  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.
