This paper is concerned with the numerical simulation of three dimensional time-dependent inverse source problems of acoustic waves. The reconstructions of both multiple stationary point sources and a moving point source are considered. The modified method of fundamental solutions (MMFS), which expands the solution utilizing the time convolution of the Green's function and the signal function, is proposed to solve the problem. For the reconstruction of a moving point source, moreover, the MMFS is simplified as a simple sampling method at each time step. Numerical experiments are provided to show the effectiveness of the proposed methods.

中文翻译：

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声波三维时变点源重建的数值方案

本文主要研究声波三维时变逆源问题的数值模拟。考虑了多个静止点源和移动点源的重建。为了解决该问题，提出了利用格林函数和信号函数的时间卷积扩展解的基本解法(MMFS)的改进方法。此外，对于运动点源的重建，MMFS 被简化为每个时间步的简单采样方法。提供了数值实验来证明所提出方法的有效性。