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Numerical comparison of high-order absorbing boundary conditions and perfectly matched layers for a dispersive one-dimensional medium

机译:一维分散介质的高阶吸收边界条件和完美匹配层的数值比较

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摘要

High-order absorbing boundary conditions (ABC) and perfectly matched layers (PML) are two powerful methods to numerically solve wave problems in unbounded domains. The aim of the proposed study is to analyze and compare the performance of these methods in the one-dimensional problem governed by the dispersive wave equation. The PMLs proposed in literature for time-harmonic dynamics are applied to time-dependent wave problems, and linear, quadratic and cubic polynomial stretching functions are considered. The resulting PMLs exhibit a double absorbing action: (i) they reduce the amplitude of the incident waves and (ii) they delay the wave propagation. Then the ABC proposed by Givoli and Neta and those proposed by Hagstrom, Mar-Or and Givoli are considered. The former are a reformulation of the Higdon high-order non-reflecting boundary conditions, the latter improve the Higdon conditions and extend them to take into account evanescent waves. The accuracy of the PMLs and ABCs, implemented in a finite element code, is first investigated with respect to the frequency of the incident wave, being it progressive or evanescent. Then the response to a wave train characterized by a broad frequency spectrum, resulting from an impulsive force, is studied. A detailed analysis is performed to detect the influence of the parameters of both the ABCs and the PMLs on the absorption of waves. The performances of PMLs and ABCs are compared, and merits and drawbacks of the two methods are pointed out.
机译:高阶吸收边界条件(ABC)和完美匹配层(PML)是在数值上解决无界域中波动问题的两种有效方法。拟议研究的目的是分析和比较这些方法在色散波动方程控制的一维问题中的性能。文献中提出的用于时谐动力学的PML应用于时变波问题,并考虑了线性,二次和三次多项式拉伸函数。所得的PML具有双重吸收作用:(i)减小入射波的振幅,(ii)延迟波的传播。然后考虑由Givoli和Neta提出的ABC以及Hagstrom,Mar-Or和Givoli提出的ABC。前者是Higdon高阶非反射边界条件的重新表述,后者是改善Higdon条件并扩展它们以考虑e逝波的条件。首先针对入射波的频率(无论是渐进的还是渐逝的)研究以有限元代码实现的PML和ABC的精度。然后研究了由脉冲力引起的对以宽频谱为特征的波列的响应。进行了详细的分析,以检测ABC和PML的参数对波吸收的影响。比较了PML和ABC的性能,指出了两种方法的优缺点。

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