卷积四阶方法用于时域散射中的无界穿透界面
Convolution quadrature methods for time-domain scattering from unbounded penetrable interfaces
AI总结：
本文提出了一种边界积分方程方法，用于求解二维空间中存在无界穿透界面的声学和电磁时域散射问题，采用卷积四阶方法与最近引入的加窗格林函数（WGF）方法相结合，将问题转化为有限数量的频域问题，并通过WGF方法将这些问题转化为有界的界面，从而有效减少误差。
摘要：
本文提出了一类边界积分方程方法，用于求解二维空间中存在无界穿透界面的声学和电磁时域散射问题。所提出的方法依赖于卷积四阶（CQ）方法与最近引入的加窗格林函数（WGF）方法相结合。如同标准的有界障碍物时域散射问题一样，使用用户选择的CQ方法将问题转化为有限数量的（复）频域问题，这些问题定义在包含穿透无界界面的域上。然后，每个频域传输问题被公式化为一个第二类积分方程，通过WGF方法有效地转化为有界界面——该方法引入的误差随着窗口大小的增加而超代数地减小。由此得到的加窗积分方程可以通过任何（加速或非加速）现成的亥姆霍兹边界积分方程求解器来求解，该求解器能够处理具有大虚部的复波数。本文采用基于阿尔佩特四阶规则的高阶尼斯特罗姆方法。各种数值示例，包括开放波导中的波传播以及多层介质的散射，展示了所提出方法的能力。
英文摘要：
This paper presents a class of boundary integral equation methods for the numerical solution of acoustic and electromagnetic time-domain scattering problems in the presence of unbounded penetrable interfaces in two-spatial dimensions. The proposed methodology relies on Convolution Quadrature (CQ) methods in conjunction with the recently introduced Windowed Green Function (WGF) method. As in standard time-domain scattering from bounded obstacles, a CQ method of the user's choice is utilized to transform the problem into a finite number of (complex) frequency-domain problems posed on the domains involving penetrable unbounded interfaces. Each one of the frequency-domain transmission problems is then formulated as a second-kind integral equation that is effectively reduced to a bounded interface by means of the WGF method---which introduces errors that decrease super-algebraically fast as the window size increases. The resulting windowed integral equations can then be solved by means of any (accelerated or unaccelerated) off-the-shelf Helmholtz boundary integral equation solver capable of handling complex wavenumbers with a large imaginary part. A high-order Nyström method based on Alpert quadrature rules is utilized here. A variety of numerical examples including wave propagation in open waveguides as well as scattering from multiply layered media demonstrate the capabilities of the proposed approach.
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