时谐散射问题的数值计算的研究

发布时间：2018-05-16 09:03

本文选题：散射问题 + 优化的　；参考：《长春工业大学》2016年硕士论文

【摘要】：本论文主要研究散射问题的数值计算方法,其中包括时谐声波散射问题和双层介质散射问题。在本文中给出了一种优化的完美匹配层(PML)计算方法,并分析了优化的PML方法的收敛性。在本论文中,首先对声波与电磁波的散射问题的用途、基本定义以及国内外相关发展现状给出简单介绍;其次对于声波时谐散射问题,构造一种优化的PML方法,并且给出算法的适定性和收敛性;第三,对于双层介质散射问题,给出当波数为分段常数时的一种数值计算方法,即单轴的优化PML方法,并讨论了算法的收敛性。在声波时谐散射问题的优化的完美匹配层(PML)方法中,引入了一个带有小参数0?的吸收函数,不仅使得散射问题的数值计算不依赖PML层的厚度?,而且给问题的收敛性分析带来方便。我们证明了只要0?充分小,优化的PML解指数收敛于此问题的解。在解双层介质散射问题的优化完美匹配层(PML)方法中,我们构造了单轴的PML层,在吸收函数中引入了一个小参数0?,并且证明了只要参数0?充分小,优化的PML解指数收敛于原双层介质散射问题的解。
[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.
【学位授予单位】：长春工业大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O411;O241

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