从多层问题到多个两层问题：一种新型频时混合多重散射积分方程求解器
From multi-layered problems to multiple two-layered problems: a novel frequency-time hybrid multiple-scattering integral equation solver
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中文总结 AI 辅助
该研究针对多层介质时变波动方程，提出频时混合多重散射积分方程求解器，将N层问题转化为N-1个两层子问题，兼具高精度、可并行性，经数值算例验证了效率与精度。
中文摘要 AI 辅助
本文针对一般多层介质中的时变波动方程问题，提出了一种新型频时混合多重散射（FTH-MS）积分方程求解器，其可扩展性随层数N的增加而显著提升。鉴于波动传播的有限速度，该新方法提出了一种创新的多重散射思路，将原始N层问题重新建模为N-1个两层子问题的序列，其主要优势在于：（i）与多层介质中的复杂问题相比，每个子问题具有更简单的波动散射特性；（ii）可利用傅里叶变换和频域边界积分方程（BIE）方法开发高精度求解器；（iii）每次多重散射步骤中子问题的数值评估可并行化。本文提出了乘法型和加法型两种策略，并严格推导了等价性结果，表明M阶多重散射求和可在某一时刻T(M)之前提供解的等价表示。由于两层问题的完美匹配层（PML）截断具有指数收敛的已有结果，所有子问题均通过基于傅里叶变换和PML-BIE方法的FTH方法进行数值求解，其数值评估采用基于切比雪夫的矩形-极坐标求解器，具有高精度。本文给出了数值算例，以验证所提方法的效率和精度。
英文摘要
This paper proposes a novel frequency-time hybrid multiple scattering (FTH-MS) integral equation solver for time-dependent wave equation problems in general multi-layered media, with remarkable scalability with respect to the number of layers $N$. In light of the finite speed of wave propagation, the new methodology provides an innovative multiple-scattering idea of re-modeling the original $N$-layered problem into a sequence of $N-1$ two-layered sub-problems, for which the main advantages lie in that (i) each sub-problem enjoys much simpler wave scattering properties compared with the complicated problem in a multi-layered medium, (ii) it enables to develop high-accuracy solver utilizing Fourier transform and frequency-domain boundary integral equation (BIE) method; and (iii) numerical evaluation of the sub-problems in each multiple scattering step can be parallelized. Both multiplicative- and additive-type strategies are developed and equivalence results, which indicate that the $M$-th order multiple scattering sums can provide equivalent representations of the solutions up to a certain time $T(M)$, are rigorously derived. Owing to the existed result of exponential convergence of the perfectly-matched-layer (PML) truncation for two-layered problem, all the sub-problems is numerically resolved by means of the FTH method based on the Fourier transform and the PML-BIE method whose numerical evaluation is addressed utilizing the Chebyshev-based rectangular-polar solver with high accuracy. Numerical examples are presented to validate the efficiency and accuracy of the proposed method.
