the inverse scattering theory of inhomogeneous media. The transmission eigenvalues can be used to estimate the properties of scatterers and have important theoretical significance in the uniqueness and reconstruction of inverse scattering theory. Based on the variational schemes of non-conforming element method and mixed element method for Helmholtz transmission eigenvalue problem, a two-grid discretization scheme for non-conforming element method and hybrid element method is established. Using this scheme, the solution of the transmission eigenvalue problem on fine mesh 蟺 H is reduced to the solution of the original eigenvalue problem and its conjugate problem on the rough grid. Then, the solutions of two linear algebraic equations of block diagonal matrix with positive definite sparse Hermite are obtained on the fine grid 蟺 H. For the two-grid discrete scheme of nonconforming element method, the asymptotic optimal accuracy of the solution is proved in this paper, and the validity of the scheme is verified by a numerical example of the modified Zienkiewicz element in two-dimensional and three-dimensional cases. For the mixed element method, the effectiveness of the scheme is verified by numerical experiments.
【學(xué)位授予單位】：貴州師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O241.8

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

1 ZENG Fang;SUN JiGuang;XU LiWei;;A spectral projection method for transmission eigenvalues[J];Science China(Mathematics);2016年08期

2 Karel Kolman;A Two-Level Method for Nonsymmetric Eigenvalue Problems[J];Acta Mathematicae Applicatae Sinica(English Series);2005年01期

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本文編號：1968602