本文選題：散射問題 + 優(yōu)化的�。� 參考：《長春工業(yè)大學》2016年碩士論文

【摘要】：本論文主要研究散射問題的數(shù)值計算方法,其中包括時諧聲波散射問題和雙層介質(zhì)散射問題。在本文中給出了一種優(yōu)化的完美匹配層(PML)計算方法,并分析了優(yōu)化的PML方法的收斂性。在本論文中,首先對聲波與電磁波的散射問題的用途、基本定義以及國內(nèi)外相關發(fā)展現(xiàn)狀給出簡單介紹;其次對于聲波時諧散射問題,構(gòu)造一種優(yōu)化的PML方法,并且給出算法的適定性和收斂性;第三,對于雙層介質(zhì)散射問題,給出當波數(shù)為分段常數(shù)時的一種數(shù)值計算方法,即單軸的優(yōu)化PML方法,并討論了算法的收斂性。在聲波時諧散射問題的優(yōu)化的完美匹配層(PML)方法中,引入了一個帶有小參數(shù)0?的吸收函數(shù),不僅使得散射問題的數(shù)值計算不依賴PML層的厚度?,而且給問題的收斂性分析帶來方便。我們證明了只要0?充分小,優(yōu)化的PML解指數(shù)收斂于此問題的解。在解雙層介質(zhì)散射問題的優(yōu)化完美匹配層(PML)方法中,我們構(gòu)造了單軸的PML層,在吸收函數(shù)中引入了一個小參數(shù)0?,并且證明了只要參數(shù)0?充分小,優(yōu)化的PML解指數(shù)收斂于原雙層介質(zhì)散射問題的解。
[Abstract]:In this paper, we mainly study the numerical method of scattering problem, including time-harmonic acoustic scattering problem and two-layer medium scattering problem. In this paper, an optimized perfectly matched layer (PML) algorithm is presented, and the convergence of the optimized PML method is analyzed. In this paper, the purpose, basic definition and development status of acoustic wave and electromagnetic wave scattering problem are introduced briefly, and then an optimized PML method is constructed for acoustic wave time-harmonic scattering problem. Thirdly, for the two-layer dielectric scattering problem, a numerical calculation method called uniaxial optimal PML method is given when the wavenumber is a piecewise constant, and the convergence of the algorithm is discussed. A perfectly matched layer (PML) method with small parameters 0? The absorption function not only makes the numerical calculation of the scattering problem independent of the thickness of the PML layer, but also facilitates the convergence analysis of the problem. We proved it was just 0? Sufficiently small, the optimized PML solution exponentially converges to the solution of the problem. In the optimal perfectly matched layer (PML) method for solving the scattering problem of two-layer media, we construct a uniaxial PML layer, and introduce a small parameter 0 in the absorption function, and prove that only the parameter 0? Sufficiently small, the optimized PML solution exponentially converges to the solution of the original two-layer scattering problem.
【學位授予單位】：長春工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2016
【分類號】：O411;O241

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本文編號：1896248