This paper proposes a frequency-time hybrid solver for the time-dependent wave equation in two-dimensional interior spatial domains. The approach relies on four main elements, namely, 1) A multiple scattering strategy that decomposes a given interior time-domain problem into a sequence of limited-duration time-domain problems of scattering by overlapping open arcs, each one of which is reduced (by means of the Fourier transform) to a sequence of Helmholtz frequency-domain problems; 2) Boundary integral equations on overlapping boundary patches for the solution of the frequency-domain problems in point 1); 3) A smooth "Time-windowing and recentering" methodology that enables both treatment of incident signals of long duration and long time simulation; and, 4) A Fourier transform algorithm that delivers numerically dispersionless, spectrally-accurate time evolution for given incident fields. By recasting the interior time-domain problem in terms of a sequence of open-arc multiple scattering events, the proposed approach regularizes the full interior frequency domain problem-which, if obtained by either Fourier or Laplace transformation of the corresponding interior time-domain problem, must encapsulate infinitely many scattering events, giving rise to non-uniqueness and eigenfunctions in the Fourier case, and ill conditioning in the Laplace case. Numerical examples are included which demonstrate the accuracy and efficiency of the proposed methodology.

翻译：本文提出一种用于二维内部空间区域中时变波动方程的频时混合求解器。该方法基于四个核心要素：1）多重散射策略，将给定的内部时域问题分解为一系列由重叠开放弧段散射构成的有限时段时域问题，每个问题通过傅立叶变换简化为一系列亥姆霍兹频域问题；2）基于重叠边界片的边界积分方程，用于求解1）中的频域问题；3）平滑的“时间加窗与重定中心”方法，可处理长持续时间的入射信号与长时间模拟；4）一种傅立叶变换算法，能够对给定入射场实现数值上无色散、谱精度的时间演化。通过将内部时域问题转化为一系列开放弧段多重散射事件，该方法实现了对整个内部频域问题的正则化——若直接对相应内部时域问题实施傅立叶或拉普拉斯变换，所得频域问题必须包含无穷多次散射事件，在傅立叶变换情形下会导致非唯一性与本征函数问题，在拉普拉斯变换情形下则引发病态性。文中包含数值算例，验证了所提方法的精度与效率。